Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Warning: Cannot modify header information - headers already sent by (output started at /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php:2581) in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/Feed/ChannelFeed.php on line 104
Warning: Cannot modify header information - headers already sent by (output started at /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php:2581) in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/Feed/ChannelFeed.php on line 109
Warning: Cannot modify header information - headers already sent by (output started at /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php:2581) in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/Request/WebResponse.php on line 80
Warning: Cannot modify header information - headers already sent by (output started at /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php:2581) in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/Request/WebResponse.php on line 80
Warning: Cannot modify header information - headers already sent by (output started at /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php:2581) in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/Request/WebResponse.php on line 80 https://wiki.ccarh.org/index.php?action=history&feed=atom&title=Base_40Base 40 - Revision history2026-08-06T00:05:01ZRevision history for this page on the wikiMediaWiki 1.43.0 Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627 https://wiki.ccarh.org/index.php?title=Base_40&diff=8871&oldid=prevCraig at 23:51, 24 December 20192019-12-24T23:51:17Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:51, 24 December 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td>
<td colspan="2" class="diff-lineno">Line 2:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The base-40 system <del style="font-weight: bold; text-decoration: none;">is a method for encoding </del>pitches as integers <del style="font-weight: bold; text-decoration: none;">in such </del>a <del style="font-weight: bold; text-decoration: none;">way </del>that <del style="font-weight: bold; text-decoration: none;">the diatonic interval with chromatic alteration is represented </del>as the difference between any two <del style="font-weight: bold; text-decoration: none;">numbers in the system</del>. It can be used to encoding diatonic pitches names with chromatic alterations up to double sharps or flats. The base-40 pitch space can be built up from the property that a minor second is a difference of 5 between two pitch numbers, and major seconds are a difference of 6. The C chroma value is set to the value 2 rather than 0 so that the octave values for C&#x266d; and C&#x266d;&#x266d; remain in the same octave as C&#x266e; just above these pitches when using division by the base to extract the octave number. Here is a complete table of the base-40 chroma, <del style="font-weight: bold; text-decoration: none;">using </del>C<del style="font-weight: bold; text-decoration: none;">=</del>2 <del style="font-weight: bold; text-decoration: none;">as the reference</del>:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The base-40 system <ins style="font-weight: bold; text-decoration: none;">represents </ins>pitches as integers<ins style="font-weight: bold; text-decoration: none;">, and it is </ins>a <ins style="font-weight: bold; text-decoration: none;">method of representing pitch </ins>that <ins style="font-weight: bold; text-decoration: none;">allows intervals to be calculated </ins>as the difference between any two <ins style="font-weight: bold; text-decoration: none;">pitch integers</ins>. It can be used to encoding diatonic pitches names with chromatic alterations up to double sharps or flats. <ins style="font-weight: bold; text-decoration: none;">In particular, this allows a simple algorithm to transpose music by adding a transposition interval to the starting pitches to calculate the transposed pitch.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The base-40 pitch space can be built up from the property that a minor second is a difference of 5 between two pitch numbers, and major seconds are a difference of 6. The C chroma value is set to the value 2 rather than 0 so that the octave values for C&#x266d; and C&#x266d;&#x266d; remain in the same octave as C&#x266e; just above these pitches when using division by the base to extract the octave number. Here is a complete table of the base-40 chroma, <ins style="font-weight: bold; text-decoration: none;">placing </ins>C <ins style="font-weight: bold; text-decoration: none;">pitch classes at position </ins>2:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>Craig Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581 https://wiki.ccarh.org/index.php?title=Base_40&diff=8870&oldid=prevCraig: /* Transposition */2019-12-24T23:41:21Z<p><span class="autocomment">Transposition</span></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 23:41, 24 December 2019</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l215">Line 215:</td>
<td colspan="2" class="diff-lineno">Line 215:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Transposition =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= Transposition =</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Transposition of notes within the base-40 system is simple: just add a constant interval to the base-40 pitch numbers. Below is an example <del style="font-weight: bold; text-decoration: none;">which transpose </del>the music up a major second. In the base-40 system, a major second is represented by the integer 6, so add 6 to all of the pitch numbers in the original music to transpose them up a major second.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Transposition of notes within the base-40 system is simple: just add a constant interval to the base-40 pitch numbers. Below is an example <ins style="font-weight: bold; text-decoration: none;">that transposes </ins>the music up a major second. In the base-40 system, a major second is represented by the integer 6, so add 6 to all of the pitch numbers in the original music to transpose them up a major second.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[image:transpose.svg|700px|center]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[image:transpose.svg|700px|center]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">= Generalization =</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">There are other higher-order bases that can be used to handle accidentals beyond double sharps and flats. Here is the equation to calculate the base according to the maximum number of sharp/flats on a note:</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> base = 7 * (2 * max + 1) + 5</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">For example, when max=2, then base=40. When max=3, then base=54. Another convent base is when max=42 and base=600.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= References =</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>= References =</div></td></tr>
</table>Craig Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2627
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581 https://wiki.ccarh.org/index.php?title=Base_40&diff=3862&oldid=prevCraig at 02:04, 28 February 20132013-02-28T02:04:23Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
<col class="diff-content" />
<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 02:04, 28 February 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l92">Line 92:</td>
<td colspan="2" class="diff-lineno">Line 92:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></table></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></table></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></center></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">The "base-40" name for the system refers to the property that an octave is represented by the integer 40. C4 is 162 while C5 is 162+40=202. To extract the octave number from a pitch value, just divide by 40. To extract the chroma from the pitch value, subtract the octave times 40.</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> octave = value / 40</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> chroma = value - octave * 40</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To calculate an absolute pitch such as G4 (The G above middle C), multiply the octave by 40 and add the chroma value for the G pitch-class: </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>To calculate an absolute pitch such as G4 (The G above middle C), multiply the octave by 40 and add the chroma value for the G pitch-class: </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"> pitch = octave * 40 + chroma</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> G4 = 4 * 40 + 25 = 160 + 25 = 185</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> G4 = 4 * 40 + 25 = 160 + 25 = 185</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Alternatively, G4 can be calculated by adding 3 half-steps (major seconds) and one minor second to C4 (represented as the number 162 in base-40):</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Alternatively, G4 can be calculated by adding 3 half-steps (major seconds) and one minor second to C4 (represented as the number 162 in base-40):</div></td></tr>
</table>Craig Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
Warning: unexpected NAN value was coerced to string in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 3151
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581 https://wiki.ccarh.org/index.php?title=Base_40&diff=3861&oldid=prevCraig at 01:59, 28 February 20132013-02-28T01:59:44Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:59, 28 February 2013</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
<td colspan="2" class="diff-lineno">Line 1:</td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The base-40 system is a method <del style="font-weight: bold; text-decoration: none;">to encoded </del>pitches as integers in such a way that the diatonic interval with chromatic alteration is represented as the difference between any two numbers in the system. It <del style="font-weight: bold; text-decoration: none;">is a method of </del>encoding diatonic pitches with <del style="font-weight: bold; text-decoration: none;">accidentals </del>up to double sharps or flats. The base-40 <del style="font-weight: bold; text-decoration: none;">chroma for pitches </del>can be built up from the property that a minor second is a difference of 5 between pitch numbers <del style="font-weight: bold; text-decoration: none;">in the base-40 system</del>, and major seconds are a difference of 6. The C chroma value is set to the value 2 rather than 0 so that the octave values for C&#x266d; and C&#x266d;&#x266d; remain in the same octave as C&#x266e; just above these pitches when using division by the base to extract the octave number. Here is a complete table of the base-40 chroma, using C=2 as the reference:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">__TOC__</ins></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The base-40 system is a method <ins style="font-weight: bold; text-decoration: none;">for encoding </ins>pitches as integers in such a way that the diatonic interval with chromatic alteration is represented as the difference between any two numbers in the system. It <ins style="font-weight: bold; text-decoration: none;">can be used to </ins>encoding diatonic pitches <ins style="font-weight: bold; text-decoration: none;">names </ins>with <ins style="font-weight: bold; text-decoration: none;">chromatic alterations </ins>up to double sharps or flats. The base-40 <ins style="font-weight: bold; text-decoration: none;">pitch space </ins>can be built up from the property that a minor second is a difference of 5 between <ins style="font-weight: bold; text-decoration: none;">two </ins>pitch numbers, and major seconds are a difference of 6. The C chroma value is set to the value 2 rather than 0 so that the octave values for C&#x266d; and C&#x266d;&#x266d; remain in the same octave as C&#x266e; just above these pitches when using division by the base to extract the octave number. Here is a complete table of the base-40 chroma, using C=2 as the reference:</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l99">Line 99:</td>
<td colspan="2" class="diff-lineno">Line 102:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Intervals=</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=Intervals=</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"> </del>A useful property of the base-40 system is that the difference between pitch numbers in the base-40 system represent one-to-one mappings with diatonic intervals with chromatic alterations:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>A useful property of the base-40 system is that the difference between pitch numbers in the base-40 system represent one-to-one mappings with diatonic intervals with chromatic alterations:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><center></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l217">Line 217:</td>
<td colspan="2" class="diff-lineno">Line 220:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* http://extra.humdrum.org/man/notearray/#base40</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* http://extra.humdrum.org/man/notearray/#base40</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* http://extra.humdrum.org/man/transpose</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* http://extra.humdrum.org/man/transpose</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=Exercises=</ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[image:base40exercise.svg|700px|center]]</ins></div></td></tr>
</table>Craig Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581
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Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/MessageCache.php on line 198
Deprecated: ord(): Providing a string that is not one byte long is deprecated. Use ord($str[0]) instead in /disk/data1/ccarh-project/ccarhwiki-v1.43.0/mediawiki-1.43.0/includes/language/Language.php on line 2581 https://wiki.ccarh.org/index.php?title=Base_40&diff=3859&oldid=prevCraig: Created page with "The base-40 system is a method to encoded pitches as integers in such a way that the diatonic interval with chromatic alteration is represented as the difference between any t..."2013-02-28T01:47:41Z<p>Created page with "The base-40 system is a method to encoded pitches as integers in such a way that the diatonic interval with chromatic alteration is represented as the difference between any t..."</p>
<p><b>New page</b></p><div>The base-40 system is a method to encoded pitches as integers in such a way that the diatonic interval with chromatic alteration is represented as the difference between any two numbers in the system. It is a method of encoding diatonic pitches with accidentals up to double sharps or flats. The base-40 chroma for pitches can be built up from the property that a minor second is a difference of 5 between pitch numbers in the base-40 system, and major seconds are a difference of 6. The C chroma value is set to the value 2 rather than 0 so that the octave values for C&#x266d; and C&#x266d;&#x266d; remain in the same octave as C&#x266e; just above these pitches when using division by the base to extract the octave number. Here is a complete table of the base-40 chroma, using C=2 as the reference:<br />
<br />
<br />
<center><br />
<table cellspacing=10 cellpadding=6><br />
<tr><td colspan=7><center><b>Base-40 chroma values (pitch classes)</b></center></td></tr><br />
<br />
<tr valign=top><br />
<br />
<td><br />
<table><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
<tr><td align=right>0</td><td width=5>=</td><td>C&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>1</td><td width=5>=</td><td>C&#x266d;</td></tr><br />
<tr><td align=right>2</td><td width=5>=</td><td>C&#x266e;</td></tr><br />
<tr><td align=right>3</td><td width=5>=</td><td>C&#x266f;</td></tr><br />
<tr><td align=right>4</td><td width=5>=</td><td>C&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>5</td><td width=5>=</td><td>[<i>D</i>&#x266d;&#x266d;&#x266d;]</td></tr><br />
<tr><td align=right>6</td><td width=5>=</td><td>D&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>7</td><td width=5>=</td><td>D&#x266d;</td></tr><br />
<tr><td align=right>8</td><td width=5>=</td><td>D&#x266e;</td></tr><br />
<tr><td align=right>9</td><td width=5>=</td><td>D&#x266f;</td></tr><br />
<tr><td align=right>10</td><td width=5>=</td><td>D&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>11</td><td width=5>=</td><td>[<i>E</i>&#x266d;&#x266d;&#x266d;]</td></tr><br />
<tr><td align=right>12</td><td width=5>=</td><td>E&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>13</td><td width=5>=</td><td>E&#x266d;</td></tr><br />
<tr><td align=right>14</td><td width=5>=</td><td>E&#x266e;</td></tr><br />
<tr><td align=right>15</td><td width=5>=</td><td>E&#x266f;</td></tr><br />
<tr><td align=right>16</td><td width=5>=</td><td>E&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
<tr><td align=right>17</td><td width=5>=</td><td>F&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>18</td><td width=5>=</td><td>F&#x266d;</td></tr><br />
<tr><td align=right>19</td><td width=5>=</td><td>F&#x266e;</td></tr><br />
<tr><td align=right>20</td><td width=5>=</td><td>F&#x266f;</td></tr><br />
<tr><td align=right>21</td><td width=5>=</td><td>F&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>22</td><td width=5>=</td><td><i>unused</i></td></tr><br />
<tr><td align=right>23</td><td width=5>=</td><td>G&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>24</td><td width=5>=</td><td>G&#x266d;</td></tr><br />
<tr><td align=right>25</td><td width=5>=</td><td>G&#x266e;</td></tr><br />
<tr><td align=right>26</td><td width=5>=</td><td>G&#x266f;</td></tr><br />
<tr><td align=right>27</td><td width=5>=</td><td>G&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>28</td><td width=5>=</td><td>[<i>A</i>&#x266d;&#x266d;&#x266d;]</td></tr><br />
<tr><td align=right>29</td><td width=5>=</td><td>A&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>30</td><td width=5>=</td><td>A&#x266d;</td></tr><br />
<tr><td align=right>31</td><td width=5>=</td><td>A&#x266e;</td></tr><br />
<tr><td align=right>32</td><td width=5>=</td><td>A&#x266f;</td></tr><br />
<tr><td align=right>33</td><td width=5>=</td><td>A&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>34</td><td width=5>=</td><td>[<i>B</i>&#x266d;&#x266d;&#x266d;]</td></tr><br />
<tr><td align=right>35</td><td width=5>=</td><td>B&#x266d;&#x266d;</td></tr><br />
<tr><td align=right>36</td><td width=5>=</td><td>B&#x266d;</td></tr><br />
<tr><td align=right>37</td><td width=5>=</td><td>B&#x266e;</td></tr><br />
<tr><td align=right>38</td><td width=5>=</td><td>B&#x266f;</td></tr><br />
<tr><td align=right>39</td><td width=5>=</td><td>B&#x266f;&#x266f;</td></tr><br />
</table><br />
</td><br />
<br />
</tr><br />
<br />
</table><br />
</center><br />
<br />
To calculate an absolute pitch such as G4 (The G above middle C), multiply the octave by 40 and add the chroma value for the G pitch-class: <br />
G4 = 4 * 40 + 25 = 160 + 25 = 185<br />
Alternatively, G4 can be calculated by adding 3 half-steps (major seconds) and one minor second to C4 (represented as the number 162 in base-40):<br />
G4 = C4 + 3 * M2 + m2 = 162 + 3 * 6 + 5 = 162 + 23 = 185<br />
<br />
Note that base-40 pitch representations preserve chromatic alterations of diatonic pitch-classes (up to double sharps/flats). Therefore F&#x266f;4 (180) is not in the same as the base-40 pitch G&#x266d;4 (184). <br />
<br />
=Intervals=<br />
<br />
A useful property of the base-40 system is that the difference between pitch numbers in the base-40 system represent one-to-one mappings with diatonic intervals with chromatic alterations:<br />
<br />
<center><br />
<table cellpadding=6 cellspacing=10><br />
<tr><td colspan=7><center><b>Base-40 interval classes</b> (d=diminished, m=minor, M=major, P=perfect, A=augmented)</center></td></tr><br />
<br />
<tr valign=top><br />
<br />
<td><br />
<table><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
<tr><td align=right>-2</td><td width=5>=</td><td>dd1</td></tr><br />
<tr><td align=right>-1</td><td width=5>=</td><td>d1</td></tr><br />
<tr><td align=right>0</td><td width=5>=</td><td>P1</td></tr><br />
<tr><td align=right>1</td><td width=5>=</td><td>A1</td></tr><br />
<tr><td align=right>2</td><td width=5>=</td><td>AA1</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>3</td><td width=5>=</td><td>[<i>dd2</i>]</td></tr><br />
<tr><td align=right>4</td><td width=5>=</td><td>d2</td></tr><br />
<tr><td align=right>5</td><td width=5>=</td><td>m2</td></tr><br />
<tr><td align=right>6</td><td width=5>=</td><td>M2</td></tr><br />
<tr><td align=right>7</td><td width=5>=</td><td>A2</td></tr><br />
<tr><td align=right>8</td><td width=5>=</td><td>AA2</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>9</td><td width=5>=</td><td>[<i>dd3</i>]</td></tr><br />
<tr><td align=right>10</td><td width=5>=</td><td>d3</td></tr><br />
<tr><td align=right>11</td><td width=5>=</td><td>m3</td></tr><br />
<tr><td align=right>12</td><td width=5>=</td><td>M3</td></tr><br />
<tr><td align=right>13</td><td width=5>=</td><td>A3</td></tr><br />
<tr><td align=right>14</td><td width=5>=</td><td>AA3</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
<tr><td align=right>15</td><td width=5>=</td><td>dd4</td></tr><br />
<tr><td align=right>16</td><td width=5>=</td><td>d4</td></tr><br />
<tr><td align=right>17</td><td width=5>=</td><td>P4</td></tr><br />
<tr><td align=right>18</td><td width=5>=</td><td>A4</td></tr><br />
<tr><td align=right>19</td><td width=5>=</td><td>AA4</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>20</td><td width=5>=</td><td><i>unused</i></td></tr><br />
<tr><td align=right>21</td><td width=5>=</td><td>dd5</td></tr><br />
<tr><td align=right>22</td><td width=5>=</td><td>d5</td></tr><br />
<tr><td align=right>23</td><td width=5>=</td><td>P5</td></tr><br />
<tr><td align=right>24</td><td width=5>=</td><td>A5</td></tr><br />
<tr><td align=right>25</td><td width=5>=</td><td>AA5</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>26</td><td width=5>=</td><td>[<i>dd6</i>]</td></tr><br />
<tr><td align=right>27</td><td width=5>=</td><td>d6</td></tr><br />
<tr><td align=right>38</td><td width=5>=</td><td>m6</td></tr><br />
<tr><td align=right>29</td><td width=5>=</td><td>M6</td></tr><br />
<tr><td align=right>30</td><td width=5>=</td><td>A6</td></tr><br />
<tr><td align=right>31</td><td width=5>=</td><td>AA6</td></tr><br />
<tr><td align=right></td><td width=5></td><td></td></tr><br />
</table><br />
</td><br />
<br />
<td><br />
<table><br />
<tr><td align=right>32</td><td width=5>=</td><td>[<i>dd7</i>]</td></tr><br />
<tr><td align=right>33</td><td width=5>=</td><td>d7</td></tr><br />
<tr><td align=right>34</td><td width=5>=</td><td>m7</td></tr><br />
<tr><td align=right>35</td><td width=5>=</td><td>M7</td></tr><br />
<tr><td align=right>36</td><td width=5>=</td><td>A7</td></tr><br />
<tr><td align=right>37</td><td width=5>=</td><td>AA7</td></tr><br />
<tr><td align=right>(40</td><td width=5>=</td><td><i>octave</i>)</td></tr><br />
</table><br />
</td><br />
<br />
</tr><br />
<br />
</table><br />
</center><br />
<br />
<p> <br />
As an example, consider the interval between E4 (174) and C4 (162) which is 174-162 = 12, representing a major third according to the table<br />
shown above. All intervals can be constructed by observing that major seconds are 6 and minor seconds are 5, so note that a major third, consisting<br />
of two major seconds, is 6&nbsp;+&nbsp;6&nbsp;=&nbsp;12. Below is an example segment of music with the pitches labeled in<br />
the base-40 system. Try subtracting values and comparing the results to numbers in the base-40 interval-class table above.<br />
<br />
<br />
[[image:intervals.svg|700px|center]]<br />
<br />
= Transposition =<br />
<br />
Transposition of notes within the base-40 system is simple: just add a constant interval to the base-40 pitch numbers. Below is an example which transpose the music up a major second. In the base-40 system, a major second is represented by the integer 6, so add 6 to all of the pitch numbers in the original music to transpose them up a major second.<br />
<br />
[[image:transpose.svg|700px|center]]<br />
<br />
<br />
= References =<br />
<br />
* [http://www.ccarh.org/publications/reprints/base40 A Base-40 Number-line Representation of Musical Pitch Notation], Walter Hewlet, <i>Musikometrika</i> 4 (1992), 1-14.<br />
* http://extra.humdrum.org/man/notearray/#base40<br />
* http://extra.humdrum.org/man/transpose</div>Craig