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A study of musical scales (2017)

ianring.com

31–40 of 45 posts

Re: A study of musical scales (2017)

#31
post #22

Earlier quoted context omitted.

That's the first thing that the author states. I'll bet you know more music than me, but maybe that puts me more into the target audience. It's a very interesting way to explore essentially the whole of western music. I did some similar "modeling" when I was learning, too, mostly because it's an effective way for me to commit things to memory. I remember struggling with using tones/scale degrees or intervals as a bas…

The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.

The specific use case for equal temperament is more or less how do make a fixed tuning instrument sound "good enough", without resorting to a very large amount of keys or buttons to adjust the tuning so the chords sound right. Although it was developed around Western music, I don't think that Western scales per se are necessarily the constraining factor.

Certainly just intonation sounds more pure on a fixed tuning instrument if you play within the constraints of the tuning ratios chosen. Step outside those constraints, and the sound is usually pretty awful.

12TET also has some "musical usefulness" on its own. The system introduced a sort of tonal ambiguity in modulation -- the commas that normally result in a more just / Pythagorean type style (https://en.wikipedia.org/wiki/Comma_(music)) get "blurred", and this is a characteristic musicians can exploit. Furthermore, in my experience, for sounds with lots of overtones (sawtooth synth waves, distorted guitars, etc.), that slightly detuned third in a 12TET trichord ends up sounding "thicker" for a lack of a better word, with the detuned beating more adding to the texture. This is best heard on a synthesizer where it's easy to flip between two tunings: to me, that, say, 1980s "power chord sawtooth stab" type of sound just doesn't sound as "thick" in just tuning, in my opinion. (In fact, when programming a synthesizer, people often slightly detune oscillators for this exact same reason!)

Nonetheless, it would be interesting if more "adaptive" type just intonation type systems came out that more approximate what non-fixed pitch instruments do (adjusting the notes to a "correct" your tuning during any modulation). Pure sounding triads also are useful, and you really can't do it super exact with 12TET, it's always "good enough". :) Hermode tuning is the only major one I know of, it is implemented in some synthesizers and DAWs. I haven't tried it yet -- my bet is you still would be a bit constrained (no dramatic 20th century classical type of chromatic modulation or the like), but you'll gain some freedom to modulate compared to a fixed just tuning setting.

Re: A study of musical scales (2017)

#32

Earlier quoted context omitted.

I tried listening to a 15-tone ET piano piece ones. Sure, maybe I'm not worthy, and too limited in my musical understanding (although I have been a musicians since the age of 6 and i'm now 43), but it just sounded like a piano out of tune. 12-tet is more than enough to experiment with for the rest of my life

You have been listening to 12-tet literally your entire life, so microtonal music is inevitably going to sound strange. Having said that, 15-tet is pretty rancid. 22-tet can be much more consonant. Try this, which is in just intonation: https://www.youtube.com/watch?v=1uZUQqOLyPQ It's contemporary but still sort-of accessible for many people.

Yes, also this one, which is for microtonal piano (also in JI): https://www.youtube.com/watch?v=ZkaGm8B8CZI

Re: A study of musical scales (2017)

#33

The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.

When I first learned about music theory, it surprised me how common this is. I liked the idea of scales that made certain intervals sound nice in terms of simple fractions, and wrote a computer program to search for them. I found an interesting scale and posted it to the music stackexchange: https://imgur.com/a/iBwxC4T

It caused a long discussion between the people there, and I learned a lot, but my post was eventually deleted. Somebody posted a follow-up question trying to figure out what the terms were really supposed to mean, but it doesn't seem to me they ever managed to agree: https://music.stackexchange.com/questions/66620

Re: A study of musical scales (2017)

#34

The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.

When I first learned about music theory, it surprised me how common this is. I liked the idea of scales that made certain intervals sound nice in terms of simple fractions, and wrote a computer program to search for them. I found an interesting scale and posted it to the music stackexchange: https://imgur.com/a/iBwxC4T It caused a long discussion between the people there, and I learned a lot, but my post was eventual…

I think a tuning is a set of intervals which an instrument is configured to play. A tuning is also a temperament if it is a compromise of another tuning in order to make the configuration technically feasible (or for other convenience reasons). A scale is then some combination of notes within a tuning or temperament? I don't know, it seemed like they were more concerned with nitpicking words than answering your actual question, which was interesting and not hard to understand.

Re: A study of musical scales (2017)

#35

Earlier quoted context omitted.

The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.

> The problem is that the twelve-tone system was designed for a very specific "use case" This isn't really correct though. Twelve is used because it has certain properties of divisibility that make life easier for the musician. When the wavelengths of two notes form simple mathematical ratios, they have a stability that sounds nice, and this makes it easier to construct intervals and chords. Wouldn't choosing a non-t…

Sorry, I made a mistake: I specifically wanted to make that remark about the equal temperament tuning, not twelve tones in general.

Re: A study of musical scales (2017)

#36

The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.

When I first learned about music theory, it surprised me how common this is. I liked the idea of scales that made certain intervals sound nice in terms of simple fractions, and wrote a computer program to search for them. I found an interesting scale and posted it to the music stackexchange: https://imgur.com/a/iBwxC4T It caused a long discussion between the people there, and I learned a lot, but my post was eventual…

Wow, another interesting parallel between music and programming - senselessly overzealous arguments.

Re: A study of musical scales (2017)

#37

Earlier quoted context omitted.

When I first learned about music theory, it surprised me how common this is. I liked the idea of scales that made certain intervals sound nice in terms of simple fractions, and wrote a computer program to search for them. I found an interesting scale and posted it to the music stackexchange: https://imgur.com/a/iBwxC4T It caused a long discussion between the people there, and I learned a lot, but my post was eventual…

I think a tuning is a set of intervals which an instrument is configured to play. A tuning is also a temperament if it is a compromise of another tuning in order to make the configuration technically feasible (or for other convenience reasons). A scale is then some combination of notes within a tuning or temperament? I don't know, it seemed like they were more concerned with nitpicking words than answering your actua…

That seems like a reasonable definition. In my view, temperaments only apply to keyboard and electronic instruments. String instruments are tuned so the open strings are in perfect intervals, then we just cope with it. Wind instruments are all over the place, depending on how you blow and how loud. I saw a viola da gamba with double frets, and the gambist told me it was so he could manage different temperaments. An orchestra is untempered, for all practical purposes.

I think that a scale and its temperaments are in addition to being an artistic choice, also a technology. Prior to electronic music and professional technicians, a tuning system had to be something that a musician could carry out themselves, possibly quite frequently. The 12 tone system is the simplest consonant system, possibly making it the easiest and quickest to tune.

Re: A study of musical scales (2017)

#38
post #22

The problem with this is is that it accepts the twelve-tone equal temperament system as a sort of absolute frame of reference, rather than the compromise/approximation that it is. Musical scales are not just check-box menu choices out of twelve-tone equal temperament.

That's the first thing that the author states. I'll bet you know more music than me, but maybe that puts me more into the target audience. It's a very interesting way to explore essentially the whole of western music. I did some similar "modeling" when I was learning, too, mostly because it's an effective way for me to commit things to memory. I remember struggling with using tones/scale degrees or intervals as a bas…

The issue I have is that, by ignoring the just scales that equal temperament is an approximation of, you ignore the fundamental mathematical foundations of tonal music. Without that, there are a lot of things you can't say about equal temperament, and the things that remain are kind of superficial.

Re: A study of musical scales (2017)

#39

Earlier quoted context omitted.

The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.

> The problem is that the twelve-tone system was designed for a very specific "use case" This isn't really correct though. Twelve is used because it has certain properties of divisibility that make life easier for the musician. When the wavelengths of two notes form simple mathematical ratios, they have a stability that sounds nice, and this makes it easier to construct intervals and chords. Wouldn't choosing a non-t…

> wavelengths of two notes form simple mathematical ratios, they have a stability that sounds nice

O.o that is called resonance and it sounds harmonious.

Re: A study of musical scales (2017)

#40

Earlier quoted context omitted.

The problem is that the twelve-tone system was designed for a very specific "use case", in the context of a certain kind of music: classical/Baroque revolving around major and minor scales, modulating around the cycle of fifths. For anything else, it is basically a misuse. Mass produced equal temperament instruments are used all over the world and basically turn the local music into shlocky pop.

> The problem is that the twelve-tone system was designed for a very specific "use case" This isn't really correct though. Twelve is used because it has certain properties of divisibility that make life easier for the musician. When the wavelengths of two notes form simple mathematical ratios, they have a stability that sounds nice, and this makes it easier to construct intervals and chords. Wouldn't choosing a non-t…

Twelve is used because it has certain properties of divisibility that make life easier for the musician.

Not true. It's used because (in short) when you try to construct a scale from octaves and fifths, finding a certain number of octaves that are close to another number of fifths (which comes to finding continued fraction approximants to 117/200, i.e. log 3/log 2 - 1) there are very few contenders, and only 12 notes per octave has neither too few nor too many for our tastes. It's based on the coincidence that 7 octaves is very nearly 12 fifths, i.e. 2^7~(3/2)^12.

Also, the idea that symmetry sounds nice is intuitively appealing, but nothing sounds better to us, more pleasing, than the (highly irregular) major scale, or scarier, more ominous than diminished and augmented chords - musically, a square and equilateral triangle. Or more disorienting than a whole tone scale - a hexagon.

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