Did humans invent music, or discover it?

[WordMan]

@Autolycus

Fascinating. As a music-lover and psychology lit. dabbler, where would one go to read more about this?

Music, The Brain, And Ecstasy: How Music Captures Our Imagination: Robert...

Try this.

[jovan]

@Autolycus

Fascinating. As a music-lover and psychology lit. dabbler, where would one go to read more about this?

I’ve only skimmed both of these works but you might want to check out:
Musicophilia by Oliver Sacks (can never go wrong with him!)
This is your Brain on Music by Daniel Levitin

The second one is really introductory, but it goes over some of what I talked about.

If you’re feeling ambitious, or are a psychology grad student, you might go to the Bible:

Auditory Scene Analysis by Albert Bregman

That’s pretty much The Book on the subject matter, and there’s a big chapter on music, but be warned: it’s tedious. I mention it because, hey, it’s the Dope.

[Chronos]

And just to give actual numbers for an equal-tempered scale:

Let’s call the frequency of the first note of the scale “1”. Then the scale of frequencies (rounded to six digits) will go
1.00000
1.05946
1.12246
1.18921
1.25992 ~= 1.25 = 5/4
1.33484 ~= 1.3 = 4/3
1.41421
1.49831 ~= 1.5 = 3/2
1.58740
1.68179 ~= 1.6 = 5/3
1.78180
1.88775
2.00000 = 2

The octave is the only one of these simple ratios that’s exact, in this temperament, but 5/4, 4/3, 3/2, and 5/3 are all reasonably close, and will remain reasonably close to the same degree when they’re transposed to some other scale.

[Frylock]

@Francis_Vaughan

If you ran the process past 11 notes it fills in the next sequence to give you a 41 note scale. Some music is scored for this scale. You can also stop at 5 notes. A heck of a lot of music is based on that scale.

A. I didn’t know there was that kind of rationale for the pentatonic scale so thanks for that

B. I am finding a lot of references to a 19 tone scale on youtube, but I can’t find references to a 41 tone scale on youtube or elsewhere. Do you have anything you can point me to?

[Frylock]

@jovan

Sounds that exhibit this behaviour are a minority, but since our vocal cords are one of the places where they do occur, they are extremely important to us. Hence, any other harmonic sound will trigger our brain circuitry dedicated to recognising voices.

So here be the math: the most consonant interval is the octave. It is a 2:1 pitch ratio. If I play a sound with the partials 100, 200, 300 and 400 Hz, the note an octave above will have the partials 200, 400, 600, 800. Every partial of the second note is also a partial of the first. Even if the sounds don’t completely perceptually fuse together, there will be an important part of your auditory cortex screaming “belongs together!”

BTW I believe the above answers my question from this long-past thread.

[nudgenudge]

@Frylock

@Francis Vaughan

If you ran the process past 11 notes it fills in the next sequence to give you a 41 note scale. Some music is scored for this scale. You can also stop at 5 notes. A heck of a lot of music is based on that scale.

I didn’t know there was that kind of rationale for the pentatonic scale so thanks for that

It’s not a rationale for pentatonic scales. The familar pentatonic scales are not equal-tempered. They instead consist of five consonant-sounding intervals that fall between unison and the octave at unequal intervals. An equal-tempered five-note scale is not particularly consonant, and nothing like a pentatonic.

[Frylock]

@nudgenudge

It’s not a rationale for pentatonic scales. The familar pentatonic scales are not equal-tempered. They instead consist of five consonant-sounding intervals that fall between unison and the octave at unequal intervals. An equal-tempered five-note scale is not particularly consonant, and nothing like a pentatonic.

Hrm, I guess I misunderstood.

My thinking was:

Start from C, go up by fifths.

C G D A E B

Put them in alphabetical order:

C D E G A B

That B is fairly close to that C, so voila–you’ve got the pentatonic scale: CDEGA.

I figured that’s what he meant. Are you sure it’s not? Here’s the relevant text:

@Vaughn

This turned out to work because the ratio 3:2 (the fifth) could be used to cycle though the 11 notes (the cycle of fifths) and would get close enough (mostly) to the note you really wanted. Start on the root, multiply by 3/2, that is your next note of the cycle. Multiply that by 3/2. If the frequency is larger than an octave from the root, divide it by two to pull it back into the octave. Repeat until you have “filled” the octave. (That is the process returns a note close to the root). This process gets you your 11 note scale. The sticking point can be the definition of “filled” as it is impossible for the process to exactly return to the octave. (Unique prime factorisation theorem sees to this.) So you terminate the process when the note returned is close enough to the octave that you don’t care. If you ran the process past 11 notes it fills in the next sequence to give you a 41 note scale. Some music is scored for this scale. You can also stop at 5 notes. A heck of a lot of music is based on that scale.

[nudgenudge]

@Frylock

Hrm, I guess I misunderstood.

My thinking was:

Start from C, go up by fifths.

C G D A E B

Put them in alphabetical order:

C D E G A B

That B is fairly close to that C, so voila–you’ve got the pentatonic scale: CDEGA.

I figured that’s what he meant. Are you sure it’s not? Here’s the relevant text:

Why stop at B? The next note in that system would be, let’s see, F. It doesn’t mean that we should conclude that the system naturally suggests a seven-note scale.

I’m not sure what was meant by the post you quoted. The circle of fifths is usually something that is referred to within the context of equal temperament. If the point is that you can get close to consonant intervals by multiplying by 3/2 enough times then, yes, that is true, but it doesn’t mean that there is anything magical about five intervals, or about the ratio of 3/2.

[Frylock]

@nudgenudge

Why stop at B?

Wasn’t that clearly explained both in what I said and in the quoted text? Because it’s “pretty close” to C.

But anyway, you’ve succeeded in bringing me to the point that I don’t know which of you to believe, so I hope to simply watch the ensuing cite fight.

[Francis_Vaughan]

Pentatonic simply means five notes. There is more than one pentatonic scale. The major and minor pentatonics are the best known. You can have a lot of fun trying others. Pythagoras derived the minor pentatonic from ratios of 3 and 2. But not with a form that is a cycle of fifths (that would require only powers of three in the numerator, and powers of two in the denominator only, whereas his intonation has both possibilities.) That it also can be derived from the cycle does however remain interesting.

but it doesn’t mean that there is anything magical about five intervals, or about the ratio of 3/2

Absolutely. The insistence on 3/2 ratio is arguably a problem, and even Pythagoras’ use of only 3 and 2 (both 3/2 and 2/3) still doesn’t really work that well. Adding 5 to the mix seems to be better. One wonders if 7 might be an idea too, but those partials might be too low level to matter. What we do see is a lot of near coincidental ratios, and within in the morass of the brain’s processing one wonders whether the mix of these coincidences is not part of the overall tonality perceived, rather than just the pure ratio of the partial of the fundamental. The slight mis-match of the ratios being as important and the ratios themselves.