Diasem: Difference between revisions
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Diasem is a max-variety-3 scale equivalent to semaphore[9] with two small steps made larger and the other two made smaller. |
+cats, formatting. BTW: interesting way for graphical representation |
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'''Diasem''' is a [[ | '''Diasem''' is a [[Maximum variety|max-variety-3]] scale 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," and is also a pun based on the [[diesis]], a defining step size in the scale. | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Comparison with semaphore and meantone in 62edo | |+ Comparison with semaphore and meantone in 62edo | ||
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| Meantone || 5L2s || 10\62, 6\62 || ├─────────┼─────┼─────────╫─────────┼─────┼─────────╫─────────┤ | | Meantone || 5L2s || 10\62, 6\62 || ├─────────┼─────┼─────────╫─────────┼─────┼─────────╫─────────┤ | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ Common Diasem Tunings | |+ Common Diasem Tunings | ||
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| 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 | | 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 | ||
|} | |} | ||
[[Category:Scale]] | |||
[[Category:26edo]] | |||
[[Category:31edo]] | |||
Revision as of 12:02, 28 December 2020
Diasem is a max-variety-3 scale 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," and is also a pun based on the diesis, a defining step size in the scale.
| Name | Structure | Step Sizes | Graphical Representation |
|---|---|---|---|
| Semaphore | 5L4s | 10\62, 3\62 | ├─────────┼──┼─────────┼──┼─────────┼──┼─────────┼──┼─────────┤ |
| Diasem | 5L2m2s | 10\62, 4\62, 2\62 | ├─────────┼───┼─────────┼─┼─────────┼───┼─────────┼─┼─────────┤ |
| Meantone | 5L2s | 10\62, 6\62 | ├─────────┼─────┼─────────╫─────────┼─────┼─────────╫─────────┤ |
| Tuning | L:m:s | Good Just Approximations | Degrees | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 26edo | 4:2:1 | Neogothic thirds | 0.000 | 184.615 | 276.923 | 461.538 | 507.692 | 692.308 | 784.615 | 969.231 | 1015.385 | 1200.000 |
| 31edo | 5:2:1 | Pental thirds and 7/5 | 0.000 | 193.548 | 270.968 | 464.516 | 503.226 | 696.774 | 774.194 | 967.742 | 1006.452 | 1200.000 |
| 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 |