Three tuning systems that dominated western music for centuries all fit into the same family!
• Pythagorean tuning has a lot of fifths with frequency ratios of exactly 3/2. It may go back to Mesopotamia, but it was discussed by Greek mathematicians - and it was widely used in medieval European music, especially before 1300. Medieval musicians loved fifths!
• Quarter-comma meantone has a lot of thirds with frequency ratios of exactly 5/4. It was introduced around 1550 and was popular for keyboard instruments until around 1690, since Baroque musicians loved these nice thirds.
• Equal temperament has the same frequency ratio between each pair of neighboring notes. It was widely adopted in France and Germany by the late 1700s and in England by the early 1800s, since musicians started wanting to easily switch between all possible keys.
In my article here I explain how you can get all 3 of these systems, and infinitely many others, just by adjusting the value of one parameter!
https://johncarlosbaez.wordpress.com/2023/12/18/quarter-comma-meantone-part-2/
John Carlos Baez /
npub17u…8pd6m
2023-12-24 12:00:29
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npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6mPublished at
2023-12-24 12:00:29Event JSON
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"content": "Three tuning systems that dominated western music for centuries all fit into the same family!\n\n• Pythagorean tuning has a lot of fifths with frequency ratios of exactly 3/2. It may go back to Mesopotamia, but it was discussed by Greek mathematicians - and it was widely used in medieval European music, especially before 1300. Medieval musicians loved fifths!\n\n• Quarter-comma meantone has a lot of thirds with frequency ratios of exactly 5/4. It was introduced around 1550 and was popular for keyboard instruments until around 1690, since Baroque musicians loved these nice thirds.\n\n• Equal temperament has the same frequency ratio between each pair of neighboring notes. It was widely adopted in France and Germany by the late 1700s and in England by the early 1800s, since musicians started wanting to easily switch between all possible keys.\n\nIn my article here I explain how you can get all 3 of these systems, and infinitely many others, just by adjusting the value of one parameter!\n\nhttps://johncarlosbaez.wordpress.com/2023/12/18/quarter-comma-meantone-part-2/",
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