Re: [tuning] How "infinite" the tonal lattice?

Polychroni!
I must interject my own warning here as to perceptible limits. I believe that the research
is very limited and much more work really needs to be done before we start drawing lines in
the sand. I wish to take an example from a very unlikely source. Stockhausen's Hymnen. In the
second region there is a chord that descend a tritone over quite a few minutes. On one level
such things are not heard but "felt" which is exactly what Karl was up to. Few in the Lab
would hear anything at all.
Much has been said as to how high a limit one can use. Let me point out that the Ancient
Greeks far surpassed these limits. The method in many cases was by the use of "means" or
"medients". The Persians also used high ratios in the same way. That various "means" where
used along with limits is something we should not over look or cease to investigate.
Another point is that various intonation systems allow new" structural" possibilities. In
the 1-3-7-9-11-15 eikosany we have 2 opposite notes the 1-7-9 and the 3-11-15 a 56/55 apart. A
mere 31 cent interval. You could temper this out over the series of just intervals it would
take you to get there, but it would not be the same. I am sure that Dan Wolf would agree with
me that after working and hearing this structure a shift to one or the other expresses a leap
beyond its ratio size and is heard as a "structural" leap.
Partch work with limits was an examination of the Lambdoma at its different size levels.
For a great part the structural Possibilities is what attracted him to build instrument in
this tuning. As Dan could also point out , he did not limit himself to this singular
structural perspective. Many of his composition were based on ideas outside the diamond but
could be done with a diamond master set. He knows more about this than me. As far as
Practicality what is more impractical than his set of instruments! Art is not Practical,
nuclear weapons as a deterrent are. Infinity is not so bad

I agree with the cowboy "Don't Fence me in!

Polychroni wrote:

> As a sub-amateur in tuning, I'd like to ask the following question.
>
> After having read the _JI Primer_, much is made out of the "infinite" tonal
> lattice. But, clearly, their are limits, both physical and perceptional,
> on how fine an increment can be discerned. And, since some intervals are
> indiscernible, it would seem that the _practically_ the lattice is finite.
>
> Is it reasonable to superimpose a "discernability grid" or a "precision
> grid", or some other such grid, on top of the tonal lattice, thereby
> joining like-tones (hmm..., 'homotones'?), into a finite, practical
> lattice?
>
> Best regards,
>
> Polychroni Moniodis
> Ypsilanti, MI
>
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-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com

Paul!
Both your arguments here and in the latter post are well taken!
I acknowledge the validity of "punning" as being musical significant and useful. I wanted
to pointed out to Polychroni that there is a breath of the situation that regardless of what
decides to do personally these decisions are not universal, final or conclusive. Whenever I
use any tuning I am always aware of what I am not doing!

"Paul H. Erlich" wrote:

>
> I feel that any composer should be free to draw the line anywhere she sees
> fit, based on her own perception of her compositional materials, her likely
> uses of duration, timbre, etc. The Fokker periodicity block formalism I
> pointed Polychroni to allows one to take any equivalences, whether as large
> as 31� or as small as a fraction of a cent, and construct a finite pitch
> system which mirrors the entire infinite lattice using only those
> equivalences. No one is saying that 31� or even much smaller intervals can't
> be perceived as structurally distant on the lattice if the composition uses
> them that way. At the same time, finity can open up compositional
> possibilities absent on the infinite lattice through the use of "punning" --
> at which point temperament and/or adaptive tuning become useful options. The
> commonest Western progressions rely on "punning" through the syntonic comma,
> an interval which in pure just intonation would come out to 21.5�. However,
> if one wrote a piece in just intonation in which the melodic interval of
> syntonic comma was a motivically emphasized feature, one could
> compositionally project it as a significant move in the harmonic lattice.
> These are not contradictions, they are merely alternate possibilities in the
> vast field of musical composition, and a demonstration that musical context
> is everything when dealing with these abstract "lines in the sand".
>

-- Kraig Grady
North American Embassy of Anaphoria island
www.anaphoria.com