11/9: Difference between revisions

In the 11-limit hexad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Many temperaments, including [[17edo]], [[24edo]], [[31edo]], [[41edo]], [[58edo]], [[72edo]], [[130edo]], [[202edo]], [[Gamelismic clan#Miracle|miracle]], [[Breedsmic temperaments#Harry|harry]], and [[Schismatic family#Sesquiquartififths|sesquart]], conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament [[Breed family#Jove, aka Wonder|jove]].