9L 2s (3/1-equivalent): Difference between revisions
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{{Infobox MOS}} | {{Infobox MOS}} | ||
{{MOS intro|Other Names=sub-Arcturus}} | {{MOS intro|Other Names=sub-Arcturus}} | ||
This MOS family is the simplest tritave-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth. Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila continuum and the bottom of the syntonic continuum. | |||
This MOS family is the simplest [[tritave]]-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth. | |||
Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila [[continuum]] and the bottom of the syntonic continuum. | |||
== Modes == | |||
{{MOS modes}} | |||
== Intervals == | |||
{{MOS intervals}} | |||
== Scale tree == | == Scale tree == | ||
{{Scale tree|depth=6|Comments=21/13:Golden Sub-Arcturus is near here}} | {{Scale tree|depth=6|Comments=21/13:Golden Sub-Arcturus is near here}} | ||
{{todo|expand}} | |||
[[Category:Arcturus]] | [[Category:Arcturus]] | ||
Revision as of 02:26, 16 December 2024
| ↖ 8L 1s⟨3/1⟩ | ↑ 9L 1s⟨3/1⟩ | 10L 1s⟨3/1⟩ ↗ |
| ← 8L 2s⟨3/1⟩ | 9L 2s (3/1-equivalent) | 10L 2s⟨3/1⟩ → |
| ↙ 8L 3s⟨3/1⟩ | ↓ 9L 3s⟨3/1⟩ | 10L 3s⟨3/1⟩ ↘ |
┌╥╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
sLLLLsLLLLL
Generator size(edt)
Related MOS scales
Equal tunings(edt)
9L 2s⟨3/1⟩, also called sub-Arcturus, is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 9 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1037.4 ¢ to 1056.6 ¢, or from 845.3 ¢ to 864.5 ¢.
This MOS family is the simplest tritave-equivalent scale using an "ordinary" ~5:3 as a generator. Of course, it is on the extremely flat end of what is "ordinary", being the same size as a neutral sixth.
Coincidentally, its categorical name in this scale happens to be "sixth" also, just not in the "ordinary" diatonic sense of the name. Because this "sixth" is so flat, "sixths" in the range of propriety lead, in three steps, when tritave reduced, into the Mavila continuum and the bottom of the syntonic continuum.
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 10|0 | 1 | LLLLLsLLLLs |
| 9|1 | 7 | LLLLsLLLLLs |
| 8|2 | 2 | LLLLsLLLLsL |
| 7|3 | 8 | LLLsLLLLLsL |
| 6|4 | 3 | LLLsLLLLsLL |
| 5|5 | 9 | LLsLLLLLsLL |
| 4|6 | 4 | LLsLLLLsLLL |
| 3|7 | 10 | LsLLLLLsLLL |
| 2|8 | 5 | LsLLLLsLLLL |
| 1|9 | 11 | sLLLLLsLLLL |
| 0|10 | 6 | sLLLLsLLLLL |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0 ¢ |
| 1-mosstep | Minor 1-mosstep | m1ms | s | 0.0 ¢ to 172.9 ¢ |
| Major 1-mosstep | M1ms | L | 172.9 ¢ to 211.3 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 211.3 ¢ to 345.8 ¢ |
| Major 2-mosstep | M2ms | 2L | 345.8 ¢ to 422.7 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 422.7 ¢ to 518.7 ¢ |
| Major 3-mosstep | M3ms | 3L | 518.7 ¢ to 634.0 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 634.0 ¢ to 691.6 ¢ |
| Major 4-mosstep | M4ms | 4L | 691.6 ¢ to 845.3 ¢ | |
| 5-mosstep | Perfect 5-mosstep | P5ms | 4L + s | 845.3 ¢ to 864.5 ¢ |
| Augmented 5-mosstep | A5ms | 5L | 864.5 ¢ to 1056.6 ¢ | |
| 6-mosstep | Diminished 6-mosstep | d6ms | 4L + 2s | 845.3 ¢ to 1037.4 ¢ |
| Perfect 6-mosstep | P6ms | 5L + s | 1037.4 ¢ to 1056.6 ¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | 5L + 2s | 1056.6 ¢ to 1210.3 ¢ |
| Major 7-mosstep | M7ms | 6L + s | 1210.3 ¢ to 1268.0 ¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | 6L + 2s | 1268.0 ¢ to 1383.2 ¢ |
| Major 8-mosstep | M8ms | 7L + s | 1383.2 ¢ to 1479.3 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 1479.3 ¢ to 1556.1 ¢ |
| Major 9-mosstep | M9ms | 8L + s | 1556.1 ¢ to 1690.6 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 1690.6 ¢ to 1729.1 ¢ |
| Major 10-mosstep | M10ms | 9L + s | 1729.1 ¢ to 1902.0 ¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 9L + 2s | 1902.0 ¢ |