@@ Line 1: / Line 1: @@
-'''16ED5/3''' 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 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 just fifth and octave to within 20¢, making it a flexible non-octave scale.
+== 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).
+{| class="wikitable"
+!Degree
+!Cents
+!Approximate intervals
+!Mos-interval
+!Diatonic interval
+!Notation
+|-
+|'''0'''
+|'''0'''
+|'''1'''
+|'''unison'''
+|'''unison'''
+|'''A'''
+|-
+|1
+|55.2724
+|31/30, 33/32
+|aug unison
+|quatertone
+|A#
+|-
+|2
+|110.5448
+|16/15
+|min mos2nd
+|minor second
+|Bb
+|-
+|3
+|165.8173
+|11/10
+|maj mos2nd
+|neutral second
+|B
+|-
+|4
+|221.0897
+|8/7, 17/15
+|min mos3rd
+|major second
+|Cb
+|-
+|5
+|276.3621
+|7/6, 20/17, 75/64
+|maj mos3rd
+|subminor third
+|C
+|-
+|6
+|331.6345
+|6/5, 17/14
+|dim mos4th
+|minor third
+|Db
+|-
+|''7''
+|''386.9069''
+|''5/4''
+|''perf mos4th''
+|major third
+|D
+|-
+|8
+|442.1794
+|9/7, 22/17
+|aug mos4th
+|supermajor third
+|D#
+|-
+|''9''
+|''497.4517''
+|4/3
+|''perf mos5th''
+|just fourth
+|E
+|-
+|10
+|552.7242
+|11/8
+|aug mos5th
+|wide fourth
+|E#
+|-
+|11
+|607.9966
+|10/7
+|min mos6th
+|large tritone
+|Fb
+|-
+|12
+|663.269
+|22/15, 72/49
+|maj mos6th
+|narrow fifth
+|F
+|-
+|13
+|718.54145
+|3/2, 50/33
+|min mos7th
+|acute fifth
+|F#
+|-
+|14
+|773.8129
+|25/16
+|maj mos7th
+|subminor sixth
+|G
+|-
+|15
+|829.0863
+|8/5, 13/8
+|dim mos8ave
+|minor sixth
+|G#
+|-
+|'''16'''
+|'''884.3587'''
+|'''5/3'''
+|'''mosoctave'''
+|'''major sixth'''
+|'''A'''
+|-
+|17
+|939.6311
+|12/7, 19/11
+|aug mos8ave
+|supermajor sixth
+|A#
+|-
+|18
+|994.9035
+|16/9
+|min mos9th
+|minor seventh
+|Bb
+|-
+|19
+|1050.1760
+|11/6
+|maj mos9th
+|neutral seventh
+|B
+|-
+|20
+|1105.4484
+|17/9, 40/21
+|min mos10th
+|major seventh
+|Cb
+|-
+|21
+|1160.7208
+|35/18, 43/22
+|maj mos10th
+|narrow octave
+|C
+|-
+|22
+|1215.9932
+|2/1
+|dim mos11th
+|octave
+|C#
+|}
+These intervals are close to a few other related non-octave scales:
 {| class="wikitable"
 |+
@@ Line 7: / Line 181: @@
 !ed5/3
 ![[43ed4]]
-!ed16/21
+!ed16\21
 |-
 |1
@@ Line 104: / Line 278: @@
 |893.0233
 |914.2857
+|}
+== MOS Scales ==
+edVI supports the same [[MOS scale|MOS scales]] as [[16edo]], as such it contains the following scales:
+{| class="wikitable"
+!Periods
+per octave
+!Generator
+!Pattern
+|-
+|1
+|1\16
+|1L ns (pathological)
+|-
+|1
+|3\16
+|1L 4s, 5L 1s
+|-
+|1
+|5\16
+|3L 4s, 3L 7s
+|-
+|1
+|7\16
+|2L 5s, 7L 2s
+|-
+|2
+|1\16
+|2L 8s, 2L 10s, 2L 12s
+|-
+|2
+|3\16
+|4L 2s, 6L 4s
+|-
+|4
+|1\16
+|4L 4s, 4L 8s
+|}
+For the 2L 5s scale, the genchain is this:
+{| class="wikitable"
+|B#
+|F#
+|C#
+|G#
+|D#
+|A#
+|E#
+|B
+|F
+|C
+|G
+|D
+|A
+|E
+|Bb
+|Fb
+|Cb
+|Gb
+|Db
+|Ab
+|Eb
+|Bbb
+|Fbb
+|Cbb
+|Gbb
+|-
+|A2
+|A6
+|A3
+|A7
+|A5
+|A1
+|A4
+|M2
+|M6
+|M3
+|M7
+|P5
+|P1
+|P4
+|m2
+|m6
+|m3
+|m7
+|d5
+|d1
+|d4
+|d2
+|d6
+|d3
+|d7
 |}
 [[Category:EdVI]]
 [[Category:Nonoctave]]

16ed5/3: Difference between revisions