Why 12 notes in Western music? • Hacker News Board

Re: Why 12 notes in Western music?

#151

Post by hoseja » Tue, Aug 30, 2022, 9:42 AM UTC

ordu wrote: post #150

hoseja wrote: post #148

Earlier quoted context omitted.

What? No, you said it, the ear splits the sound into frequencies and physically puts sensors into places where they resonate. Octave resonates in the same place. (but higher octave resonates in one additional place)

No, octave resonates in two different places. If we talk about octave as of sum of two sines.

I was sloppy. First i meant the octave as two separate tones (one after another), then I meant only the higher pitched one.

The higher tone also excites the sensors for the lower tone.

Wait, does it? I might be spouting bullshit, sorry.

Re: Why 12 notes in Western music?

#152

Post by ordu » Tue, Aug 30, 2022, 10:06 AM UTC

hoseja wrote: post #151

ordu wrote: post #150

Earlier quoted context omitted.

No, octave resonates in two different places. If we talk about octave as of sum of two sines.

I was sloppy. First i meant the octave as two separate tones (one after another), then I meant only the higher pitched one. The higher tone also excites the sensors for the lower tone. Wait, does it? I might be spouting bullshit, sorry.

> Wait, does it?

Thinking about it, I'm not so sure it doesn't. I'm not a physicist to know it for sure.

Re: Why 12 notes in Western music?

#153

Post by tzs » Tue, Aug 30, 2022, 10:34 AM UTC

tripa wrote: post #78

joegahona wrote: post #55

Earlier quoted context omitted.

I don't remember where I learned this, but what you said is more accurate than what I said -- the concept was definitely known well before Beethoven, but my understanding is it wasn't the standard tuning on keyboard instruments until much later, and came to its fruition with all the atonal music of the early 20th century. I think composers even went so far as to assign emotions/moods to various keys based on each key…

More generally, I'd be curious to know how they'd practically tune a keyboard to 12TET before the electronic chromatic tuner got around. Start with Pythagorean fifths then compress ever-so slightly? How'd you keep them… equal?

Build a 12-TET fretted string instrument and tune your keyboards to it, after using a tuning fork to tune the fretted instrument?

Re: Why 12 notes in Western music?

#154

Post by mcbrit » Tue, Aug 30, 2022, 10:37 AM UTC

lynndotpy wrote: post #119

mcbrit wrote: post #105

Let's talk about splitting things up in useful ways. 12=2 * 2 * 3. Splitting something in half is useful; splitting it half again remains useful. Splitting in half a third time is arguably less useful than splitting it into a third. So 12 is the made-to-order number that lets you split it in half, twice, and in thirds, once. Which naturally leads to seconds and minutes, or 60: 60=2 * 2 * 3 * 5 Because dividing the wh…

No: Having 12 notes is a neat but accidental outcome of the musical scale. On the derivation of the scale: Two pure tones go good together when they have "ratios" of frequency. So, 440Hz and 660Hz would interfere in a pleasing way. This is the same way that it's "nice" when tiles on a floor match your gait in a way you can follow a pattern, or when two blinkers sync up. So, it's nice when tones are fractions of one a…

Let me start by making the same point, but starting from a different place.

When you see pi, you look for a circle. When you see an 8 or 12 or 24 or 60, you see a few small primes multiplied together, and you might look for things that like being flexibly divided into clean subgroups.

Now I spent a couple of hours trying to extend my original argument, using the internet.

12tet (12 tone equal temperament) gives you good fourths and fifths (which as you say sound great) and TET. What you don't get is being able to correctly voice say a barbershop seventh, or persian music, or dissonant death metal, or microtonal pop.

While n-TET for any n is possible, Wikipedia lists 5, 7, 12, 15, 17, 19, 22, 23, 24, 26, 27, 29, 31, 34, 41, 46, 53, 72, and 96tet as being in use, some much more popular than others. Arabic music shifted from 17tet to 24tet, with the exception of some holdouts that find 24tet too 'commercial'.

You don't need bang-on fourths and fifths to be happy in n-tet; given n-tet, you figure out what intervals to use, what kind of chords you want to build, and what kind of scales you are willing to learn to use those chords.

So, fourths and fifths are good in 12tet, and you covered that. Is there anything else to say about 12tet and its popularity, particularly about there being 12 notes and its prime factorization into 2s and 3s?

From stackexchange: You can create a circle of any number of steps mutually prime to the total number of pitches in the octave.

And what it looks like is that you get a Circle of Fifths that has some particularly nice properties in 12tet due to the math with 2/3/5, and that makes scales and chord building particularly easy, making 12tet easy to work with, and that further popularizes 12tet. I just waved my hands there pretty hard; I did not do anywhere near enough due diligence on sources. But, yes, the number of notes does end up being important. Probably.

So I think I was minorly correct in being suspicious of '12' and how divisible it was into small primes, but majorly wrong in most other aspects.

As an aside, I did read your article, and just had a different take on what was going on; I was sure that the prime factorization structure of '12' would explain more than it does.

Re: Why 12 notes in Western music?

#155

Post by hwc » Tue, Aug 30, 2022, 12:25 PM UTC

hoseja wrote: post #151

ordu wrote: post #150

Earlier quoted context omitted.

No, octave resonates in two different places. If we talk about octave as of sum of two sines.

I was sloppy. First i meant the octave as two separate tones (one after another), then I meant only the higher pitched one. The higher tone also excites the sensors for the lower tone. Wait, does it? I might be spouting bullshit, sorry.

Every note is a sum of harmonic sine waves, usually not just a single one. The first harmonic of 440hz is 880Hz. So plucking a harp string for A4 will also produce the A5 and A6...

Re: Why 12 notes in Western music?

#156

Post by joegahona » Tue, Aug 30, 2022, 1:58 PM UTC

wizofaus wrote: post #109

joegahona wrote: post #85

Earlier quoted context omitted.

Those descriptors ("austere," etc.) have always struck me as subjective -- I'm not one to tell people what mood they're getting from certain keys. But a root major chord will have a much different feel in, e.g., C#-major on an 18th-century tuning than in equal temperament. I have this CD [1] in a box somewhere but can't find it on Youtube. It's a few Beethoven sonatas in the temperament he would've used. Just sounded…

Thanks for that link, I don't know if it demonstrates "just intonation" though? But the 1/4 Comma Meantone tuning just sounds horrible the moment a diminished chord comes into the picture.

You're right, I mis-typed -- it's meantone, not just intonation. Someone elsewhere on this HN thread argues that's the tuning Mozart himself would've been using for that piece, which is bizarre to think about once you hear it on Youtube like that!

This is truly a fascinating world. People who argue that we should be using the original temperaments that composers used do have an argument. Imagine, for example, if Shakespeare were "tuned" to be in modern UK English rather than the English of its time.

Re: Why 12 notes in Western music?

#157

Post by HelloNurse » Tue, Aug 30, 2022, 2:37 PM UTC

coldtea wrote: post #87

thaumasiotes wrote: post #83

Earlier quoted context omitted.

That would have to be a universe in which the fundamental theorem of arithemetic was false. Otherwise, the only way to cross an interval that is an integer number of octaves is to take steps that are also octaves.

What the parent proposed doesn't require different math. Just a species that hears out current slightly offset divisions in 12-tet as perfect, as opposed to only hearing integral ratios as perfect.

Distinguishing different pitches implies distinguishing dissonant intervals from consonant intervals: there is no way they can sound equally "perfect".

What is definitely possible, instead, is liking dissonant intervals more than consonant intervals, for example because they sound "fatter".

Re: Why 12 notes in Western music?

#158

Post by crubier » Tue, Aug 30, 2022, 2:56 PM UTC

ordu wrote: post #152

hoseja wrote: post #151

Earlier quoted context omitted.

I was sloppy. First i meant the octave as two separate tones (one after another), then I meant only the higher pitched one. The higher tone also excites the sensors for the lower tone. Wait, does it? I might be spouting bullshit, sorry.

> Wait, does it? Thinking about it, I'm not so sure it doesn't. I'm not a physicist to know it for sure.

It depends on what type of oscillator we are talking about, but strings, chambers or beam oscillators for example will resonate at double frequency of their main frequency.

The octave rule definitely has some physical/biological founding, it’s not purely cultural. Although culture also plays a role in its preponderance.

Re: Why 12 notes in Western music?

#159

Post by lachlan_gray » Tue, Aug 30, 2022, 3:14 PM UTC

Another nice thing about 12 notes is that 12 has lots of factors. It leads to a lot of cool symmetries which I think have to do with how we understand music.

For example, since 12 is divisible by 3 and 4, diminished chords (4 notes separated by intervals of 3) and augmented chords (3 by 4) don’t have a definitive centre to our ear. As a result they both create different flavours of uncertainty and suspense.

But if you break the symmetry, e.g. by moving any note in an augmented chord one to the left on a piano, the chord takes on a colour (in this case becomes a major chord).

Other equal temperament scales would end up having similar patterns, but at the cost of complexity. having closer to 20 or 30 notes in an octave would increase the number of patterns to recognize, and probably make them less distinct to us without practice.

It’s also interesting to me that we put 12 numbers on clocks as well.

Re: Why 12 notes in Western music?

#160

Post by pyinstallwoes » Tue, Aug 30, 2022, 3:27 PM UTC

lachlan_gray wrote: post #159

Another nice thing about 12 notes is that 12 has lots of factors. It leads to a lot of cool symmetries which I think have to do with how we understand music. For example, since 12 is divisible by 3 and 4, diminished chords (4 notes separated by intervals of 3) and augmented chords (3 by 4) don’t have a definitive centre to our ear. As a result they both create different flavours of uncertainty and suspense. But if yo…

And 12 months in a year. Around around frequencies abound. In ratio and interval, all things are sound. Rational reasoning abound, just don’t be too loud.

A note here. A note there. A harmonic there and there. You say blue, I say G, and now we aught to see the cymatics inside you and me! Altogether now, ratio, ratios, frequency make everything between you and me. Hey now, hey now, just make music, it’s what we all need now.