source file: mills2.txt Date: Mon, 8 Jul 1996 16:48:28 -0700 Subject: RE: TUNING digest 773 From: PAULE Perhaps the most interesting of the TUNING digests I have seen! (~100 of them). On Henk Badings and Nazism, we can get all the Wagner CDs we want, and rightly so. I would hesitate to censor a Nazi's speeches, let alone his music. Every time I walk into a record store, I go directly to the section after Bach, only to find Baden followed by Baermann. The few selections of Badings I have heard have been breathtaking, and I haven't even heard his microtonal work. It would be a true loss to humanity if Badings' music were to disappear into the shadows of history, but it seems as if it already has. Any information on how to obtain LPs or cassettes of his music would be much appreciated! The question of tuning a harmonica is a truly interesting one. Although meantone is the best possible tuning to get all six consonant triads in a diatonic scale, only three of these triads are possible on the diatonic harmonica (CEG, DFA, and GDB -- I believe there is a draw G in the lower register, isn't there?). So the intervals AC and EB do not need to be tuned precisely. If the presence of two different-sized whole tones is not disturbing to you, you can try 1/1 9/8 5/4 27/20 3/2 27/16 15/8 1/1. More radically, if you allow the draw G to be different from the blow G, you might want to try 1/1 10/9 5/4 4/3 (3/2 or 40/27) 5/3 50/27 2/1, where 3/2 is the blow G and 40/27 is the draw G. The chromatic harmonica, as described by Pat, is a different beast, I'll have to think about it. It seems less restrictive in that G does not have to be in tune with D or B. But the problem of getting the dominant seventh chord to sound just without destroying the usual intervals seems futile. Equal temperament (of the 12 variety) is a pretty good compromise here. Which leads me to Harold Fortuin's post. While the 31-note scale has both beautiful diatonic scales and 4/5/6/7 chords, unfortunately the latter are not included in the former. The 4/5/6/7 chord appears as a German sixth (such as A-flat C E-flat F#) in the meantone interpretation of 31tet, and the minor version of this chord could be expressed as A-flat B D F#. These could fit into traditional harmony quite well, and their pure tuning would allow one to "sit" on them or resolve to them with auxilliary progressions before allowing them to perform their traditional function: A-flat and F# each resolve by a diatonic semitone to a G. The 11-limit intervals are quite good but do not show up in traditional harmonic formulae; incorporating them into traditional harmony would be a challenge, but certainly one of the most worthy challenges in music today. Harold, I can tell you far more about the 22-tone scale, based on research I have done (soon to be published). Here 7-limit chords become the basic consonances and triads are incomplete. There are other similarities with jazz as well. I offer to send you a copy of my paper and other material in exchange for recordings of your music, both past and future. I will e-mail you to see if you agree to this offer. Other references would include Yasser's _Theory of Evolving Tonality_ and van Eck's _J. S. Bach's Critique of Pure Music_. Yasser shouldn't be taken too seriously, but my imagination was sparked more by this book than any other. van Eck incorporates more modern psychoacoustics than any of your references, and certainly deals with "traditional" harmony, though microtones are not really dealt with. In any case, good luck to you, I think your approach is among the most likely to meet with success in the future of music. Thanks to all for the suggestions of xenharmonic vocal compositions. I am definitely going to check some of these out. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 9 Jul 1996 02:52 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA04449; Mon, 8 Jul 1996 17:52:07 -0700 Date: Mon, 8 Jul 1996 17:52:07 -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