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}}.

One approach to ed12/5 tunings is to ~~tteat~~ 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.

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 ==

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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}}.
-One approach to ed12/5 tunings is to tteat 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.
+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 ==