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Comment by rspeer | Hacker News Reader

> Minor third is not a simple fraction - is that the reason to exclude it from the scale?

The minor third is a 6:5 ratio. Does that change your mind?

Where do your tones and semitones come from? You've just rejected the explanation for why we have a 12-tone scale (it is a local optimum of tuning, closed under the operation of transposition, that satisfies lots of nice ratios), so what do you propose instead? Saying "no one can explain" is a cop-out.

To follow up: Major and minor scales are 7-tone subsets of the 12-tone scale that were discovered first. They allow for many of the same possibilities, but they're not closed under transposition, which is why we now have the 12-tone scale that includes all of them.

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Please read wikipedia article on temperament. 7-note scales were "discovered" long before equal temperament was introduced. Equal temperament is a relatively recent invention, initially was very controversial, and remained so for a long time. In other cultures, there's still a variety of scales and temperaments that have nothing to do with 7-note scales at all. (Jazz uses variety of scales, too - some even with 2 semitones in a row). There's only one thing people seem to agree on: the role of fifth (3/2).

This is exactly what I'm telling you. Why are you being condescending to me about it? You're the one claiming that the semitones of the 12-tone scale are some sort of fundamental axiom.

Why didn't you know where minor thirds come from?

Why do you seem to be denying that simple harmonic ratios are where harmony comes from? (EDIT: he's not, it's fine)

Why are you promoting a theory of music with absurd axioms, which manage to explain the octatonic scale (which almost nobody uses) better than the pentatonic scale (which almost everybody uses)? That's not a sign of a good theory.

Please read the part of the article starting with "The twelfth root of two may be irrational, but it turns out to almost create several nice ratios". The author excludes minor third from the set of "nice ratios". I referred to this while calling it a voodoo.

Dude, if you can't hear it, it doesn't matter. You'll never listen to Coletrane's "Night Train" and have your head explode when you realize he's jumping from Dorian to Mixolodian to whatever the fuck was that!?

A simplified explanation is not voodoo.

Yes, he chose to list only the intervals in the major scale. Showing the intervals in the major and minor scale at the same time would have been very confusing.

I understand now that you weren't trying to say that minor thirds were a hole in the theory he presented, but that they were a hole in the way he presented it. I took issue when I thought you were criticizing the theory itself, because what he presented is a simplified view of generally accepted foundations of harmony. I apologize for mis-characterizing your position there.

There is more that could have been said -- and it sounds like we agree on what could have been said -- but I think it's not necessary to go into all the details of the construction of scales, including temperament, just to write a blog post. Describing temperament accurately, without handwaving, requires a book.

BTW, please read something like "Musimathics", it'll be better than trying to learn music theory from Wikipedia.

I'm not learning it from wikipedia. I'm playing for 50+ years. Best resource is Jazz Piano Book by M.Levine. (I read lots of others, but... everything I learned, I learned from this one).

Okay, yeah. I bristled at your suggestion that I should go learn temperament from Wikipedia, when I was making an effort to not bring up temperament to keep my reply focused.

I thought you didn't understand harmony, you thought I didn't understand temperament, I was talking from a historical point of view, you were talking from a jazz point of view.

We might disagree on two kind of minor points:

* How this blog post should have been written

* I'm uncomfortable with describing fundamentals of music from a jazz point of view, because that seems to me to be putting the effect before the cause.

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