source file: mills2.txt Date: Mon, 9 Sep 1996 10:06:23 -0700 Subject: Harmonic tunings and spectral compositions From: Franck Jedrzejewski 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 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Mon, 9 Sep 1996 20:54 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA32312; Mon, 9 Sep 1996 20:56:16 +0200 Received: from eartha.mills.edu by ns (smtpxd); id XA32530 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA12868; Mon, 9 Sep 1996 11:56:14 -0700 Date: Mon, 9 Sep 1996 11:56:14 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu