6L 3s: Difference between revisions

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'''6L 3s''' is a MOS pattern with period 1\3.  
'''6L 3s''' is a MOS pattern with period 1\3.  


The tiny region between 26\171 and 281\1848 is the ''terrain'' region, giving the [[terrain9|abitonic scale]] for the remarkable terrain temperament [[Chromatic_pair|chromatic pair]]. If you feel that is too small a region to allocate or prefer edos of a more usual size, you can call it the region between 5/33 and 6/39, but that misses the extreme accuracy of this temperament.
The tiny region between 26\171 and 281\1848 is the ''terrain'' region, giving the [[terrain9|abitonic scale]] for the remarkable terrain temperament [[chromatic pair]]. If you feel that is too small a region to allocate or prefer EDOs of a more usual size, you can call it the region between 5/33 and 6/39, but that misses the extreme accuracy of this temperament.


For a more down-to-earth temperament, try [[Triforce|triforce]].
For a more down-to-earth temperament, try [[triforce]].
 
== Modes ==
* 6|0 LLsLLsLLs
* 3|3 LsLLsLLsL
* 0|6 sLLsLLsLL


== Scales ==
== Scales ==
Line 20: Line 25:


== Scale tree ==
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 133.3333 cents (1\9) to 200 cents (1\6)
* Chroma-negative generator: 200 cents (1\6) to 266.6667 cents (2\9)
{| class="wikitable center-all"
{| class="wikitable center-all"
! colspan="6" | Generator
! colspan="6" | Generator
Line 42: Line 51:
| || || || || 7\57 || || 147.368 || 7 || 5 || 1.400 ||
| || || || || 7\57 || || 147.368 || 7 || 5 || 1.400 ||
|-
|-
| || || || || || 10\81 || 148.148 || 10 || 7 || 1.428 ||
| || || || || || 10\81 || 148.148 || 10 || 7 || 1.429 ||
|-
|-
| || || 3\24 || || || || 150.000 || 3 || 2 || 1.500 ||  
| || || 3\24 || || || || 150.000 || 3 || 2 || 1.500 ||  
|-
|-
| || || || || || 11\87 || 151.724 || 11 || 7 || 1.571 || Hemimist
| || || || || || 11\87 || 151.724 || 11 || 7 || 1.571 || [[Hemimist]]
|-
|-
| || || || || 8\63 || || 152.381 || 8 || 5 || 1.600 ||
| || || || || 8\63 || || 152.381 || 8 || 5 || 1.600 ||
|-
|-
| || || || || || 13\102 || 152.911 || 13 || 8 || 1.625 || Unnamed golden tuning<br>Triforce (optimal around here)
| || || || || || 13\102 || 152.911 || 13 || 8 || 1.625 || Golden [[triforce]] (152.7864¢)
|-
|-
| || || || 5\39 || || || 153.846 || 5 || 3 || 1.667 ||
| || || || 5\39 || || || 153.846 || 5 || 3 || 1.667 ||
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| || || || 5\36 || || || 166.667 || 5 || 2 || 2.500 ||  
| || || || 5\36 || || || 166.667 || 5 || 2 || 2.500 ||  
|-
|-
| || || || || || 13\93 || 167.742 || 13 || 5 || 2.600 || Unnamed golden tuning
| || || || || || 13\93 || 167.742 || 13 || 5 || 2.600 || Unnamed golden tuning (167.9285¢)
|-
|-
| || || || || 8\57 || || 168.421 || 8 || 3 || 2.667 ||
| || || || || 8\57 || || 168.421 || 8 || 3 || 2.667 ||
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| || || || || 7\48 || || 175.000 || 7 || 2 || 3.500 ||
| || || || || 7\48 || || 175.000 || 7 || 2 || 3.500 ||
|-
|-
| || || || || || 11\75 || 176.000 || 11 || 3 || 3.667 || Oodako
| || || || || || 11\75 || 176.000 || 11 || 3 || 3.667 || [[Oodako]]
|-
|-
| || || || 4\27 || || || 177.778 || 4 || 1 || 4.000 ||
| || || || 4\27 || || || 177.778 || 4 || 1 || 4.000 ||
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| || || || || 5\33 || || 181.818 || 5 || 1 || 5.000 ||  
| || || || || 5\33 || || 181.818 || 5 || 1 || 5.000 ||  
|-
|-
| || || || || || 6\39 || 184.615 || 6 || 1 || 6.000 || Mirkat
| || || || || || 6\39 || 184.615 || 6 || 1 || 6.000 || [[Mirkat]]
|-
|-
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
| 1\6 || || || || || || 200.000 || 1 || 0 || → inf ||
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[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
[[Category:9-tone scales]]
[[Category:Hyrulic| ]] <!-- main article -->
[[Category:Hyrulic| ]] <!-- main article -->

Revision as of 22:15, 17 May 2022

↖ 5L 2s ↑ 6L 2s 7L 2s ↗
← 5L 3s 6L 3s 7L 3s →
↙ 5L 4s ↓ 6L 4s 7L 4s ↘
Scale structure
Step pattern LLsLLsLLs
sLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 1\9 to 1\6 (133.3 ¢ to 200.0 ¢)
Dark 1\6 to 2\9 (200.0 ¢ to 266.7 ¢)
TAMNAMS information
Name hyrulic
Prefix hyru-
Abbrev. hy
Related MOS scales
Parent 3L 3s
Sister 3L 6s
Daughters 9L 6s, 6L 9s
Neutralized 3L 6s
2-Flought 15L 3s, 6L 12s
Equal tunings
Equalized (L:s = 1:1) 1\9 (133.3 ¢)
Supersoft (L:s = 4:3) 4\33 (145.5 ¢)
Soft (L:s = 3:2) 3\24 (150.0 ¢)
Semisoft (L:s = 5:3) 5\39 (153.8 ¢)
Basic (L:s = 2:1) 2\15 (160.0 ¢)
Semihard (L:s = 5:2) 5\36 (166.7 ¢)
Hard (L:s = 3:1) 3\21 (171.4 ¢)
Superhard (L:s = 4:1) 4\27 (177.8 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
View • Talk • Edit

6L 3s is a MOS pattern with period 1\3.

The tiny region between 26\171 and 281\1848 is the terrain region, giving the abitonic scale for the remarkable terrain temperament chromatic pair. If you feel that is too small a region to allocate or prefer EDOs of a more usual size, you can call it the region between 5/33 and 6/39, but that misses the extreme accuracy of this temperament.

For a more down-to-earth temperament, try triforce.

Modes

  • 6|0 LLsLLsLLs
  • 3|3 LsLLsLLsL
  • 0|6 sLLsLLsLL

Scales

Scale tree

Generator ranges:

  • Chroma-positive generator: 133.3333 cents (1\9) to 200 cents (1\6)
  • Chroma-negative generator: 200 cents (1\6) to 266.6667 cents (2\9)
Generator Cents L s L/s Comments
1\9 133.333 1 1 1.000
6\51 141.176 6 5 1.200
5\42 142.857 5 4 1.250
9\75 144.000 9 7 1.286
4\33 145.455 4 3 1.333
11\90 146.667 11 8 1.375
7\57 147.368 7 5 1.400
10\81 148.148 10 7 1.429
3\24 150.000 3 2 1.500
11\87 151.724 11 7 1.571 Hemimist
8\63 152.381 8 5 1.600
13\102 152.911 13 8 1.625 Golden triforce (152.7864¢)
5\39 153.846 5 3 1.667
12\93 154.839 12 7 1.714
7\54 155.556 7 4 1.750
9\69 156.522 9 5 1.800
2\15 160.000 2 1 2.000 Basic hyrulic
9\66 163.636 9 4 2.250
7\51 164.706 7 3 2.333
12\87 165.517 12 5 2.400
5\36 166.667 5 2 2.500
13\93 167.742 13 5 2.600 Unnamed golden tuning (167.9285¢)
8\57 168.421 8 3 2.667
11\78 169.231 11 4 2.750
3\21 171.439 3 1 3.000
10\69 173.913 10 3 3.333
7\48 175.000 7 2 3.500
11\75 176.000 11 3 3.667 Oodako
4\27 177.778 4 1 4.000
9\60 180.000 9 2 4.500
5\33 181.818 5 1 5.000
6\39 184.615 6 1 6.000 Mirkat
1\6 200.000 1 0 → inf
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