My approach was not made known 6 years ago to the piano community, but published already 21 years ago in a euro piano article from 1988, as Stopper temperament, where i published this method along with the usage of a twelfth spanner tool and the discovery of the natural form of the fifth circle which is in fact a nineteen octaves and twelve twelfths circle. This article has been published in 5 languages . (German, english, italian, french and danish.) Gary Schulze´s article is not an introduction of a general P12 tuning approach. He was rather trying to compensate for inharmonicity to make intervals like double octaves, twelfths, fifhts and triple octaves as pure as possible. In his article he is favoring a 31th root of six equal temperament to achive this inharmonicity compensation, what is a different thing from a general pure twelfth tuning world view. Bernhard Stopper Am 27.04.2009 um 12:39 schrieb Richard Brekne: > Seriously tho... there is a good deal written actually now about > P-12ths. I'd suggest starting with Gary's article from 1982. It > contains some very fine observations that you wont find anywhere > else. Hunting through the archives can be time consuming... but > there are some good tidbits there. Stopper made himself known to us > about 6 years back and has a well pondered out specific system and > analysis of P-12ths in classic interval fraction form. I think he > removed that paper from his website but if he will share it with you > it is also a good read. >
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