Re: [MMM] EDOs in "atonal" music

Igs:
> > > Actually, that scale is just 3-out-of-22-EDO with the "octave wrap"
> > > removed, or in other words 22 equal divisions of 8/1.

Me:
> > Did you misspeak? If I have 11 divisions getting me to less than an
> > octave, how can 22 of those divisions get me to 3 octaves?

Igs:
> 8/1=3600 cents. 3600/22=163.6363... You said 11 equal divisions of 1800 cents.

Me, now:
Um, yeah. That's called me being a bonehead.

I could have chosen (and almost did) a more off-kilter number, like 1715. That wouldn't be a multiple of 1200 cents for 343 iterations. But I think we can agree that the number probably wouldn't matter, because there would still be consonances inadvertently lurking in there somewhere.

> > Only if you're trying to make tonal music. If you're trying to make
> > atonal music, then it's no easier or harder to use the scale in, say,
> > serial construction, but you're less likely to hit an accidentally
> > strongly tonal interval.
>
> That is probably true. But the same could be said of 8-EDO.

If you consciously ignore the octave. I'll ignore that since we currently seem to have a difference of opinion about what an octave is in relation to the word "consonance".

> I guess that's where my idea of "consonance" differs from others. I see
> consonance as something that sounds "good", not something that sounds...
> unnoticeable. I'll grant that the octave is a very important ingredient in how
> we make music. But the idea that the "most consonant"--i.e. "most pleasant
> -sounding" interval is 1/1, followed by 2/1, 3/1, 4/1, and 5/1, and THEN 3/2,
> etc.--seems ass-backwards to me.

I don't think "consonant" as used on these lists really CAN mean "pleasant-sounding", regardless of whether that's the way it's often used. After a half-hour drone on 1/1, I'll bet most of us would find any change to any other interval more pleasant-sounding than more 1/1. And, as someone said -- Kyle Gann, maybe? I read his Web site several times a few months ago -- the 386-cent M3 often sounds "sad" to people who are used to hearing the 400-cent version. I also agree that it's foolish to say that 1/1 sounds "better" than 2/1, and saying that 2/1 sounds "better" than 5/4 is simply off-base.

"Consonance" seems to be a term of art that means "more closely related to". 1/1 is most closely related to itself; 2/1 is next closely related to 1/1. 3/2 seems next, and 4/3 and 5/4 seem to be closely related to 1/1, similar in distance to each other but both farther away from 1/1 than 3/2 is. Regardless of what measure might be useful for that distance -- Tenney Height seems like something close but perhaps not perfect -- the fact is that some intervals seem to be less closely related to a given root tone than others are.

Does that mean that any of these "sound better" than the others? I don't think so. Debussy sounds better to me than Mozart, generally speaking. Rush sounds better to me than bubble-gum pop music. Rush and Debussy use a lot more dissonant notes than Mozart and Britney Spears.

In some cases, you want very closely related notes because they impart a restful or clear or rooted quality, in some cases you want distantly related notes because you want a tense or more ambiguous or unrooted quality. But is ambiguity "worse" than clarity? Not in most art, and certainly not in music; "better" or "worse" depends on context. Fish sauce is awesome in Thai food, but not so much on ice cream. Or so I'd guess. :)

Regards,
Jake