User:CompactStar/Ed8/5: Difference between revisions
CompactStar (talk | contribs) No edit summary |
CompactStar (talk | contribs) No edit summary |
||
| Line 3: | Line 3: | ||
Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by being important in modern tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by being important in modern tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy. | ||
Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves | Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in [[meantone]]. Whereas in meantone it takes 4 [[3/2]] to get [[5/4]], here it takes 4 3/2 to get to [[6/5]], which creates a [[rank-2 temperament]] tempering out the comma [[16875/16384]]. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-optimal tuning range. | ||
Revision as of 08:19, 13 March 2023
Ed8/5 is division of the just minor sixth (8/5) into n parts.
Division of 8/5 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of equivalence is still in its infancy. The utility of 8/5 (or another sixth) as a base though, is apparent by being important in modern tonal harmony and factoring into chord inversions. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
Incidentally, one way to treat 8/5 as an equivalence is the use of the classic minor triad 10:12:15:(16) as the fundamental complete sonority in a very similar way to the classic major triad 4:5:6:(8) in meantone. Whereas in meantone it takes 4 3/2 to get 5/4, here it takes 4 3/2 to get to 6/5, which creates a rank-2 temperament tempering out the comma 16875/16384. This temperament yields MOS scales of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>. However, this temperament can sometimes result in pseudo-octaves particularly in near-optimal tuning range.