source file: mills2.txt Date: Thu, 19 Dec 1996 13:00:42 -0800 Subject: 41-TET and those difficult synths From: Carter Scholz While I certainly agree with Brian that synthesizers are too difficult to tune -- this is why the neglected MIDI Tuning Spec was devised -- his test case of realizing a 41-TET piano sonata on a synth with just one tuning table (even a 12/octave table) is perhaps simpler than he suggests. Lest someone be discouraged from exploring 41-TET, I offer a simple-minded solution that requires 4 MIDI channels, no channel-clogging messages, and a single tuning table (even a 12/octave table will do). It can be generalized to any ET. Tune the table to the following degrees of the 41-TET scale: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41 -- that is, every fourth degree, for an equal note spacing of 117.06 cents. Set the synth's global pitch-bend range to one semitone. Send MIDI channel 2 an initial pitch bend equal to 29.26 cents; bend channel 3 by 58.53 cents; and bend channel 4 by 87.80 cents. You now have degrees 1, 5, 9... playable on channel 1, degrees 2, 6, 10... on channel 2, degrees 3, 7, 11... on channel 3 and so forth. You still have to assign notes to the proper channel, which may be a non-trivial task depending on the composition, but at least you can get the pitches without inserting a lot of messages -- just one pitch bend at the start of each track. This doesn't invalidate Brian's point. The technique works only with ETs, and it eats up n MIDI channels per timbre (where ñgrees/12). So if you're trying to realize an octet in Partch-43, you would run up against the very real problems Brian describes. Still, I thought I should pass the tehcnique on, simple as it is, in case it wasn't obvious to some readers of the list. (It occurs to me that some just scales. e.g. tetrachordal types, might have internal congruences and repetitions that could exploit such fixed channel offsets. These would, though, require tedious calculation on a case-by-case basis. It would be an interesting exercise to determine if the Partch scale is sufficiently self-similar to use this technique.) Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 20 Dec 1996 02:38 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10966; Fri, 20 Dec 1996 02:40:51 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA10964 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA08398; Thu, 19 Dec 1996 17:40:48 -0800 Date: Thu, 19 Dec 1996 17:40:48 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu