User:CompactStar/Ed8/5: Difference between revisions

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'''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 minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice 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 does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/5 scales have a perceptually important [[Pseudo-octave|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~~-~~CTE tuning range~~.

One way to approach some ed8/5 tunings 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 scale]]s of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>.

[[CTE]] and near-CTE tunings of said temperament introduce pseudo-octaves, which may be considered a hindrance due to distracting from the 10:12:15:16 sonority, or it may be considered beneficial if one wants to combine that sonority with traditional octave-based harmony and melody.

== Specific examples ==

[[7ed8/5]] (includes link to music smaple)

[[Category:Equal-step tuning]]

[[Category:Ed8/5]]

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+{{Editable user page}}
 '''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 minor sixth) as a base though, is apparent by appearing in the famous "Neapolitan" sixth triad in common-practice 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 does not necessarily imply directly using this interval as an [[equivalence]]. Many, though not all, ed8/5 scales have a perceptually important [[Pseudo-octave|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-CTE tuning range.
+One way to approach some ed8/5 tunings 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 scale]]s of the families 1L 4s<8/5>, 1L 5s<8/5>, 6L 1s<8/5>, 6L 7s<8/5>, and 6L 13s<8/5>.
+[[CTE]] and near-CTE tunings of said temperament introduce pseudo-octaves, which may be considered a hindrance due to distracting from the 10:12:15:16 sonority, or it may be considered beneficial if one wants to combine that sonority with traditional octave-based harmony and melody.
+== Specific examples ==
+[[7ed8/5]] (includes link to music smaple)
 [[Category:Equal-step tuning]]
 [[Category:Ed8/5]]