John Carlos Baez on Nostr: In Pythagorean tuning, we try to force all frequency ratios to be powers of 3/2. In ...
In Pythagorean tuning, we try to force all frequency ratios to be powers of 3/2. In music, 3/2 is the 'perfect fifth': the sweetest of intervals except for the octave.
If we start with some frequency and go up and down by powers of 3/2, we create the 'circle of fifths' shown here. It's almost a 12-pointed star, with one point for each note in the 12-tone equal-tempered scale.
Almost - but not quite! When we go up 12 perfect fifths, we get a note that's almost but not quite 2ā· times the frequency we started with. In other words, it's almost but not quite 7 octaves higher. So there's a glitch.
Here I've stuck that glitch at the opposite from the note labeled 1. The spot directly opposite 1 is called the 'tritone', or sometimes 'diabolus in musica' - the devil in music. š
The size of the glitch is called the 'Pythagorean comma'. It's
(3/2)Ā¹Ā² / 2ā· ā 129.74633789 / 128 ā 1.01364326477
https://en.wikipedia.org/wiki/Pythagorean_tuninghttps://en.wikipedia.org/wiki/Pythagorean_comma Published at
2023-10-05 07:13:16Event JSON
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"content": "In Pythagorean tuning, we try to force all frequency ratios to be powers of 3/2. In music, 3/2 is the 'perfect fifth': the sweetest of intervals except for the octave.\n\nIf we start with some frequency and go up and down by powers of 3/2, we create the 'circle of fifths' shown here. It's almost a 12-pointed star, with one point for each note in the 12-tone equal-tempered scale. \n\nAlmost - but not quite! When we go up 12 perfect fifths, we get a note that's almost but not quite 2ā· times the frequency we started with. In other words, it's almost but not quite 7 octaves higher. So there's a glitch.\n\nHere I've stuck that glitch at the opposite from the note labeled 1. The spot directly opposite 1 is called the 'tritone', or sometimes 'diabolus in musica' - the devil in music. š \n\nThe size of the glitch is called the 'Pythagorean comma'. It's\n\n(3/2)Ā¹Ā² / 2ā· ā 129.74633789 / 128 ā 1.01364326477\n\nhttps://en.wikipedia.org/wiki/Pythagorean_tuning\nhttps://en.wikipedia.org/wiki/Pythagorean_comma\n\nhttps://media.mathstodon.xyz/media_attachments/files/111/181/039/976/449/841/original/6423e662f54d0985.jpg",
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