This video explains the origin of the 12-tone scale: why it takes the form it does, and the considerations that shape any tonal system.
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CORRECTION: at 15:07 I say that you have to go to 29-TET to beat 12-TET on average proximity to the consonant ratios. In fact, 19-TET beats it on the ratios shown (which is clear from the image on screen), and also beats it (barely, depending on how you count) over 11 common Just Intonation intervals. However 19-TET does include some pretty dissonant intervals, so the guidelines as presented would still lean towards 12-TET. Similarly, 24-TET, having exactly twice the notes of 12-TET, contains all the same intervals as 12-TET, so it is obviously a tie in terms of proximity to consonant intervals, but has extra dissonant intervals.
0:00 intro
0:50 basics (pitch, octaves, intervals, and consonance)
3:02 the most consonant intervals
4:39 consonant intervals among overtones
6:05 consonant intervals in human speech
7:54 building to 12 tones
8:28 guidelines for our tonal system
11:15 other systems
11:39 inconsistency among equivalent intervals
13:01 equal temperament
14:22 other equal temperament options
15:17 discussion of compromises
16:47 channel announcement
Paper cited: [ Ссылка ]
See also: [ Ссылка ]
Nuances of consonance:
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Wikipedia: [ Ссылка ]
Vihart's magnum opus: [ Ссылка ]
Further reading:
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