User:CompactStar/Ed12/5: Difference between revisions
CompactStar (talk | contribs) Created page with "The '''equal division of 12/5''' ('''ed12/5''') is a tuning obtained by dividing the classic minor tenth (12/5) into a number of equal steps. == Properties..." |
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== Properties == | == Properties == | ||
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 5 | 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 yields 5, 7, 12, 19, and 31 note MOS (coincidentally similar to meantone). | 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 yields 5, 7, 12, 19, and 31 note MOS (coincidentally similar to meantone). | ||
Revision as of 00:59, 23 May 2023
The equal division of 12/5 (ed12/5) is a tuning obtained by dividing the classic minor tenth (12/5) into a number of equal steps.
Properties
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 yields 5, 7, 12, 19, and 31 note MOS (coincidentally similar to meantone).