Ed4/3: Difference between revisions

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<font style="font-size: 19.5px;">Division of a fourth (e. g. 4/3 or 15/11) into n equal parts</font>

Division of e. g. the 4:3 or the 15:11 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 4:3, 15:11 or another fourth as a base though, is apparent by being used at the base of so much Neo-~~Medievall~~ harmony. 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 4:3 or the 15:11 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 4:3, 15:11 or another fourth as a base though, is apparent by being used at the base of so much Neo-Medieval harmony. 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 4/3, 15/11, or 7/5 as an equivalence is the use of the 12:13:14:(16), 11:12:13:(15), or 10:11:12:(14) 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 eight 7/6, 13/11, or 6/5 to get to 13/12 or 12/11 (tempering out the comma 5764801/5750784, 815730721/808582500, or 42875/42768). So, doing this yields 13, 15, and 28 note MOS for ED(4/3)s; 11, 13, and 24 note MOS for ED(15/11)s or ED(7/5)s, the 24 note MOS of the two temperaments being mirror images of each other (13L 11s for ED(15/11)s vs 11L 13s for ED(7/5)s). While the notes are rather closer together, the scheme is uncannily similar to meantone.

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 <font style="font-size: 19.5px;">Division of a fourth (e. g. 4/3 or 15/11) into n equal parts</font>
-Division of e. g. the 4:3 or the 15:11 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 4:3, 15:11 or another fourth as a base though, is apparent by being used at the base of so much Neo-Medievall harmony. 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 4:3 or the 15:11 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 4:3, 15:11 or another fourth as a base though, is apparent by being used at the base of so much Neo-Medieval harmony. 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 4/3, 15/11, or 7/5 as an equivalence is the use of the 12:13:14:(16), 11:12:13:(15), or 10:11:12:(14) 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 eight 7/6, 13/11, or 6/5 to get to 13/12 or 12/11 (tempering out the comma 5764801/5750784, 815730721/808582500, or 42875/42768). So, doing this yields 13, 15, and 28 note MOS for ED(4/3)s; 11, 13, and 24 note MOS for ED(15/11)s or ED(7/5)s, the 24 note MOS of the two temperaments being mirror images of each other (13L 11s for ED(15/11)s vs 11L 13s for ED(7/5)s). While the notes are rather closer together, the scheme is uncannily similar to meantone.