Ed5/3: Difference between revisions

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== Properties ==

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 [[equivalence]] has not even been posed yet. The utility of 5:3, 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 [[Sensi|sensi]] 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.

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 [[equivalence]] has not even been posed yet. The utility of 5:3, 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 [[Sensi|sensi]] temperament or factoring into chord inversions. It is also one of the most consonant intervals in the range between 3/2 and 2/1. 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.

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.

==Individual pages for ED5/3s==

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 == Properties ==
-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 [[equivalence]] has not even been posed yet. The utility of 5:3, 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 [[Sensi|sensi]] 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.
+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 [[equivalence]] has not even been posed yet. The utility of 5:3, 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 [[Sensi|sensi]] temperament or factoring into chord inversions. It is also one of the most consonant intervals in the range between 3/2 and 2/1. 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.
+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.
 ==Individual pages for ED5/3s==