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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Second Channel: https://www.youtube.com/channel/UCdix3BN0gkC1tnjG8xTyyUg
If this doesn't make sense, check out the Music Theory Distilled series first: https://www.youtube.com/playlist?list=PL618khw0A-t4q9AEsgmfHjqklmkx-PGKq
CORRECTIONS:
- at 12:17 the final, highest example was supposed to be 32/15:5/3 but the audio playing is actually (roughly) 32/15:8/5, defeating the demonstration. (The ratio on screen is correct for what is shown on screen, but the audio is wrong, playing roughly a fourth instead of a third.) Thanks to the golden-eared @JonHarris7 for the tip!
- 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: https://www.jneurosci.org/content/23/18/7160
See also: https://www.pnas.org/content/104/23/9852
Nuances of consonance:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4568680/
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2607353/
Wikipedia: https://en.wikipedia.org/wiki/Consonance_and_dissonance
Vihart's magnum opus: https://www.youtube.com/watch?v=4niz8TfY794
Further reading:
https://thinkzone.wlonk.com/Music/12Tone.htm
https://music.stackexchange.com/questions/24/why-are-there-twelve-notes-in-an-octave
https://www.reddit.com/r/musictheory/comments/33xhrv/is_the_choice_of_12tet_tuning_purely_cultural_or/
https://www.quora.com/How-did-Western-music-%E2%80%9Csettle%E2%80%9D-on-a-12-tone-scale
http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html
