User:CompactStar/Ed12/5: Difference between revisions
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The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony{{clarify}}, and being the absolute widest range most generally used in popular songs{{citation needed}}. | The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony{{clarify}}, and being the absolute widest range most generally used in popular songs{{citation needed}}. | ||
One approach to ed12/5 tunings is to | One approach to ed12/5 tunings is to treat 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 a "macro-meantone"{{idiosyncratic}} as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note [[MOS]] in exactly the same families as flattone, just with a period of 12/5 instead of 2/1. | ||
== Individual pages for ED12/5s == | == Individual pages for ED12/5s == | ||
Revision as of 01:57, 25 April 2025
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 does not necessarily imply directly using this interval as an equivalence. Many, though not all, ed12/5 scales have a perceptually important false octave, with various degrees of accuracy.
The structural utility of 12/5 (or another minor tenth) is hinted by its being the base of so much common practice tonal harmony[clarification needed], and being the absolute widest range most generally used in popular songs[citation needed].
One approach to ed12/5 tunings is to treat 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 a "macro-meantone"[idiosyncratic term] as if you logarithmically stretch 2/1, 3/2, and 5/4 by 26%, you will get intervals very close to 12/5, 5/3, and 4/3 respectively. As a consequence, this temperament yields 5, 7, 12, 19, and 26 note MOS in exactly the same families as flattone, just with a period of 12/5 instead of 2/1.