The “432 Hz vs. 440 Hz” conspiracy theory

Re:The “432 Hz vs. 440 Hz” conspiracy theory by rspeer on Monday October 24, 2016 @09:43PM (#12784576)

There's something special about 432 Hz that has nothing to do with how the music is perceived -- if you're tuning the traditional way, by forming fifths above and below A as ratios of 3/2 and 2/3, then a lot of the numbers you hit are nice integer numbers of hertz as well, because 432 is 2^4 * 3^3.

Meaningless in practice, but it makes it convenient to describe the tuning of, for example, a stringed instrument.

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Re:The “432 Hz vs. 440 Hz” conspiracy theory by elihu on Monday October 24, 2016 @10:18PM (#12784745)

Main> majscale
[(1,1),(9,8),(5,4),(4,3),(3,2),(5,3),(15,8),(2,1)]

Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) majscale

[432.0,486.0,540.0,576.0,648.0,720.0,810.0,864.0]

That's pretty cool. The whole major scale comes out as whole numbers in just intonation. (In 12-tone equal temperament it doesn't, because 12TET uses the 12th root of 2 as a uniform division of the octave.) This looks like your explanation isn't just a neat trick, it's likely to be the reason why 432hz was proposed as a standard in the first place.

Main> let scale = [(1,1),(16,15),(10,9),(9,8),(6,5),(5,4),(4,3),(45,32),(3,2),(8,5),(5,3),(15,8),(9,5),(15,8),(2,1)]

Main> map (\(x,y) -> (432.0 * (fromIntegral x)) / (fromIntegral y)) scale

[432.0,460.8,480.0,486.0,518.4,540.0,576.0,607.5,648.0,691.2,720.0,810.0,777.6,810.0,864.0]

..and if we construct a more chromatic scale, not all of them come out quite as whole numbers, but we don't have any repeating decimals or anything like that (though we would if we included weirder intervals like 8/7). Nice.

edit: This works for a just major scale constructed starting from A. If you construct a scale from a different root note, it might not work out quite as cleanly.

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Re:The “432 Hz vs. 440 Hz” conspiracy theory by rspeer on Tuesday October 25, 2016 @03:10AM (#12785877)

I was thinking it's kind of sad that A minor is the scale that's more fundamental in musical notation -- going up to C with a just minor third gets you the not-so-pretty 518.4 because there's no factor of 5 to divide by.

But really, the moment you decide thirds and fifths both matter, and you want to build them on more than one note, you have to either continuously re-tune or give up on JI and worry about temperament instead. The numbers work great in a Pythagorean tuning, where only fifths matter: that tuning gets you both A=432 and C=512 (middle C = 256).

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Re:The “432 Hz vs. 440 Hz” conspiracy theory by mxfh on Tuesday October 25, 2016 @06:28AM (#12786691)

If it's a high composite number is all you need, then why not define 440 Hz as any highly composite number of your liking, ignore the SI-related-fractions and don't worry about odd ratios anymore. Or is this more about an issue with cumbersome input on digital (tuning) devices?

Just to pick two:

45360/100 is not that far away either

55440 (a superior highly composite number, 2ˆ4 ⋅ 3ˆ2 ⋅ 5 ⋅ 7 ⋅ 11 ) would have a built in Base-10 mnemonic

https://en.wikipedia.org/wiki/Highly_composite_number

https://en.wikipedia.org/wiki/Superior_highly_composite_numb...

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Re:The “432 Hz vs. 440 Hz” conspiracy theory by rspeer on Tuesday October 25, 2016 @02:26PM (#12790285)

Well, we've never really used prime factors of 7 and 11 in Western music.

Even introducing the factors of 5 creates centuries of complications (temperament) that caused us to finally give up and throw out all the integer factors, replacing them with the twelfth root of 2.

(Anyone who wants to reply saying that factors of 7 explain "blue notes", please be specific about how this works. I think this is a fictitious idea in music theory that propagates itself because it would be really cool if it were true, but the usual explanations produce false predictions.)

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