Fwd: [tuning-math] otonally-weighted lattices (was: from the realms of private correspondence)

IMHO, the question of whether you want to weight things
otonally or utonally might entail issues of what timbres
and textures you're intending to use.
One unstated criterion of good counterpoint, for example
has come to be that more of the consonances should imply
utonal shapes than otonal shapes (except, generally, at
points of "resolution").
In looking at numerous ensembles styles from various
cultures, I've developed the opinion that otonality
is more likely to predominate in denser, more spectrally
arithmetic and less "controlled" textures, idioms, whereas
the utonal is likely to predominate either in thinner
textures with more fixed parts and less
arithmetic harmonic spectra.
Not that this is absolutely true; my point is that
you might want to ask yourself how the intervals
are going to be used before trying to decide which
of them are "better".

---- Original message ----
>Date: Sat, 9 Nov 2002 02:10:19 -0800
>From: "monz" <monz@attglobal.net>
>Subject: [tuning-math] otonally-weighted lattices (was:
from the realms of private correspondence)
>To: <tuning-math@yahoogroups.com>
>
>
>hi paul,
>
>
>> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
>> To: <tuning-math@yahoogroups.com>
>> Sent: Friday, November 08, 2002 3:39 PM
>> Subject: [tuning-math] Re: from the realms of private
correspondence
>>
>>
>> <snip> ... i don't see how one could ever hope to
>> embody favoritism for otonal over utonal in a lattice,
>> as much as i believe in such favoritism myself.
>
>
>hmmm ... wow, you really "struck a chord" here
>with me!
>
>several years ago, when i had first moved to San Diego
>and was setting up the Sonic Arts website, i was
>pondering how one might favor otonality in a lattice.
>
>i haven't thought about it since then, and don't really
>remember what ideas i had come up with, but i do recall
>that i was trying to incorporate Erv Wilson's famous
>"harmonic spiral" diagram into my own lattice formula,
>whereby the angles and lengths of each prime-axis would
>radiate outward from each lattice-point according to
>the measurements in Erv's diagram.
>
>any thoughts on that?
>
>
>
>-monz
>
>
>
>
>
>
>
>
>
>
>
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--- In tuning-math@y..., <Josh@o...> wrote:
> IMHO, the question of whether you want to weight things
> otonally or utonally might entail issues of what timbres
> and textures you're intending to use.

i don't know what it means to weight things otonally or utonally.

> One unstated criterion of good counterpoint, for example
> has come to be that more of the consonances should imply
> utonal shapes than otonal shapes (except, generally, at
> points of "resolution").

can you give an example? i could imagine some serious controversy on
this point -- george secor seems to feel that utonalities, even mere
7-limit ones, sound like "parodies" of true just intonation
chords . . . personally, i feel that this conclusion may come from an
over-reliance on synthesized chords -- with acoustic instruments, in
particular the guitar, the overtones of utonal chords induce
sympathetic vibrations among the strings which make the chord very
much an "attractor" when attempting to tune a nearby chord "justly".

> In looking at numerous ensembles styles from various
> cultures, I've developed the opinion that otonality
> is more likely to predominate in denser, more spectrally
> arithmetic and less "controlled" textures, idioms, whereas
> the utonal is likely to predominate either in thinner
> textures with more fixed parts and less
> arithmetic harmonic spectra.

what do you mean by "less arithmetic harmonic spectra"? do you mean
inharmonic spectra? personally, i see no way for utonalities to arise
without the presence of harmonic partials to "match up"; meanwhile,
otonalities are powerful "attractors" even for inharmonic timbres or
sine waves, due to the confluence of the combinational tones, and of
course virtual pitch . . .

> Not that this is absolutely true; my point is that
> you might want to ask yourself how the intervals
> are going to be used before trying to decide which
> of them are "better".

true enough . . . admittedly, we're in some pretty abstract territory
here, which may be why this discussion is not going on on the tuning
list but rather here on tuning-math.