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{{MOS intro}}
{{MOS intro}}
There are two notable low-harmonic-entropy scales with this [[MOS scale|MOS]] pattern. The first is [[tetracot]], in which four generators make a 3/2. The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "luna", "hemithird", and "hemiwürschmidt" all have 6-note MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].
 
There are two notable low-harmonic-entropy scales with this [[MOS scale|MOS]] pattern. The first is [[tetracot]], in which four [[generator]]s make a [[3/2]].  
 
The second is a scale in which two generators make a 5/4, which could be referred to by various names. The temperaments "[[luna]]", "[[hemithird]]", and "[[hemiwürschmidt]]" all have [[hexatonic|6-note]] MOSes that are very similar. But perhaps it is best known as [[roulette6]], the six note haplitonic scale for the roulette [[Chromatic pair]].


This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is larger than the others.
This scale can be seen as the equal-tempered whole-tone scale ([[6edo]]), but with one "whole tone" that is larger than the others.


Other scales include very improper (incomplete) versions of porcupine, negri, etc.
Other scales include very improper (incomplete) versions of [[porcupine]], [[negri]], etc.
 
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}


== Modes ==
=== Generator chain ===
* 5|0 Lsssss
{{MOS genchain}}
* 4|1 sLssss
 
* 3|2 ssLsss
=== Modes ===
* 2|3 sssLss
{{MOS mode degrees}}
* 1|4 ssssLs
* 0|5 sssssL


== Scales ==
== Scales ==
=== Scale list ===
* [[Roulette6]]
* [[Roulette6]]
* [[Tutone6]]
* [[Tutone6]]
Line 30: Line 38:
* [[Glacial6]]
* [[Glacial6]]


== Scale tree ==
=== Scale tree ===
Generator ranges:
{{MOS tuning spectrum
* Chroma-positive generator: 1000 cents (5\6) to 1200 cents (1\1)
| 6/5 = [[Luna]]/[[hemithirds]]/[[hemiwürschmidt]]<br />[[Didacus]]/[[roulette]]<br />[[Isra]]/[[tutone]]/[[leantone]]
* Chroma-negative generator: 0 cents (0\1) to 200 cents (1\6)
| 5/4 = Isra/leantone
 
| 9/7 = Isra/deutone
{| class="wikitable center-all"
| 4/3 = [[Spell]]
! colspan="6" rowspan="2" | Generator <br><small>(Chroma-positive)</small>
| 3/2 = [[Glacial]]
! colspan="2" | Cents
| 13/8 = Wilson Golden 2 (1018.6773{{c}})
! rowspan="2" | L
| 9/5 = [[Tetracot]]
! rowspan="2" | s
| 7/3 = [[Porcupine]] (incomplete)
! rowspan="2" | L/s
| 12/5 = Porcupine/[[porcupinefish]]
! rowspan="2" | Comments
| 13/5 = Wilson Golden 1 (1042.4790{{c}})
|-
| 11/4 = [[Nusecond]]
! <small>Chroma-positive</small>
| 7/2 = [[Progression]] (incomplete)
! <small>Chroma-negative</small>
| 9/2 = [[Negri]] (incomplete)
|-
| 5/1 = [[Miracle]] (incomplete)
| 5\6 || || || || || || 1000.000 || 200.000 || 1 || 1 || 1.000 ||
| 6/1 = [[Passion]] (incomplete) ↓, [[ripple]] (incomplete) ↓
|-
}}
| || || || || || 26\31 || 1006.452 || 193.548 || 6 || 5 || 1.200 || [[Luna]]/[[hemithirds]]/[[hemiwürschmidt]], [[didacus]]/[[roulette]], [[isra]]/[[tutone]]/[[leantone]]
|-
| || || || || 21\25 || || 1008.000 || 192.000 || 5 || 4 || 1.250 || Isra/[[leantone]]
|-
| || || || || || 37\44 || 1009.091 || 190.909 || 9 || 7 || 1.286 || Isra/[[deutone]]
|-
| || || || 16\19 || || || 1010.526 || 189.474 || 4 || 3 || 1.333 || [[Spell]]
|-
| || || || || || 43\51 || 1011.765 || 188.235 || 11 || 8 || 1.375 ||
|-
| || || || || 27\32 || || 1012.500 || 187.500 || 7 || 5 || 1.400 ||
|-
| || || || || || 38\45 || 1013.333 || 186.667 || 10 || 7 || 1.429 ||
|-
| || || 11\13 || || || || 1015.385 || 184.615 || 3 || 2 || 1.500 || [[Glacial]]
|-
| || || || || || 39\46 || 1017.391 || 182.609 || 11 || 7 || 1.571 ||
|-
| || || || || 28\33 || || 1018.182 || 181.818 || 8 || 5 || 1.600 ||
|-
| || || || || || 45\53 || 1018.868 || 181.132 || 13 || 8 || 1.625 || Wilson Golden 2 (1018.6773¢)
|-
| || || || 17\20 || || || 1020.000 || 180.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 40\47 || 1021.277 || 178.723 || 12 || 7 || 1.714 ||
|-
| || || || || 23\27 || || 1022.222 || 177.778 || 7 || 4 || 1.750 ||
|-
| || || || || || 29\34 || 1023.529 || 176.471 || 9 || 5 || 1.800 || [[Tetracot]]
|-
| || 6\7 || || || || || 1028.571 || 171.429 || 2 || 1 || 2.000 || Basic 1L 5s <br>(Generators smaller than this are proper)
|-
| || || || || || 25\29 || 1034.483 || 165.517 || 9 || 4 || 2.250 ||
|-
| || || || || 19\22 || || 1036.364 || 163.636 || 7 || 3 || 2.333 || [[Porcupine]] (incomplete)
|-
| || || || || || 32\37 || 1037.838 || 162.162 || 12 || 5 || 2.400 || Porcupine/[[porcupinefish]]
|-
| || || || 13\15 || || || 1040.000 || 160.000 || 5 || 2 || 2.500 ||
|-
| || || || || || 33\38 || 1042.105 || 157.895 || 13 || 5 || 2.600 || [[Hemikleismic]] <br>Wilson Golden 1 (1042.4790¢)
|-
| || || || || 20\23 || || 1043.478 || 156.522 || 8 || 3 || 2.667 ||
|-
| || || || || || 27\31 || 1045.161 || 154.839 || 11 || 4 || 2.750 || [[Nusecond]]
|-
| || || 7\8 || || || || 1050.000 || 150.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 22\25 || 1056.000 || 144.000 || 10 || 3 || 3.333 ||
|-
| || || || || 15\17 || || 1058.824 || 141.176 || 7 || 2 || 3.500 || [[Progression]] (incomplete)
|-
| || || || || || 23\26 || 1061.538 || 138.462 || 11 || 3 || 3.667 ||
|-
| || || || 8\9 || || || 1066.667 || 133.333 || 4 || 1 || 4.000 ||
|-
| || || || || || 17\19 || 1073.684 || 126.316 || 9 || 2 || 4.500 || [[Negri]] (incomplete)
|-
| || || || || 9\10 || || 1080.000 || 120.000 || 5 || 1 || 5.000 || [[Miracle]] (incomplete)
|-
| || || || || || 10\11 || 1090.909 || 109.091 || 6 || 1 || 6.000 || [[Passion]]↓ (incomplete), [[ripple]]↓ (incomplete)
|-
| 1\1 || || || || || || 1200.000 || 0.000 || 1 || 0 || → inf ||
|}


[[Category:6-tone scales]]
[[Category:6-tone scales]]
Retrieved from "https://en.xen.wiki/w/1L_5s"