Skip to main content
Get your Wikispaces Classroom now:
the easiest way to manage your class.
xenharmonic (microtonal wiki)
Pages and Files
XA Facebook Group
XA IRC Chat
Lists and Galleries
Backing up this wiki
Division of a sixth (e. g. 5/3 or 11/7) into n equal parts
Division of e. g. the 5:3 or the 11:7 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of
has not even been posed yet. The utility of 5:3 or 11:7 or another sixth as a base though, is apparent by being named directly in the standard definition of such as the octave based
temperament or factoring into chord inversions. Many, though not all, of these scales have a pseudo (false) octave, with various degrees of accuracy, but which context(s), if any, it is very perceptually important in is as yet an open question.
Incidentally, one way to treat 5/3 or 11/7 as an equivalence is the use of the 6:7:8:(10) or 7:8:9:(11) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes four 4/3 to get to 8/7 (tempering out the comma 225/224) or four 9/7 to get to 9/8 (tempering out the comma 5929/5832). So, doing this yields 7, 9, and 16 note MOS either way, the 16 note MOS of the two temperaments being mirror images of each other (7L 9s for ed(5/3)s vs 9L 7s for ed(11/7)s). While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it (even better than for edfs as the generator it uses is an excellent fit for heptatonic MOS) if it hasn't been named yet.
help on how to format text
Contributions to http://xenharmonic.wikispaces.com/ are licensed under a
Creative Commons Attribution Share-Alike Non-Commercial 3.0 License
Portions not contributed by visitors are Copyright 2017 Tangient LLC
TES: The largest network of teachers in the world
Turn off "Getting Started"