An Evening with Erlich

>My paper, for the sake of brevity, sticks with the simple
>ETs, with at most one decent approximation to each just interval.

I think that sticking to under 35/oct is a good choice for the paper.

>There may be some wonderful scales in 41tET for all I know.

You do go up to 210 TET or something at one point in the paper, searching
for a better tuning for the decatonic scales. But you don't say much on
what means you used to search this tunings.

>Well, the only real problem in ET's over 34/oct is that consistency is
>not really relevant anymore, since there might be an adequate
>approximation for a given interval which is not the closest
>approximation.

This is the real meat of my question about the 1% thing. What does it mean
"adequate"? Certainly you don't claim that all scales over 35 sound alike...

>"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?

>Carl, perhaps you could do me a favor and stick something like this into
>the .pdf version of my paper?

I am right now working two jobs... But I am planning to do some work on
xenharmonic theory in August (when I'll have my own computer again). I
want to put up a web page where all sorts of stuff on alternate tunings can
be published in pdf format. I'd be happy to work with you on making a
really nice version of you paper for it then.

>No, according to Gary, a factor of 3 will only produce steely coldness
>if there are no higher prime factors in the ratio.

That's what I thought.

>Powers of 3 are candidates, since they only have factors of 3.

Maybe I mis-understand what you mean by "power". I call this interval:

(3/2)^3

An interval with a factors of two and three, and a power of three. The
interval is a 27/16.

(5/4)^3

This interval has factors of two and five, and a power of three. It is a
125/64. It has a power of three, but no factor of three.

>>Sort of like you could tell what prime limit music on a 33 is, playing at
>>45 rpms, but not what odd limit the same music was without hearing it at
>>actual speed?
>
>See, I have no problem with this, since the melodic and harmonic
>vocabularies both figure into the pitch sets that are heard, and the
>pitch set determines the character of the music to a large extent. I
>already stated where I think the odd-limit concept is useful.

Fair enough.

>I think Partch was right that an interval's allowance for mistuning, as
>regards the interval's ability to be recognized as the just ratio, is
>inversely proportional to the ODD limit. 81/64, if recognizable at all
>(I don't think so), has an EXTREMELY small allowance for mistuning.

Ah. Well, that works. Thing is, "sensitivity to mistuning" can mean so
many things. I'm just now seeing how you're using it here, and I can't say
that it is in any way incorrect.

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. Further, it seems to matter to
this type of sensitivity wether an interval is mis-tuned sharp or flat.

>Most people who have made the comparison (including me) consider 19tET,
>whose 3/2 is 7.5 cents flat, to have better triads than 12tET. Do you
>disagree?

Yes. 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. Neither really sounds just. I don't really think there's
a 4-5-6 chord I'd call "better" than 12 until 31. That's not to say that
19, 22 and 29 don't have good triads, because they do. I do think that 19
has clearly better 10-12-15 and 4-5-6-7 chords than does 12.

>Yes, exactly. Contextually, not acoustically.

Here it is folks. The bones of the bone. What do I think? I think that
acoustic perception is much less fixed than some people would like. I
think that I could train subjects to detect (at least as well as they have
detected anything so far in a lab) any type of interval class I wanted with
little more than classical conditioning.

If, through context in music (working on the tendency for us to hear things
as part of a harmonic series, which I do believe is more than a learned
response) I have learned to hear 81/64 as a 3-ness, even if played only as
a dyad, I appologize.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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?

And what was the problem with decatonic scales on the 22TET instrument? I
have a friend who plays guitar, who I hope to convince to get a microtonal
guitar, and so far the only one I'm convinced will do what he wants it to
do is 19. I'd appreciate any input you or anybody else has in this area.
(There were, once upon a time, a load of people refretting to 22 on this
forum)... What News?

Carl

>...do you really think eq temps are "easier?" ... I've heard a BUNCH of
>music in pure tunings that didn't take much skill or imagination to play.

I can't recall, but perhaps Joe was referring to the complexities of
adaptive JI?