User:CompactStar/Ed12/5: Difference between revisions

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Division of 12/5 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 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, 19, and 31 note MOS in exactly the same families as meantone, just with a ~~different~~ period.

Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch 2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, 19, and 31 note MOS in exactly the same families as meantone, just with a period of 12/5 instead of 2/1.

== Individual pages for ED12/5s ==

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 Division of 12/5 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 12/5 (or another minor tenth) as a base though, is apparent by, beside being the base of so much common practice tonal harmony, and being the absolute widest range most generally used in popular songs. Many, though not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
-Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch  2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, 19, and 31 note MOS in exactly the same families as meantone, just with a different period.
+Incidentally, one way to treat 12/5 as an equivalence is the use of the 3:4:5 chord as the fundamental complete sonority in a very similar way to the 4:5:6 chord in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get to [[5/4]], here it takes 4 [[5/3]] to get [[4/3]] (tempering out the comma [[15625/15552]] in the 12/5.3.4 fractional subgroup). This temperament is literally a "macro-meantone" as if you logarithmically stretch  2/1, 3/2, and 5/4 by about 25-30%, you will get intervals of approximately 12/5, 5/3, and 4/3 respectively. As a consequence, thhis temperament yields 5, 7, 12, 19, and 31 note MOS in exactly the same families as meantone, just with a period of 12/5 instead of 2/1.
 == Individual pages for ED12/5s ==