Schillinger, Double Equal Temperament, and McLaren

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>Schillinger only claims that "the micro-units are the best
>averages for
>all differences between units of the 12th root of 2 and just intonation
>(natural scale)".

No, Schillinger also claims that his system can represent "mean
temperament," which must mean meantone temperament. This was both in
your original quote and in Brian McLaren's Xenharmonikon 17 article, "A
Short History of Microtonality in the 20th Century." But Schillinger is
incorrect. Meantone tuning, the tuning of choice for music from
1500-1700 and much music thereafter, is built upon consecutive perfect
fifths of 694.8 to 698.4 cents. 144tET ("double equal temperament")
contains no intervals between 691.7 and 700 cents, so cannot represent
meantone tuning. 288tET does have a 695.8-cent interval, so it can be
used to represent meantone tuning.

Although I'm probably one of very few people to have already read
McLaren's XH17 article, it does contain other factual inaccuracies, some
McLaren's own. For example, a positive tuning is one with perfect fifths
larger than 700 cents, not necessarily one with perfect fifths larger
than the just 3/2 (702 cents). However, the article is amazingly
comprehensive and I wish I had had access to all that information
earlier. Apparantly, Bosanquet studied 22-tET extensively, and Ogolevets
proclaimed it the future of music (along with 17-tET). The section of my
paper entitled "History of 22" now seems really underinformed. But my
chances of ever being able to get a hold of those writings seems very
small -- anyone know if McLaren actually had the primary sources on
hand?

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