Reply to David Mezquita

Hello David,

I really feel like an old experienced tuner,
cause I am on the tuninglist now for more than a month. :-)

> From: "David Mezquita" <DMEZQUI@teleline.es>

> A Palestrina vocal work, for example, sounds much better with just
> intonation, because of its harmonic clarity and its diatonic construction.
> But in19th Century works we can often find accords of dim. 7th (C#-E-G-Bb)
> that play a very important role in the harmony because of their ambiguity,
> and this polivalence is lost with just intonation.

What do you mean with the ambiguity of a chord? I understand you mean this
chord has no real root, or maybe a lot of possible roots. I do agree, a
traditional dim chord is an ET4(an octave divided in 4 equal parts).
But a dim chord also exist in JI:

note e : g : bes : des
common subharmonic 5 : 6 : 7
common harmonic : 1/7 : 1/6 : 1/5
otonal 25 : 30 : 35 : 42
utonal 1/42 : 1/35 : 1/30 : 1/25

As you see, 5,6,7 there is no multiple of 2 (4,8,16,32..) involved.
So in JI a clear root is missing as well.
You are right. Now it's not as polyvalent as in ET, because 5:6 is not equal
to 6:7, being the same interval in ET.

Therefor I like a recalculation of JI at each very moment, adapted to the
context. So chords can softly fluctuate. Retuning on the flight as you wish.

Peter Mulkers (Belgium)

Peter Mulkers wrote:

>What do you mean with the ambiguity of a chord? I understand you mean this
>chord has no real root, or maybe a lot of possible roots. I do agree, a
>traditional dim chord is an ET4(an octave divided in 4 equal parts).
>But a dim chord also exist in JI:
>
>note e : g : bes : des
>common subharmonic 5 : 6 : 7
>common harmonic : 1/7 : 1/6 : 1/5
>otonal 25 : 30 : 35 : 42
>utonal 1/42 : 1/35 : 1/30 : 1/25

You are right. It exists in JI, and it was in fact a common chord in the
Baroque. But it was normally used over the 7th note of a minor scale (for
example G#-B-D-F in A minor), and the resolution tended to be the tonica or
a near chord. The accord had no ambiguity, because G# was not Ab, B was not
Cb, etc... So it is logical to play it in JI.

But in 19th Century the notes of this chord were modified enharmonically, so
that the chord can bring you easily to at least 4 tonalities. That's why I
said "ambiguity". In ET the four Modulations are identic, so that ET offers
more possibilities for modulating. I'm not saying that the whole work sounds
better in ET. So I agree fully with your words...

>Therefor I like a recalculation of JI at each very moment, adapted to the
>context. So chords can softly fluctuate. Retuning on the flight as you
wish.

That's it... One has to analise the work, understand the harmonic and the
melodic structure and many other things, and then decide about the
intonation.

David Mezquita.

On Sun, 21 Mar 1999, Peter Mulkers wrote:

> From: "Peter Mulkers" <P.Mulkers@gmx.net>
>
> Hello David,
>
> I really feel like an old experienced tuner,
> cause I am on the tuninglist now for more than a month. :-)
>
>
> Therefor I like a recalculation of JI at each very moment, adapted to the
> context. So chords can softly fluctuate. Retuning on the flight as you wish.
>
>
> Peter Mulkers (Belgium)
>
> ------------------------------------------------------------------------

Mr. Mulkers, This is precisely one of the models I have been grappling
with for sometime now in connection with my work on Turkish music. I am
inclined to think in terms of constantly changing `local' scales at the
micro level running within the framework of a `global' or macro setting.
However, in Turkish music these local scales do not necessarily have to be
JI.

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Can Akkoc
Alabama School of Mathematics and Science
Mobile, Alabama 36604-2519
Phone: (334) 441-2126
Fax : (334) 441-3290