1L 6s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Periods = 1
{{MOS intro}}
| nLargeSteps = 1
==Name==
| nSmallSteps = 6
[[TAMNAMS]] suggests the temperament-agnostic name '''onyx''' for this scale. The name comes from ''a lot'' of naming puns and references, namely:
| Equalized = 6
| Collapsed = 1
| Pattern = Lssssss
|Name=onyx}}


{{MOS intro}}
*The name sounds like its step counts of '''one''' large step and '''six''' small steps.
There is one notable low-harmonic-entropy scale with this [[MOS]] pattern: [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]].
*Onyxes come in different colors and types, which is a metaphor for this scale's generator range being quite large and containing the generator ranges of other MOS scales, such as [[7L 1s]], [[8L 1s]], and [[9L 1s]].
 
==Theory ==


Other scales include very improper (incomplete) versions of [[negri]], 12edo, etc.
===Low harmonic entropy scales===
There is one notable harmonic entropy minimum: [[porcupine]], in which the generator is around 150¢ to 170¢, two generators make a [[6/5]] (315.6¢), and three make a [[4/3]] (498¢).


== Modes ==
==Modes==
Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]], proposed by [[William Lynch]]. Descriptive mode names reference the page's original descriptions of the modes.
Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]], proposed by [[William Lynch]]. Descriptive mode names reference the page's original descriptions of the modes.
{| class="wikitable"
{| class="wikitable"
Line 34: Line 33:
|<nowiki>4|2</nowiki>
|<nowiki>4|2</nowiki>
|zebrian
|zebrian
|Bright minor
| Bright minor
|-
|-
|sssLsss
|sssLsss
Line 41: Line 40:
|Symmetric minor
|Symmetric minor
|-
|-
|ssssLss
| ssssLss
|<nowiki>2|4</nowiki>
|<nowiki>2|4</nowiki>
|gazellian
|gazellian
|Bright diminished
| Bright diminished
|-
|-
|sssssLs
|sssssLs
Line 54: Line 53:
|<nowiki>0|6</nowiki>
|<nowiki>0|6</nowiki>
|pandian
|pandian
|Magical seventh
| Magical seventh
|}
|}


== Scale tree ==
==Scale tree==
Generator ranges:
Generator ranges:
* Chroma-positive generator: 1028.5714 cents (6\7) to 1200 cents (1\1)
* Chroma-positive generator: 1028.5714 cents (6\7) to 1200 cents (1\1)
* Chroma-negative generator: 0 cents (0\1) to 171.4286 cents (1\7)
*Chroma-negative generator: 0 cents (0\1) to 171.4286 cents (1\7)


{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" rowspan="2" | Generator <br><small>(Chroma-positive)</small>
! colspan="6" rowspan="2" |Generator <br><small>(Chroma-positive)</small>
! colspan="2" | Cents
! colspan="2" |Cents
! rowspan="2" | L
! rowspan="2" |L
! rowspan="2" | s
! rowspan="2" | s
! rowspan="2" | L/s
! rowspan="2" | L/s
! rowspan="2" | Comments
! rowspan="2" |Comments
|-
|-
! <small>Chroma-positive</small>
!<small>Chroma-positive</small>
! <small>Chroma-negative</small>
!<small>Chroma-negative</small>
|-
|-
| 6\7 || || || || || || 1028.571 || 171.429 || 1 || 1 || 1.000 ||  
| 6\7|| || || || || ||1028.571||171.429||1||1||1.000||  
|-
|-
| || || || || || 31\36 || 1033.333 || 166.667 || 6 || 5 || 1.200 ||
| || || || || ||31\36||1033.333||166.667||6 || 5||1.200||
|-
|-
| || || || || 25\29 || || 1034.483 || 165.517 || 5 || 4 || 1.250 ||
| || || || ||25\29|| ||1034.483||165.517|| 5|| 4||1.250||
|-
|-
| || || || || || 44\51 || 1035.294 || 164.706 || 9 || 7 || 1.286 ||  
| || || || || ||44\51||1035.294||164.706||9 || 7 || 1.286 ||  
|-
|-
| || || || 19\22 || || || 1036.364 || 163.636 || 4 || 3 || 1.333 ||  
| || || ||19\22 || || || 1036.364 || 163.636 || 4 || 3 || 1.333 ||  
|-
|-
| || || || || || 51\59 || 1037.288 || 162.712 || 11 || 8 || 1.375 || [[Porcupine]]/[[porcupinefish]] is around here
| || || || || || 51\59 || 1037.288 || 162.712 || 11 || 8 || 1.375 ||[[Porcupine]]/[[porcupinefish]] is around here
|-
|-
| || || || || 32\37 || || 1037.838 || 162.162 || 7 || 5 || 1.400 ||  
| || || || ||32\37|| || 1037.838 || 162.162||7||5 || 1.400 ||  
|-
|-
| || || || || || 45\52 || 1038.462 || 161.538 || 10 || 7 || 1.429 ||  
| || || || || ||45\52||1038.462||161.538 ||10|| 7||1.429||
|-
|-
| || || 13\15 || || || || 1040.000 || 160.000 || 3 || 2 || 1.500 ||  
| || ||13\15|| || || ||1040.000||160.000||3||2||1.500||
|-
|-
| || || || || || 46\53 || 1041.509 || 158.491 || 11 || 7 || 1.571 || [[Hemikleismic]]
| || || || || ||46\53||1041.509||158.491||11||7||1.571||[[Hemikleismic]]
|-
|-
| || || || || 33\38 || || 1042.105 || 157.895 || 8 || 5 || 1.600 ||  
| || || || ||33\38|| ||1042.105||157.895||8 ||5||1.600||
|-
|-
| || || || || || 53\61 || 1042.623 || 157.377 || 13 || 8 || 1.625 || Wilson Golden 1 (1042.4790¢)
| || || || || ||53\61||1042.623||157.377 || 13||8|| 1.625||Wilson Golden 1 (1042.4790¢)
|-
|-
| || || || 20\23 || || || 1043.478 || 156.522 || 5 || 3 || 1.667 ||  
| || || || 20\23|| || ||1043.478||156.522||5||3||1.667 ||
|-
|-
| || || || || || 47\54 || 1044.444 || 155.556 || 12 || 7 || 1.714 ||  
| || || || || ||47\54 || 1044.444 ||155.556||12||7||1.714||  
|-
|-
| || || || || 27\31 || || 1045.161 || 154.839 || 7 || 4 || 1.750 || [[Nusecond]]
| || || || ||27\31|| ||1045.161||154.839||7 || 4||1.750 ||[[Nusecond]]
|-
|-
| || || || || || 34\39 || 1046.154 || 153.846 || 9 || 5 || 1.800 ||
| || || || || ||34\39||1046.154||153.846||9||5 || 1.800||
|-
|-
| || 7\8 || || || || || 1050.000 || 150.000 || 2 || 1 || 2.000 || Basic onyx <br>(Generators smaller than this are proper)
| ||7\8|| || || || ||1050.000||150.000||2||1 ||2.000||Basic onyx <br>(Generators smaller than this are proper)
|-
|-
| || || || || || 29\33 || 1054.545 || 145.455 || 9 || 4 || 2.250 ||
| || || || || || 29\33||1054.545||145.455||9||4||2.250||
|-
|-
| || || || || 22\25 || || 1056.000 || 144.000 || 7 || 3 || 2.333 ||  
| || || || || 22\25 || || 1056.000 || 144.000||7||3||2.333||  
|-
|-
| || || || || || 37\42 || 1057.143 || 142.857 || 12 || 5 || 2.400 ||
| || || || || || 37\42 || 1057.143 || 142.857||12||5||2.400||
|-
|-
| || || || 15\17 || || || 1058.824 || 141.176 || 5 || 2 || 2.500 || [[Progression]] (incomplete)
| || || ||15\17 || || ||1058.824||141.176||5||2 || 2.500||[[Progression]] (incomplete)
|-
|-
| || || || || || 38\43 || 1060.465 || 139.535 || 13 || 5 || 2.600 || Golden [[jerome]] (1060.7571¢)
| || || || || || 38\43||1060.465||139.535||13||5||2.600||Golden [[jerome]] (1060.7571¢)
|-
|-
| || || || || 23\26 || || 1061.538 || 138.462 || 8 || 3 || 2.667 ||  
| || || || ||23\26|| ||1061.538||138.462 || 8||3||2.667||
|-
|-
| || || || || || 31\35 || 1062.857 || 137.143 || 11 || 4 || 2.750 ||
| || || || || ||31\35||1062.857|| 137.143||11||4||2.750||
|-
|-
| || || 8\9 || || || || 1066.667 || 133.333 || 3 || 1 || 3.000 ||  
| || ||8\9|| || || ||1066.667||133.333||3||1 || 3.000||  
|-
|-
| || || || || || 25\28 || 1071.429 || 128.571 || 10 || 3 || 3.333 ||
| || || || || ||25\28||1071.429|| 128.571||10||3||3.333||
|-
|-
| || || || || 17\19 || || 1073.684 || 126.316 || 7 || 2 || 3.500 || [[Negri]] (incomplete)
| || || || ||17\19 || ||1073.684 ||126.316 ||7 ||2 ||3.500 ||[[Negri]] (incomplete)
|-
|-
| || || || || || 26\29 || 1075.862 || 124.138 || 11 || 3 || 3.667 ||  
| || || || || ||26\29|| 1075.862||124.138||11||3||3.667||
|-
|-
| || || || 9\10 || || || 1080.000 || 120.000 || 4 || 1 || 4.000 ||
| || || ||9\10 || || || 1080.000 ||120.000||4||1 ||4.000||
|-
|-
| || || || || || 19\21 || 1085.714 || 114.286 || 9 || 2 || 4.500 || [[Miracle]] (incomplete)
| || || || || ||19\21||1085.714||114.286||9||2||4.500||[[Miracle]] (incomplete)
|-
|-
| || || || || 10\11 || || 1090.909 || 109.091 || 5 || 1 || 5.000 ||  
| || || || ||10\11|| ||1090.909||109.091||5||1||5.000||
|-
|-
| || || || || || 11\12 || 1100.000 || 100.000 || 6 || 1 || 6.000 || [[Passion]], [[ripple]] (incomplete)
| || || || || ||11\12||1100.000||100.000||6||1||6.000||[[Passion]], [[ripple]] (incomplete)
|-
|-
| 1\1 || || || || || || 1200.000 || 0.000 || 1 || 0 || → inf ||
|1\1|| || || || || ||1200.000||0.000||1||0||→ inf||
|}
|}


[[Category:7-tone scales]]
[[Category:7-tone scales]]
[[Category:Antiarcheotonic]]
[[Category:Antiarcheotonic]]

Revision as of 08:36, 3 July 2023

↑ 1L 5s 2L 5s ↗
1L 6s 2L 6s →
↓ 1L 7s 2L 7s ↘ 
┌╥┬┬┬┬┬┬┐
│║│││││││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssss
ssssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 6\7 to 1\1 (1028.6 ¢ to 1200.0 ¢)
Dark 0\1 to 1\7 (0.0 ¢ to 171.4 ¢)
TAMNAMS information
Name onyx
Prefix on-
Abbrev. on
Related MOS scales
Parent 1L 5s
Sister 6L 1s
Daughters 7L 1s, 1L 7s
Neutralized 2L 5s
2-Flought 8L 6s, 1L 13s
Equal tunings
Equalized (L:s = 1:1) 6\7 (1028.6 ¢)
Supersoft (L:s = 4:3) 19\22 (1036.4 ¢)
Soft (L:s = 3:2) 13\15 (1040.0 ¢)
Semisoft (L:s = 5:3) 20\23 (1043.5 ¢)
Basic (L:s = 2:1) 7\8 (1050.0 ¢)
Semihard (L:s = 5:2) 15\17 (1058.8 ¢)
Hard (L:s = 3:1) 8\9 (1066.7 ¢)
Superhard (L:s = 4:1) 9\10 (1080.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)

1L 6s, named onyx in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 6 small steps, repeating every octave. Generators that produce this scale range from 1028.6 ¢ to 1200 ¢, or from 0 ¢ to 171.4 ¢.

Name

TAMNAMS suggests the temperament-agnostic name onyx for this scale. The name comes from a lot of naming puns and references, namely:

  • The name sounds like its step counts of one large step and six small steps.
  • Onyxes come in different colors and types, which is a metaphor for this scale's generator range being quite large and containing the generator ranges of other MOS scales, such as 7L 1s, 8L 1s, and 9L 1s.

Theory

Low harmonic entropy scales

There is one notable harmonic entropy minimum: porcupine, in which the generator is around 150¢ to 170¢, two generators make a 6/5 (315.6¢), and three make a 4/3 (498¢).

Modes

Mode names are from Porcupine temperament modal harmony, proposed by William Lynch. Descriptive mode names reference the page's original descriptions of the modes.

Mode UDP Mode name Descriptive mode name
Lssssss 6|0 chinchillian Bright major
sLsssss 5|1 badgerian Dark major
ssLssss 4|2 zebrian Bright minor
sssLsss 3|3 dingoian Symmetric minor
ssssLss 2|4 gazellian Bright diminished
sssssLs 1|5 lemurian Dark diminished
ssssssL 0|6 pandian Magical seventh

Scale tree

Generator ranges:

  • Chroma-positive generator: 1028.5714 cents (6\7) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 171.4286 cents (1\7)
Generator
(Chroma-positive) 		Cents L s L/s Comments
Chroma-positive Chroma-negative
6\7 1028.571 171.429 1 1 1.000
31\36 1033.333 166.667 6 5 1.200
25\29 1034.483 165.517 5 4 1.250
44\51 1035.294 164.706 9 7 1.286
19\22 1036.364 163.636 4 3 1.333
51\59 1037.288 162.712 11 8 1.375 Porcupine/porcupinefish is around here
32\37 1037.838 162.162 7 5 1.400
45\52 1038.462 161.538 10 7 1.429
13\15 1040.000 160.000 3 2 1.500
46\53 1041.509 158.491 11 7 1.571 Hemikleismic
33\38 1042.105 157.895 8 5 1.600
53\61 1042.623 157.377 13 8 1.625 Wilson Golden 1 (1042.4790¢)
20\23 1043.478 156.522 5 3 1.667
47\54 1044.444 155.556 12 7 1.714
27\31 1045.161 154.839 7 4 1.750 Nusecond
34\39 1046.154 153.846 9 5 1.800
7\8 1050.000 150.000 2 1 2.000 Basic onyx
(Generators smaller than this are proper)
29\33 1054.545 145.455 9 4 2.250
22\25 1056.000 144.000 7 3 2.333
37\42 1057.143 142.857 12 5 2.400
15\17 1058.824 141.176 5 2 2.500 Progression (incomplete)
38\43 1060.465 139.535 13 5 2.600 Golden jerome (1060.7571¢)
23\26 1061.538 138.462 8 3 2.667
31\35 1062.857 137.143 11 4 2.750
8\9 1066.667 133.333 3 1 3.000
25\28 1071.429 128.571 10 3 3.333
17\19 1073.684 126.316 7 2 3.500 Negri (incomplete)
26\29 1075.862 124.138 11 3 3.667
9\10 1080.000 120.000 4 1 4.000
19\21 1085.714 114.286 9 2 4.500 Miracle (incomplete)
10\11 1090.909 109.091 5 1 5.000
11\12 1100.000 100.000 6 1 6.000 Passion, ripple (incomplete)
1\1 1200.000 0.000 1 0 → inf
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