User:CompactStar/Ed12/5
|
This user page is editable by any wiki editor.
As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages. However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits). |
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.