Harmonic tunings and spectral compositions

In TD 831 Brian McLaren writes :
> Thus it's incomprehensible why the French spectral
> composers would consider 24 tones per octave
> even *remotely* adequate to approximate the
> harmonic series.
> Even the most naive observer must conclude that
> since 24-TET yields an improvement in only the 11th
> harmonic and the 22nd, while 48-TET yields
> audible improvements in the 7th, 11th, 13th, 14th,
> 21st, 22nd and 23rd harmonics, 48-TET is obviously
> the minimum multiple of 12 tones per octave which
> produces a improvement commensurate with the
> effort in subdividing the whole tone.
> Perhaps Franck Jedrezjewski can explain this
> puzzle?

I am not sure that I could explain the puzzle but I give
some remarks on the problem pointed out by Brian.

Given a sound of frequency f, you could theoretically build all the
harmonics f, 2f, 3f, 4f, etc... Choose the first 2^n
harmonics and put them in the same octave by dividing
by a power of 2, you get what I call an "harmonic tuning"
Take n=4, you get 16 notes :
1 0 cents
17/16 105 cents
9/8 204 "
19/16 297
5/4 386
21/16 471
11/8 551
23/16 628
3/2 702
25/16 773
13/8 841
27/16 906
7/4 969
29/16 1030
15/8 1088
31/16 1145
2 1200

Take n=5, you get a 32 notes system :
1 0 cents
33/32 53
17/16 105
35/32 155
9/8 204
37/32 251
19/16 297
39/32 342
5/4 386
41/32 429
21/16 471
43/32 512
11/8 551
45/32 590
23/16 628
47/32 666
3/2 702
49/32 738
25/16 773
51/32 807
13/8 841
53/32 874
27/16 906
55/32 938
7/4 969
57/32 999
29/16 1030
59/32 1059
15/8 1088
61/32 1117
31/16 1145
63/32 1173
2 1200

Now, choose k notes in this Harmonic Tuning (HT), and find a best
approximation in terms of x-tet. That is : find x ?
(Note : You could define several "best approximation".)
This is what Brian do in TD831.

The spectral composers have others problems. They don't want
to find an approximation of their initial sounds.
They use spectras as first materials of their compositions.
They take a sound or several : a sound from the street, a sound
from a piano, evry kind of sound... But not noisy
because they want to read the composants of the sound
has frequencies. (why ? To be near electro-acoustic music research
in using spectres ? To be far from the electro-acoustic music directions
or esthetics in using discrete frequencies ?
To be in the same logic as serial compositions :
the series are in the serial music
as spectras are in spectral music : a structural element of
composition ? use to build the whole score ?)
The sound could have some harmonics very poor and partials very rich,
so they are very far from the Harmonic Tuning systems.
They usually write music for
traditionnal orchestras (that could be played everywhere,
sometimes with synth. as DX7)
with their materials, they could use microtones.
Why not quarter tones ?
Quarter tones could be played by most instrumentists
and many are used in the XXth century music.
Could they have more rich panels with other tunings ?
Maybe yes, but actually I have not seen spectral compositions
with others tunings (in the traditionnal orchestral writings).
The spectral composers problems are not to find a "good" approximation
of their spectres. They want compose pieces of music with their own
materials used as a pretext, not as an atom of the whole composition but
as a "structure". The first material must not be exactly the initial sound.
I also would like to explain that structuralism is important in the
developpement of the thinking of spectral music, a music made
by "reconstitution" of spectres, with "processus" to
move to one representation to another, and where the dividing of
the whole tone is not a structural element, neither a "processus"
of composition : for spectral composers, it's only a data.

--franck

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The answer to this is so simple. My daughter does not care about what
tuning the piano is. Usually, my piano is not very well tuned anyway.
When my daughter was very small (from one week old), I would sing along
with any tempered instrument, flute, piano, organ, so that she understands
that those are "substitution" for the correct intonation.

This phenomenon appears in many circumstances. When I was a not-so-in-tune
violinist, I myself cannot hear myself out of tune the when I was playing.
But if I put myself on tape, and listen to the tape afterwards, I can tell
thousands of notes out of tune. The reason is I practiced badly too many
times.

Some post just revealed (was it Gary?) that violinist who claim to play
tempered in fact does not do anywhere close to tempered. So how come
so many of you, and others still believe so much that violinist try to
imitate the intonation of the accompanying instruments? So any of you
tell any difference between the violinist and the accompaniment even
once before? So did it strike you that it sounded SO bad?

A friend once brought a piano professor from the Mountpellier Conservatory
to my house. We played from afternoon till midnight. After a few years,
he came and we played again. I told him that every note I play except
the A is different from the piano. He could not believe me, and went
on checking each and every note of a sonata. He was so surprised that
it really was. So nobody cares what the tuning is when there is nothing
to care about.

Neither could you noticed that pianists and violinist write music
very differently, and their use different harmony rules, because
their tunings are different!

Regards,
Linus Liu.

>
>Linus,
>
>I presume then your daughter likes the way her piano is tuned. And how might
>that be?
>
> -Paul
>
>


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