Why did they choose to split up octaves with 12 notes?

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Why did they choose to split up octaves with 12 notes? Why not 10 or 15 or 8? What was the thinking for using 12?

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I believe this is a consequence of the ‘12 equal temperament’ (12ET) idea that originated in the 16th century. During this period ‘natural philosophy’ suggested that mathematical ratios underlay those things that we experience as symmetry and harmony and so mathematicians looked for such ratios. The first and most obvious is that moving up an octave is also a doubling of the frequency of the note for example the note A4 has an associated frequency of 440 Hz while for A5 it is 880 Hz i.e. A5/A4 = 2. Now if that octave (or any octave) is split into twelve intervals, the ratio of the frequency of each note to the previous note will be the same. The value of the ratio is 1.05946, which is the twelfth root of 2 i.e. A#4/A4 = 466.1638/440 = 1.05946 and so on. To divide into 12 and get a ratio that is a twelfth root looked very nice to the mathematicians and such tuning sounded very nice on the Stratocaster of the day, the lute. No other division produced the equal ratios, so 12 stuck. OK so there is a bit of license taken with the higher decimal places in that ratio if you work a whole 8 octave piano but most of those would be beyond human abilities to discriminate between notes. I’ve not studied this, but I came across it many years ago as my working life involved a LOT of frequency calculations and manipulations and remembered it, I think, as a curiosity. There’s probably a Wikipedia page about it now.

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The Greeks had something to do with this, as well. We can easily understand the octave ratio, 2/1. Perfect fifth ratio is 3/2. Perfect fourth ratio is 4/3. Et cetera.

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FYI, equal temperament actually disallows “perfect” tuning, compromising the perfect ratios in order for music in all keys to “sound the same.” J. S. Bach was an early adopter, moving away from “perfect” and preferring “well temperament,” which was somewhere in between “perfect” and “equal.” Well temperament gives each key a slightly different character, but at least music in all keys is listenable. Equal temperament didn’t come into vogue until the 19th and 20th centuries.

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I always thought it was maths and frequency. C1 is about 32.70Hz, C2 65.41Hz, C3 130.81 and so on. It is always doubling so the intervals are in equal ratios and make it sound consistent across the keys. At least that is how I understand it without the history behind it!

Oh and different cultures do it differently too like Chinese music uses pentatonic scales. Indian music has 22 microtonal intervals

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Found the Wiki!

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I don’t think I know enough about math to understand this. Would the ratios of each note not be the same if they used other numbers? Like 10 or 15?

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Yes it would, for 10 the ratio would be the 10th root of 2, 1.07177, but you would lose those nice integer ratios for intervals that dmcleodw refers to above, 3/2 for perfect 5th etc. I didn’t mean to suggest that this was unique to 12, but that 10 etc were not tried at the time (or there is scant evidence for such attempts). There’s also the significance of 12 for Christians… apostles etc, but the reason it stuck was it sounded good on that lute. Sorry for the confusion. I should have looked for the Wiki first rather than relying on memory of something I came across about 40 years ago! :grinning_face:

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I just came across this

on decatonic scales. As an ‘untrained’ musician it’s well beyond me, but it does show the possibilities of octave division into 10 notes rather than 12.