Omnidiatonic: Difference between revisions

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-'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety|max-variety-3]] scale with the step pattern 2L 3m 2s. Omnidiatonic is a chiral scale with LmsmLsm and LmsLmsm variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar|CompactStar]] and the name "interdia" was given by [[User:Xenllium|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] andiatonic scale. As  The name "archylino" was given by [[User:AthiTrydhen|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (msLmsmL).
+'''Omnidiatonic''' (also known as '''interdia''' and '''archylino''') is a 7-note [[Maximum variety|maximum-variety-3]] scale with the [[step signature]] 2L 3M 2s. Omnidiatonic is a [[chiral]] scale with LMsMLsM and LMsLMsM variants. [[14edo]] is the first equal division that supports omnidiatonic. The name "omnidiatonic" was given by [[User:CompactStar|CompactStar]] and the name "interdia" was given by [[User:Xenllium|Xenllium]], both of which refer to this scale being intermediate between the [[5L 2s]] diatonic scale and the [[2L 5s]] antidiatonic scale. The name "archylino" was given by [[User:AthiTrydhen|Praveen Venkataramana]], which refers to intervals separated by 64/63, the Archytas comma, being mapped to the same number of scale steps of 2.3.7 JI archylino 1/1 9/8 7/6 4/3 3/2 14/9 7/4 2/1 (MsLMsML). In terms of Greek scales, this can be seen as Archytas' diatonic.
-Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, m represents 9/8, and s represents 28/27.
+Omnidiatonic can be tuned as a 7-limit JI scale or a tempered version thereof, where L represents 8/7, M represents 9/8, and s represents 28/27.
+== Modes ==
+Omnidiatonic has 14 modes total, with 7 LH and 7 RH modes.
+{| class="wikitable"
+|+Omnidiatonic modes
+!Left handed
+!Right handed
+|-
+|LMsMLsM
+|LMsLMsM
+|-
+|LsMLMsM
+|LMsMLMs
+|-
+|MLMsMLs
+|MLMsLMs
+|-
+|MLsMLMs
+|MsLMsML
+|-
+|MsMLsML
+|MsMLMsL
+|-
+|sMLMsML
+|sLMsMLM
+|-
+|sMLsMLM
+|sMLMsLM
+|}
 == Tunings ==
+{| class="wikitable"
+|+Tuning range of omnidiatonic
+!
+! Tuning range (in [[octave]]s)
+|-
+! Outer generator <br>(''G''<sub>1</sub> = L + 2M + s)
+| <math>\displaystyle \frac{1}{2} \lt G_\text{1} \lt \frac{3}{5}</math>
+|-
+! RH inner generator <br>(''G''<sub>2R</sub> = M + s)
+| <math>\displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 4 G_\text{1} - 2 \text{ for }\frac{1}{2} \lt G_\text{1} \le \frac{4}{7}</math> <br><math>\displaystyle 2 G_\text{1} - 1 \lt G_\text{2R} \lt 2 - 3 G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5}</math>
+|-
+! LH inner generator <br>(''G''<sub>2L</sub> = L + M)
+| <math>\displaystyle 2 - 3 G_\text{1} \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for } \frac{1}{2} \lt G_\text{1} \le \frac{4}{7}</math> <br><math>\displaystyle 4 G_\text{1} - 2 \lt G_\text{2L} \lt 1 - G_\text{1} \text{ for }\frac{4}{7} \le G_\text{1} \lt \frac{3}{5}</math>
+|-
+! Large step <br>(L = 1 - ''G''<sub>1</sub> - ''G''<sub>2R</sub>)
+| <math>\displaystyle \frac{1}{7} \lt L \lt \frac{1}{2}</math>
+|-
+! Middle step <br>(M = 2''G''<sub>1</sub> - 1)
+| <math>\displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt L \text{ for } \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle \frac{1}{5} (1 - 2 L) \lt M \lt \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2}</math>
+|-
+! Small step <br>(s = 1 - ''G''<sub>1</sub> - ''G''<sub>2L</sub>)
+| <math>\displaystyle \frac{1}{2} (1 - 5 L) \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} \lt L \le \frac{1}{5}</math> <br><math>\displaystyle 0 \lt s \lt \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} \le L \lt \frac{1}{2}</math>
+|}
 {|class="wikitable"
 |-
 !Tuning
 !L
-!m
+!M
 !s
 !Comments
@@ Line 41: / Line 94: @@
 |2
 |1
-|Also has antidiatonic (but non-Mavila) MOS
+|
 |-
 |rowspan="2"|[[21edo]]
@@ Line 52: / Line 105: @@
 |3
 |1
+|
+|-
+|[[22edo]]
+|7
+|2
+|1
+|Also has diatonic MOS
+|-
+|[[23edo]]
+|5
+|3
+|2
 |
 |}
+== See also ==
+* [[Nicetone]] – sister 3L 2M 2s scale
+* [[Antinicetone]] – sister 2L 2M 3s scale
+* [[5L 2s]] – LM-equalized version of omnidiatonic
+** [[5L 2s Muddles]] – other diatonic muddles
+* [[2L 5s]] – MS-equalized version of omnidiatonic
+* [[2L 3s]] – collapsed version of omnidiatonic
 [[Category:Rank-3 scales]]
+[[Category:7-tone scales]]
+[[Category:GO scales]]