Diasem: Difference between revisions

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'''Diasem''' is a [[Maximum variety|max-variety-3]] ~~[[MODMOS_Scales|MODMOS]]~~ that is equivalent to semaphore[9] with two of the small steps made larger and the other two made smaller. This results in ~~near-just septimal intervals and~~ better melodic properties than the meantone scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semaphore" since it the way it tempers the [[64/63]] is intermediate between [[superpyth]] and [[semaphore]]; it is also a pun based on the [[diesis]], a defining step size in the scale.

'''Diasem''' is a [[Maximum variety|max-variety-3]] JI scale that is equivalent to semaphore[9] with two of the small steps made larger and the other two made smaller. This results in better melodic properties than the meantone scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semaphore" since it the way it tempers the [[64/63]] is intermediate between [[superpyth]] and [[semaphore]]; it is also a pun based on the [[diesis]], a defining step size in the scale.

{| class="wikitable"

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|-

! Tuning !! L:m:s !! Good Just Approximations !! Degrees !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9

|-

| || || || 1/1 || 9/8 || 7/6 || 21/16 || 4/3 || 3/2 || 14/9 || 7/4 || 16/9 || 2/1

|-

| JI || 7.479:2.309:1 || Just 7/6, 8/7, and 3/2 || 0.000 || 203.910 || 266.871 || 470.781 || 498.045 || 701.955 || 764.916 || 968.826 || 996.090 || 1200.000

|-

| 26edo || 4:2:1 || Neogothic thirds and 8/7 || 0.000 || 184.615 || 276.923 || 461.538 || 507.692 || 692.308 || 784.615 || 969.231 || 1015.385 || 1200.000

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|-

| 36edo || 6:2:1 || Septimal thirds and 3/2 || 0.000 || 200.000 || 266.667 || 466.667 || 500.000 || 700.000 || 766.667 || 966.667 || 1000.000 || 1200.000

|-

~~| JI || 7.479:2.309:1 || Just 7/6, 8/7, and 3/2 || 0.000 || 203.910 || 266.871 || 470.781 || 498.045 || 701.955 || 764.916 || 968.826 || 996.090 || 1200.000~~

|-

~~| || || || 1/1 || 9/8 || 7/6 || 21/16 || 4/3 || 3/2 || 14/9 || 7/4 || 16/9 || 2/1~~

|}

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-'''Diasem''' is a [[Maximum variety|max-variety-3]] [[MODMOS_Scales|MODMOS]] that is equivalent to semaphore[9] with two of the small steps made larger and the other two made smaller. This results in near-just septimal intervals and better melodic properties than the meantone scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semaphore" since it the way it tempers the [[64/63]] is intermediate between [[superpyth]] and [[semaphore]]; it is also a pun based on the [[diesis]], a defining step size in the scale.
+'''Diasem''' is a [[Maximum variety|max-variety-3]] JI scale that is equivalent to semaphore[9] with two of the small steps made larger and the other two made smaller. This results in better melodic properties than the meantone scales of [[26edo]] and [[31edo]], which both support it. The scale can be generated by an alternating chain of subminor thirds and supermajor seconds. The name "diasem" is a portmanteau of "diatonic" and "semaphore" since it the way it tempers the [[64/63]] is intermediate between [[superpyth]] and [[semaphore]]; it is also a pun based on the [[diesis]], a defining step size in the scale.
 {| class="wikitable"
@@ Line 17: / Line 17: @@
 |-
 ! Tuning !! L:m:s !! Good Just Approximations !! Degrees !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
+|-
+| || || || 1/1 || 9/8 || 7/6 || 21/16 || 4/3 || 3/2 || 14/9 || 7/4 || 16/9 || 2/1
+|-
+| JI || 7.479:2.309:1 || Just 7/6, 8/7, and 3/2 || 0.000 || 203.910 || 266.871 || 470.781 || 498.045 || 701.955 || 764.916 || 968.826 || 996.090 || 1200.000
 |-
 | 26edo || 4:2:1 || Neogothic thirds and 8/7 || 0.000 || 184.615 || 276.923 || 461.538 || 507.692 || 692.308 || 784.615 || 969.231 || 1015.385 || 1200.000
@@ Line 23: / Line 27: @@
 |-
 | 36edo || 6:2:1 || Septimal thirds and 3/2 || 0.000 || 200.000 || 266.667 || 466.667 || 500.000 || 700.000 || 766.667 || 966.667 || 1000.000 || 1200.000
-|-
-| JI || 7.479:2.309:1 || Just 7/6, 8/7, and 3/2 || 0.000 || 203.910 || 266.871 || 470.781 || 498.045 || 701.955 || 764.916 || 968.826 || 996.090 || 1200.000
-|-
-| || || || 1/1 || 9/8 || 7/6 || 21/16 || 4/3 || 3/2 || 14/9 || 7/4 || 16/9 || 2/1
 |}