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A study of musical scales (2017)

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Re: A study of musical scales (2017)

#41

Post by joeminichino »

TheOtherHobbes wrote: post #28
joeminichino wrote: post #25

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.

Well. I loved the piece you linked! 22-TET does not sound nearly as dissonant to my ears as 15 does. Thank you for sharing.

Re: A study of musical scales (2017)

#42

Post by crazynick4 »

yesenadam wrote: post #40
bradford wrote: post #29

Earlier quoted context omitted.

> 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…

> 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.

Yes, the perceived consonance has less to do with the simplicity/symmetry of the concept used to construct the scale and more to do with the 'simplicity' of the denominators of the ratios that make up the intervals. The smaller (simpler) the denominators involved, the more pleasing/consonant the sound will be (provided that they're integer ratios). Frequency ratios like 3/2 and 4/3 are among the simplest possible and are both present in the major scale but absent in the latter two examples.

Re: A study of musical scales (2017)

#44

Post by yesenadam »

crazynick4 wrote: post #42
yesenadam wrote: post #40

Earlier quoted context omitted.

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…

> 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. Yes, the perceived consonance has less to do with the simplicity/symmetry of the concept used…

Hmm that's not quite what I was saying - symmetry in scales in actually unpleasant, asymmetry pleasant. It seems that with these symmetrical scales/chords, the ear suffers vertigo, cognitive dissonance, because it can't hear a tonal centre. With e.g. a major scale, the asymmetry makes it obvious what key you're in.

Re: A study of musical scales (2017)

#45

Post by crazynick4 »

yesenadam wrote: post #44
crazynick4 wrote: post #42

Earlier quoted context omitted.

> 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. Yes, the perceived consonance has less to do with the simplicity/symmetry of the concept used…

Hmm that's not quite what I was saying - symmetry in scales in actually unpleasant, asymmetry pleasant. It seems that with these symmetrical scales/chords, the ear suffers vertigo, cognitive dissonance, because it can't hear a tonal centre. With e.g. a major scale, the asymmetry makes it obvious what key you're in.

I see what you mean. Still I would argue that both tritones and minor thirds only appear to possess the symmetrical property as a result of temperament. It doesn't exist 'in nature' as such.

The frequency ratios that they represent, 7/5 and 6/5, respectively, don't lend themselves to the same type of symmetry. If you have a tritone, 7/5, you would need a 10/7 ratio to make the octave, which would be a different interval (although close).

With a minor third (6/5), if you were to stack the intervals starting from let's say 500 Hz, you would go to 600, 720, 864, and 1036.8, and you'd be off 36.8 Hz from the octave.

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