16ed5/3: Difference between revisions

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'''16ed5/3''' (or less accurately '''16edVI''') is the [[EdVI|equal division of the just major sixth]] into sixteen parts of 55.2724 [[cent|cents]] each, corresponding to 21.7106 [[edo]]. It is very closely related to the [[Escapade family|escapade temperament]].

'''16ed5/3''' (or less accurately '''16edVI''') is the [[EdVI|equal division of the just major sixth]] into sixteen parts of 55.2724 [[cent|cents]] each, corresponding to 21.7106 [[edo]]. It is very closely related to the [[Escapade family|escapade temperament]]. It is vaguely equivalent to [[22edo]].

It very accurately approximates a number of low complexity just intervals, such as: [[4/3]] (<1¢), [[5/4]] (<1¢), [[11/8]] (<2¢), [[11/10]] (<1¢), [[16/15]] (<2¢), and [[25/16]] (<2¢). It also approximates the [[3/2|just fifth]] and [[2/1|octave]] to within 17¢, making it a flexible non-octave scale. Notably, having a period of [[5/3]], the diatonic minor third ([[6/5]]) is the period-reduced diatonic octave. This means both are approximated identically (16¢ sharp).

== Intervals ==

16ed5/3 can be notated using steps 7 (~5/4) and 9 (~4/3) as generators, as these are accurate to within 0.6¢. The resulting scale is a heptatonic 2L 5s (similar to the octave repeating antidiatonic).

16ed5/3 can be notated using steps 7 (~5/4) and 9 (~4/3) as generators, as these are accurate to within 0.6¢. The resulting scale is a heptatonic 2L 5s (similar to the octave repeating antidiatonic). It can also be notated using the fifth-generated [[Blackcomb]] temperament.

{| class="wikitable center-all right-2"

! Degree

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! Mos-interval

! Diatonic interval

! ~~Notation~~

! 2L 5s<5/3> notation|- style="background: #eee"

|- style="background: #eee"

| '''0'''

| '''0.0000'''

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 {{Infobox ET}}
-'''16ed5/3''' (or less accurately '''16edVI''') is the [[EdVI|equal division of the just major sixth]] into sixteen parts of 55.2724 [[cent|cents]] each, corresponding to 21.7106 [[edo]]. It is very closely related to the [[Escapade family|escapade temperament]].
+'''16ed5/3''' (or less accurately '''16edVI''') is the [[EdVI|equal division of the just major sixth]] into sixteen parts of 55.2724 [[cent|cents]] each, corresponding to 21.7106 [[edo]]. It is very closely related to the [[Escapade family|escapade temperament]]. It is vaguely equivalent to [[22edo]].
 It very accurately approximates a number of low complexity just intervals, such as: [[4/3]] (<1¢), [[5/4]] (<1¢), [[11/8]] (<2¢), [[11/10]] (<1¢), [[16/15]] (<2¢), and [[25/16]] (<2¢). It also approximates the [[3/2|just fifth]] and [[2/1|octave]] to within 17¢, making it a flexible non-octave scale.  Notably, having a period of [[5/3]], the diatonic minor third ([[6/5]]) is the period-reduced diatonic octave. This means both are approximated identically (16¢ sharp).
 == Intervals ==
-ed5/3 can be notated using steps 7 (~5/4) and 9 (~4/3) as generators, as these are accurate to within 0.6¢. The resulting scale is a heptatonic 2L 5s (similar to the octave repeating antidiatonic).
+ed5/3 can be notated using steps 7 (~5/4) and 9 (~4/3) as generators, as these are accurate to within 0.6¢. The resulting scale is a heptatonic 2L 5s (similar to the octave repeating antidiatonic). It can also be notated using the fifth-generated [[Blackcomb]] temperament.
 {| class="wikitable center-all right-2"
 ! Degree
@@ Line 12: / Line 12: @@
 ! Mos-interval
 ! Diatonic interval
-! Notation
+! 2L 5s<5/3> notation|- style="background: #eee"
-|- style="background: #eee"
 | '''0'''
 | '''0.0000'''