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.

~~Since a~~ 4:5:6 ~~triad can be fit inside~~ 5/3, ~~traditional~~ 4:5:6~~-based harmony can also be used. In this case~~, ~~[[5ed5/3]] is a good option as it contains a neutral third~~ and ~~a close approximation to a perfect fifth which allows for neutral triads to be built~~.

If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, tempering out the comma 250/243. This yields MOS scales of 4, 5, 6, 11, and 17 notes.

==Individual pages for ED5/3s==

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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.
-Since a 4:5:6 triad can be fit inside 5/3, traditional 4:5:6-based harmony can also be used. In this case, [[5ed5/3]] is a good option as it contains a neutral third and a close approximation to a perfect fifth which allows for neutral triads to be built.
+If we instead opt to continue using 4:5:6 as the fundamental sonority, then it will take three 3/2 to get to 5/4, tempering out the comma 250/243. This yields MOS scales of 4, 5, 6, 11, and 17 notes.
 ==Individual pages for ED5/3s==