source file: m1539.txt Date: Tue, 29 Sep 1998 15:56:50 -0400 Subject: RE: elevens From: "Paul H. Erlich" >It appears there has been discussion before my subscription to the list >began concerning 11/n and n/11 consonances. I can see how a >11/6:1/1 and a 20/11:1/1 could be considered consonant, but how the >11/8 and its like? Interestingly, 11/8 is the _only_ ratio of 11 that Patrick Ozzard-Low considers a primary consonant interval in his recent giant paper. But the main reference on 11 is Partch, who considered all ratios of odd numbers up to 11, plus octave inversions and extensions of these intervals, consonant. Partch's music can be said to conform to the 11-limit under both definitions of the term "limit": the odd limit is 11 because all ratios involving odd numbers higher than 11 (including 15/8) are considered dissonant by Partch, and the prime limit is 11 because even the dissonant intervals are ratios of numbers with no prime factors above 11. Personally, I find 11-limit intervals hard to digest unless they are combind into an otonal chord like 4:5:6:7:9:11. I can even sing the 11 over a 4:5:6 major triad. However, Utonal 11-limit harmony always sounds dissonant to me, despite Partch and Johnston's theories.