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
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 > >
Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 10 Sep 1996 15:57 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA25285; Tue, 10 Sep 1996 15:58:38 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA25173 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id GAA01599; Tue, 10 Sep 1996 06:58:29 -0700 Date: Tue, 10 Sep 1996 06:58:29 -0700 Message-Id: <960910135224_71670.2576_HHB29-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu