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]] 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~~).

'''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).

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 ==

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!Right handed

|-

|~~LmsmLsm~~

|LMsMLsM

|~~LmsLmsm~~

|LMsLMsM

|-

|~~LsmLmsm~~

|LsMLMsM

|~~LmsmLms~~

|LMsMLMs

|-

|~~mLmsmLs~~

|MLMsMLs

|~~mLmsLms~~

|MLMsLMs

|-

|~~mLsmLms~~

|MLsMLMs

|~~msLmsmL~~

|MsLMsML

|-

|~~msmLsmL~~

|MsMLsML

|~~msmLmsL~~

|MsMLMsL

|-

|~~smLmsmL~~

|sMLMsML

|~~sLmsmLm~~

|sLMsMLM

|-

|~~smLsmLm~~

|sMLsMLM

|~~smLmsLm~~

|sMLMsLM

|}

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! Tuning range (in [[octave]]s)

|-

! Outer generator (''G''1 = L + 2m + s)

! Outer generator (''G''1 = L + 2M + s)

| <math>\displaystyle \frac{1}{2} < G_\text{1} < \frac{3}{5}</math>

|-

! RH inner generator (''G''2R = m + s)

! RH inner generator (''G''2R = M + s)

| <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 4 G_\text{1} - 2 \text{ for }\frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <math>\displaystyle 2 G_\text{1} - 1 < G_\text{2R} < 2 - 3 G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>

|-

! LH inner generator (''G''2L = L + m)

! LH inner generator (''G''2L = L + M)

| <math>\displaystyle 2 - 3 G_\text{1} < G_\text{2L} < 1 - G_\text{1} \text{ for } \frac{1}{2} < G_\text{1} ≤ \frac{4}{7}</math> <math>\displaystyle 4 G_\text{1} - 2 < G_\text{2L} < 1 - G_\text{1} \text{ for }\frac{4}{7} ≤ G_\text{1} < \frac{3}{5}</math>

|-

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| <math>\displaystyle \frac{1}{7} < L < \frac{1}{2}</math>

|-

! Middle step (m = 2''G''1 - 1)

! Middle step (M = 2''G''1 - 1)

| <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < L \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <math>\displaystyle \frac{1}{5} (1 - 2 L) < M < \frac{1}{3} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>

|-

! Small step (s = 1 - ''G''1 - ''G''2L)

| <math>\displaystyle \frac{1}{2} (1 - 5 L) < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <math>\displaystyle 0 < S < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>

| <math>\displaystyle \frac{1}{2} (1 - 5 L) < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{7} < L ≤ \frac{1}{5}</math> <math>\displaystyle 0 < s < \frac{1}{5} (1 - 2 L) \text{ for } \frac{1}{5} ≤ L < \frac{1}{2}</math>

|}

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!Tuning

!L

!m

!M

!s

!Comments

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== See also ==

* [[Nicetone]] – sister 3L 2m 2s scale

* [[Nicetone]] – sister 3L 2M 2s scale

* [[Antinicetone]] – sister 2L 2m 3s scale

* [[Antinicetone]] – sister 2L 2M 3s scale

* [[5L 2s]] – LM-equalized version of omnidiatonic

** [[5L 2s Muddles]] – other diatonic muddles

@@ Line 1: / Line 1: @@
-'''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]] 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).
+'''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).
-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 ==
@@ Line 11: / Line 11: @@
 !Right handed
 |-
-|LmsmLsm
+|LMsMLsM
-|LmsLmsm
+|LMsLMsM
 |-
-|LsmLmsm
+|LsMLMsM
-|LmsmLms
+|LMsMLMs
 |-
-|mLmsmLs
+|MLMsMLs
-|mLmsLms
+|MLMsLMs
 |-
-|mLsmLms
+|MLsMLMs
-|msLmsmL
+|MsLMsML
 |-
-|msmLsmL
+|MsMLsML
-|msmLmsL
+|MsMLMsL
 |-
-|smLmsmL
+|sMLMsML
-|sLmsmLm
+|sLMsMLM
 |-
-|smLsmLm
+|sMLsMLM
-|smLmsLm
+|sMLMsLM
 |}
@@ Line 39: / Line 39: @@
 ! Tuning range (in [[octave]]s)
 |-
-! Outer generator <br>(''G''<sub>1</sub> = L + 2m + 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)
+! 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)
+! 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>
 |-
@@ Line 51: / Line 51: @@
 | <math>\displaystyle \frac{1}{7} &lt; L &lt; \frac{1}{2}</math>
 |-
-! Middle step <br>(m = 2''G''<sub>1</sub> - 1)
+! 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>
+| <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>
 |}
@@ Line 62: / Line 62: @@
 !Tuning
 !L
-!m
+!M
 !s
 !Comments
@@ Line 121: / Line 121: @@
 == See also ==
-* [[Nicetone]] – sister 3L 2m 2s scale
+* [[Nicetone]] – sister 3L 2M 2s scale
-* [[Antinicetone]] – sister 2L 2m 3s scale
+* [[Antinicetone]] – sister 2L 2M 3s scale
 * [[5L 2s]] – LM-equalized version of omnidiatonic
 ** [[5L 2s Muddles]] – other diatonic muddles