RE: An Evening with Erlich (con't)

that some musicians may not be happy to give up.

>>"Musical tones normally have uypper partials within
>>this range, and since harmonic partials are integer multiples of their
>>fundamentals, they will yield the same ratio-interpretation for their
>>fundamentals as would the fundamentals transposed into this range.
>>(This is why we did not worry about overtones in the first place)."

>Is there any chance the results aren't so clear-cut when you try to apply
>the 1% idea to a system where the tones have partials?

None of this is very clear-cut anyway, since the Rameau/Parncutt idea
that chords are complex tones of complex tones is very difficult to
demonstrate experientally. Certainly the idea is difficult, if not,
impossible, to apply to utonal chords. All of the quantitative models in
the paper came from years of listening and trying to understand what I
heard in a way that could explain what I heard.

>Maybe I mis-understand what you mean by "power"

Yeah, something to the third power is a third power, not a power of
three.

>There is a type of "sensitivity to mistuning" that does not obey the
>inverse to odd limit rule. For this type of sensitivity, it seems that the
>3/2 is much more sensitive than the 7/4.

Yes, as I say in my paper, although a given amount of mistuning has less
of an effect on the ratio-interpretation of lower-limit ratios than on
the ratio-interpretaion of higher-limit ratios, it has more of an effect
on the consonance of lower-limit ratios than on the consonance of
higher-limit ratios. This is because higher-limit ratios are not very
consonant to begin with, and even going to total dissonance will not
change things much, especially if there is a lower-limit interval in the
chord.

>I think the 4-5-6 chords of 12 are at least as good as those of 19.
>I wouldn't say one is "better". The 19 major triad seems to sound much
>more aggressive, like a razor. The 12 tone 4-5-6 chord seems more tame,
>but more rough.

>I do think that 19
>has clearly better 10-12-15 and 4-5-6-7 chords than does 12.

That's odd -- so you think the tuning of the 3:2 is more important in
the major triad than in the minor triad?

Clearly the whole issue is so multidimensional. The more flavors
available to composers, the better, although the number of bad
compositions might increase as well.

>In other topics, you once posted about not using your 22TET guitar for
>decatonic music, and that you were going to check out a 31TET guitar. Have
>you done this? What do you think of 31? You use the diatonic scale?

I'm still not spending much time on microtonal guitar. I'm not getting a
good tone out of my 22TET guitar, perhaps because the truss rod is
almost completely loose and yet the fretboard is just about striaght,
just a tiny bit concave, just the way I want it. I'm thinking about
interchangeable fingerboards (including, perhaps, 31) for one of my
7-strings, maybe I should write Mark Rankin a letter.

In 31, yes, diatonic scales will predominate, the Arabic scales have
good ratios of 11, and ratios of 7 lead to micro-chromatic neighbors of
diatonic notes that might be useful for an extremely microtonal style.

>And what was the problem with decatonic scales on the 22TET instrument?

Well, my brain seems so pentatonically/heptatonically wired that all
kinds of weird stuff, even micro-chromatic stuff, seems more exciting to
me than decatonic stuff. Although there have been significant
exceptions. Certainly I'm happy with the smoothness of the 7-limit
tetrads in 22TET -- the fact that I'm playing 12TET, rather than JI,
music for hours every day probably helps to foster this impression.