source file: m1502.txt Date: Wed, 12 Aug 1998 16:55:29 -0500 (CDT) Subject: Diameter for JI? (was Re: Nano-temperament) From: Paul Hahn On Wed, 12 Aug 1998, Paul Hahn wrote: > Or, if you don't like that example, how 'bout a JI-ist who wanted to > tune up Ellis' duodene, which is a 5-limit scale with a diameter of 5. ^^^^^^^^ "Hold it, pH" I hear some of you saying, "I thought you'd only defined 'diameter' in terms of ETs. What's the diameter of a JI scale mean?" Well, it's not all that different. It still means the number of primary intervals (within the particular limit) it takes to get between the two pitches within the scale that are farthest from each other. In this case, to get from 16/15 to 45/32 takes five steps: 5/3 --3-- 5/4 --4-- 15/8 --5-- 45/32 / \ / \ / \ / 2 \ 3 \ 4 \ 5 / \ / \ / \ / 4/3 --2-- 1/1 --3-- 3/2 --4-- 9/8 / \ / \ / \ / 1 \ 2 \ 3 \ 4 / \ / \ / \ / 16/15 --1-- 8/5 --2-- 6/5 --3-- 9/5 You can substitute a 36/25 tritone for the 45/32 without reducing the number of consonant triads, and reduce the diameter from 5 to 4, but it's not as symmetrical. --pH http://library.wustl.edu/~manynote O /\ "Churchill? Can he run a hundred balls?" -\-\-- o NOTE: dehyphenate node to remove spamblock. <*>