Partch in 144-eq

[Erlich:]
> 72-tET approximates all of Partch's consonant intervals
> (i.e., all the ratios in his 11-limit tonality diamond)
> consistently and with a maximum error of ~3.9 cents. This is
> much better than any ET with lass than 118 notes.

Another reason why I like the 72-ET notation so much.

> 144-tET cannot improve upon any of 72-tET's approximations.

Well, as I said, I'm still not convinced of 144's usefulness,
but I got interested in it, and thought it worth exploring.

> Partch obtained his full 43-tone system by transposing parts
> of the tonality diamond to centers other than 1/1.
> What is important in these transpositions is that the harmonic
> integrity of the each of the diamonds be preserved, not
> that the complex, secondary ratios be represented well with
> respect to the 1/1 of the overall system (G).

You are absolutely correct.
(Do you *never* tire of me telling you that?)

I have to agree, because of your eloquent argument,
that Dan Stearns was right and I should have just left
Partch alone.

But this 144-ET notation is being explored by Stearns
as a useful notation of the virtual pitch continuum,
and I do think it succeeds admirably well in that
regard. For Stearns's compositional techniques, which
include the mixing of 12-, 19-, and 20-eq in one piece,
I think it's a good solution.

One of the big advantages it has over 72-eq is that
it provides extremely accurate notation for 11-eq
and 13-eq. This may not be very important for composers
like you and I who prefer to think ultimately in
terms of (in my case), or in relation to (in your case), JI.

But for someone like Stearns, who uses non-12-ETs a lot
without being concerned about their rational implications,
I think it's quite useful to be able to use the same
symbols for a variety of different tunings.

In this scenario, 144-eq avoids what I considered to
be the biggest problem with Blackwood's 'Microtonal Etudes'
- a separate notation for each ET.

I think I can agree with Stearns that in a compositional
situation where several different ETs are being used
at once, disregarding rational implications, the ~4-cents
maximum error of 144-eq can be considered negligible,
and its notational simplicity and flexibility is
a big advantage.

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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>
>
> [Erlich:]
>
>
> > Partch obtained his full 43-tone system by transposing parts
> > of the tonality diamond to centers other than 1/1.
> > What is important in these transpositions is that the harmonic
> > integrity of the each of the diamonds be preserved, not
> > that the complex, secondary ratios be represented well with
> > respect to the 1/1 of the overall system (G).

It seems that Partch sensed the logic of Constant structures and filled in
the gaps of a 41 tone scale that required two interchangeable notes.
Looking at the added pitches (also all epimores!) he added along
pythagorean lines more than transposing diamond section which he could have
done! Taking a look at a diamond a 3/2 away for instance and there are
pitches he could have used but didn't. The added pitches shows Partch 's
melodic sense added with his harmonic. The Diamond by itself is lacking.

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

Joe Monzo wrote:

>I have to agree, because of your eloquent argument,
>that Dan Stearns was right and I should have just left
>Partch alone.

That's too bad, because I think Partch in 72-tET is a wonderful thing. The
11-(odd)-limit intervals, which are the ones Partch considered consonant,
are all within 4 cents of their just values, which is really too small an
error to matter in a performance situation (I'm thinking string players and
singers trained in 72-tET, which is happening here in Boston).

>> [Erlich:]
>>
>>
>> > Partch obtained his full 43-tone system by transposing parts
>> > of the tonality diamond to centers other than 1/1.
>> > What is important in these transpositions is that the harmonic
>> > integrity of the each of the diamonds be preserved, not
>> > that the complex, secondary ratios be represented well with
>> > respect to the 1/1 of the overall system (G).

Kraig Grady wrote:

>
>It seems that Partch sensed the logic of Constant structures and filled in
>the gaps of a 41 tone scale that required two interchangeable notes.
>Looking at the added pitches (also all epimores!) he added along
>pythagorean lines more than transposing diamond section which he could have
>done!

These are the same thing since the diamond includes 3-limit ratios -- in the
extreme example, transposing a 3-limit tonality diamond leads to Pythagorean
tuning itself.

>The Diamond by itself is lacking.

That's for sure. It certainly doesn't represent a "finity" in the sense
Monzo has used until now. But the 41-tone scale does!