Why 12 notes in Western music? • Hacker News Board

Re: Why 12 notes in Western music?

#161

Post by hunter2_ » Tue, Aug 30, 2022, 4:07 PM UTC

hunter2_ wrote: post #123

tripa wrote: post #78

Earlier quoted context omitted.

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?

Oo I can take this one! I'm not a registered piano technician, but I've tuned my piano (and helped a few friends) for some 15 years. Aurally (as opposed to electronically) tuning a piano is actually pretty straightforward. I'll stop short of saying it's easy, but once you learn the method, it's very sensible and just a matter of practice. The general idea is to achieve consistent beat rates for a given interval -- ma…

Further reading: https://my.ptg.org/HigherLogic/System/DownloadDocumentFile.a...

Notably:

> In equal temperament, all perfect fifths are “contracted”, while all perfect fourths as “expanded”. Minor thirds are contracted, while major sixths are expanded. Major thirds are expanded, while minor sixths are contracted. The piano tech must have knowledge of the approximate beat rates the intervals of equal temperament in the temperament octave: The beat rate of perfect fourths within the temperament octave may be about 1 beat per second. The beat rate of perfect fifths within the temperament octave may be about 1/2 beat per second. The beat rate of F3-A3 major third is about 7 beats per second and that of higher thirds are faster.

In my previous comment, my memory was a bit off when I said "about half the beat rate"... that's the difference in rate between fourths and fifths, apparently.

> Example: to check the tuning of D4 within the temperament octave, play A3-D4 and G3-D4. The fourth should beat faster than the fifth. If the fifth is too fast and the fourth too pure perhaps the D4 is flat; if the fourth and fifth beat at the same rate, perhaps the D4 is flat; if the fourth beats too fast and the fifth is too pure, perhaps the D4 is sharp.

> you can use more and more checks as one progresses through the sequence and tune each new note as a “best compromise” with all the previous notes, that is, each new note will not depend only on the last note tuned, so there will be more of a chance that errors will not accumulate in the later notes tuned.

Re: Why 12 notes in Western music?

#162

Post by thaumasiotes » Tue, Aug 30, 2022, 6:02 PM UTC

coldtea wrote: post #149

thaumasiotes wrote: post #99

Earlier quoted context omitted.

> Actually it's perfectly plausible. No, for this to be plausible, you would need to have some theory of why the two notes matched with each other. There is no such theory; they have been chosen to be as unmatched as possible. > nobody in 1800 would imagine we'd enjoy listening to punk, hip hop, or Death Metal This is false. >> That hypothetical species wouldn't recognize two notes an octave apart as being similar >…

OK, I see that the discussion is futile. This is both pedantic, condescending, and unwilling to entertain an idea. In any case, just for anybody interested: > No, for this to be plausible, you would need to have some theory of why the two notes matched with each other. There is no such theory; they have been chosen to be as unmatched as possible. Nothing has in 12-tet has been "chosen to be as unmatched as possible".…

> The 12-tet values still has strict mathematical properties, it's not just some random off collection of pitches - and it could be that, which is perceived as "perfection" by the imaginary alien race (that it is equally spaced values on a logarithmic scale).

This is an analysis you can't even apply to two notes. Every pair of notes is "equally spaced along a logarithmic scale", for the same reason that every pair of geographic locations is "equally spaced" along a linear scale, and of course also equally spaced along a scale with sinusoidal spacing. You have a single data point, and it's equal to itself. The claim has no meaning unless you're simultaneously evaluating more than two things.

In reality, of course, we perceive sounds as being related to each other when they have frequencies that are related to each other. This removes the need to evaluate them against imaginary background standards.

And two notes drawn from a 12-tet scale cannot have related frequencies unless they are separated by an integer number of octaves. The period of the combination of a note with its own fifth is double the period of the base note. The combination of a note with its 12-tet fifth is aperiodic.

> Nothing has in 12-tet has been "chosen to be as unmatched as possible".

Think before you speak.

Re: Why 12 notes in Western music?

#163

Post by kazinator » Tue, Aug 30, 2022, 6:38 PM UTC

aidenn0 wrote: post #116

kazinator wrote: post #113

Earlier quoted context omitted.

Yes, the near cycle is a coincidence; it just comes from 1.5 ^ 12 ~= 129.746, which is close to the power-of-two 128. It's because 3^12 is close to 2^19, to about 1.36 percent. This is all abstract arithmetic; I don't believe it's exclusively how musicians discovered chromaticity. That likely has multiple origins, one of which is likely about filling in the five "missing" half step "slots" in a diatonic mode. The 3:2…

I'm not certain of this, but my understanding is that Pythagoras generated these notes (actually more than 12 because there was a distinction between flats and the matching sharps) circa 500 BCE, and this predates chromaticity in music in the west.

Pythagoras' research is undeniable; but he wasn't some appointed gatekeeper, from whose desk sprang forth all western music. I don't suspect that very many musicians and instrument makers between 500 BCE and 1600-something (even the few that could actually read and write!) would have known about Pythagoras' work, and based their activities on his results.

Re: Why 12 notes in Western music?

#164

Post by dublin » Wed, Aug 31, 2022, 12:37 AM UTC

Thanks for this. It is perhaps the clearest explanation ever of the musical scale, and why it is the way it is. I've literally watched dozens of YouTube videos on this topic in the past week, and none of them are as clear and insightful as this was.

You do have to wonder what an optical octave would look like, though - our visual range is, unfortunately, a bit short of an octave there... Maybe the same "tone" of a kind of extreme magenta?