Ed5/3: Difference between revisions

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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.

==Individual pages for EDVIs==

'''<big>Equal Divisions of the Just Major Sixth (5/3)</big>'''

* 7 - [[7ed5/3|Seventh root of 7/5]]

* 9 - [[9ed5/3|Ninth root of 7/5]]

* 16 - [[16ed5/3|Sixteenth root of 7/5]]

[[Category:Equal-step tuning]]

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 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.
+==Individual pages for EDVIs==
+'''<big>Equal Divisions of the Just Major Sixth (5/3)</big>'''
+* 7 - [[7ed5/3|Seventh root of 7/5]]
+* 9 - [[9ed5/3|Ninth root of 7/5]]
+* 16 - [[16ed5/3|Sixteenth root of 7/5]]
 [[Category:Equal-step tuning]]