npub105ve72qqmjxz08skum2lkds9qkj67689djwwr2a0qkrxts3hqydqm9hk8p (npub105v…hk8p) - thanks very much! A while back I wanted to carefully study the math of various historically important tuning systems, mainly these:
• Pythagorean tuning.
• just intonation systems, and especially Ptolemy’s intense diatonic scale.
• meantone temperament, and especially quarter-comma meantone, which was introduced around 1550, and then replaced just intonation, at least for keyboard music.
• a few of the most popular well-tempered scales, which starting becoming popular roughly around 1690.
• the equal-tempered 12-tone scale, which took over around 1900.
But there are actually so many well-tempered scales I doubt I'll get through most of them! These days I've got just intonation on my mind.
https://johncarlosbaez.wordpress.com/2023/10/13/perfect-fifths-in-equal-tempered-scales/
John Carlos Baez /
npub17u…8pd6m
2023-11-01 22:25:35
in reply to nevent1q…uxwt
Author Public Key
npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6mPublished at
2023-11-01 22:25:35Event JSON
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"content": "nostr:npub105ve72qqmjxz08skum2lkds9qkj67689djwwr2a0qkrxts3hqydqm9hk8p - thanks very much! A while back I wanted to carefully study the math of various historically important tuning systems, mainly these:\n\n• Pythagorean tuning.\n\n• just intonation systems, and especially Ptolemy’s intense diatonic scale.\n\n• meantone temperament, and especially quarter-comma meantone, which was introduced around 1550, and then replaced just intonation, at least for keyboard music.\n\n• a few of the most popular well-tempered scales, which starting becoming popular roughly around 1690.\n\n• the equal-tempered 12-tone scale, which took over around 1900.\n\nBut there are actually so many well-tempered scales I doubt I'll get through most of them! These days I've got just intonation on my mind.\n\nhttps://johncarlosbaez.wordpress.com/2023/10/13/perfect-fifths-in-equal-tempered-scales/",
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