RE: Xenharmonic?

While I personally am in favor of as diverse as possible a plurality of
tunings, polymicrotonality, omnimicrotonality, etc., as long as the
results are musical, there is a history of attempts to identify "the
next step" in Western tuning after 12-equal; here are some
equal-tempered examples:

8.2021: Bohlen, Pierce
16: Goldsmith
19: Salinas, Yasser
20: Balzano
24: Wychnegradsky
31: Huygens, Fokker
36: Gawel
41: von Janko
53: Mercator (did he strictly look at 3-limit? Who was the first to note
the applicability of 53 to 5-limit?)
72: Richter-Herf (Partch missed this in his list -- it would have
disturbed him that an ET could come so close to 11-limit JI!)

My paper is just another proposition along these lines, but it is, I
feel, the strongest one. I do believe that composers must be given an
alternate set of tools than 12-tone keyboards, guitars, etc. for
xenharmonic music to have a chance to naturally evolve. If the goal is
to ditch diatonicism but preserve the principles behind Western tonality
with minimal alteration, I believe 22 is the best way to go. And
harmonically, if JI is your goal, and if you believe the basic harmonies
of the diatonic scale in classical compositions can be "bent" by
variable-pitch instrumentalists to achieve just 5-limit triads, then the
basic harmonies of my 10-tone scales in 22 can be bent by about the same
amount to achieve just 7-limit tetrads. 22 also happens to be an
important number in describing ancient Indian tuning and if modern
accounts of that tuning (basically 5-limit JI) are correct, a 22-tone
"well-temperament" can be constructed which combines very close
approximations of the ancient Indian scales with a few keys of my
7-limit decatonic scales. This is analogous to a 12-tone
well-temperament with 6 pure fifths in a row and 6 fifths diminished by
1/6 pyth. comma, which contains both a pythagorean scale (in 1 key) and
a meantone scale (in 1 key).


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From: Johnny Reinhard
Subject: Re: Woodwind etc
PostedDate: 21-11-97 03:15:17
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As usual I can offer the ftp.maths.bath.ac.uk:pub/dream site
==John
>>>>> "greg" == greg phillips writes:

greg> Hi everyone,

greg> I've written a little tuning program for windows (similar to a DOS
greg> program some people have already tried). It uses a sound blaster
greg> compatible card - or PC speaker to produce notes. Its main purpose is to
greg> help people make wind chimes and tune homemade instruments. The accuracy
greg> is not perfect, but some people might find it of use - perhaps even fun.
greg> It comes with a selection of about 80 different tunings, but you can add
greg> more if you want. I'm looking for a place to leave the program, so that
greg> people can grab a copy without my assistance. Any suggestions?

greg> thanks,
greg> Greg Phillips.


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From: Daniel Wolf
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