2L 10s: Difference between revisions

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{{todo|review|inline=1|text=Adopt scale tree template, review entries}}
{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
{{MOS intro}}
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== Scale tree ==
== Scale tree ==
''Note: the following table uses the dark generator.''
''Note: The following table uses the dark generator.''


Generator ranges:
Generator ranges:
* Bright generator: 500 cents (5\12) to 600 cents (1\2)
* Bright generator: 500 cents (5\12) to 600 cents (1\2)
* Dark generator: 0 cents (0\2) to 100 cents (1\12)
* Dark generator: 0 cents (0\2) to 100 cents (1\12)
 
{{Scale tree}}
{| class="wikitable center-all"
! colspan="6" | Small step <br>(dark generator)
! Cents
! L
! s
! L/s
! Comments
|-
| 1\12 || || || || || || 100.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 5\62 || 96.774 || 6 || 5 || 1.200 ||
|-
| || || || || 4\50 || || 96.000 || 5 || 4 || 1.250 ||
|-
| || || || || || 7\88 || 95.455 || 9 || 7 || 1.286 ||
|-
| || || || 3\38 || || || 94.737 || 4 || 3 || 1.333 ||
|-
| || || || || || 8\102 || 94.118 || 11 || 8 || 1.375 ||
|-
| || || || || 5\64 || || 93.750 || 7 || 5 || 1.400 ||
|-
| || || || || || 7\90 || 93.333 || 10 || 7 || 1.429 ||
|-
| || || 2\26 || || || || 92.308 || 3 || 2 || 1.500 || [[Injera]]
|-
| || || || || || 7\92 || 91.304 || 11 || 7 || 1.571 ||
|-
| || || || || 5\66 || || 90.909 || 8 || 5 || 1.600 ||
|-
| || || || || || 8\106 || 90.566 || 13 || 8 || 1.625 || Unnamed golden tuning (90.6614¢)
|-
| || || || 3\40 || || || 90.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 7\94 || 89.362 || 12 || 7 || 1.714 ||
|-
| || || || || 4\54 || || 88.889 || 7 || 4 || 1.750 ||
|-
| || || || || || 5\68 || 88.235 || 9 || 5 || 1.800 ||
|-
| || 1\14 || || || || || 85.714 || 2 || 1 || 2.000 || Basic 2L 10s <br>(Generators larger than this are proper)
|-
| || || || || || 4\58 || 82.759 || 9 || 4 || 2.250 ||
|-
| || || || || 3\44 || || 81.818 || 7 || 3 || 2.333 ||
|-
| || || || || || 5\74 || 81.081 || 12 || 5 || 2.400 ||
|-
| || || || 2\30 || || || 80.000 || 5 || 2 || 2.500 ||
|-
| || || || || || 5\76 || 78.947 || 13 || 5 || 2.600 || Unnamed golden tuning (78.7605¢)
|-
| || || || || 3\46 || || 78.261 || 8 || 3 || 2.667 ||
|-
| || || || || || 4\62 || 77.419 || 11 || 4 || 2.750 ||
|-
| || || 1\16 || || || || 75.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 3\50 || 72.000 || 10 || 3 || 3.333 || [[Vishnu]]/[[vishnean]]
|-
| || || || || 2\34 || || 70.588 || 7 || 2 || 3.500 ||
|-
| || || || || || 3\52 || 69.231 || 11 || 3 || 3.667 ||
|-
| || || || 1\18 || || || 66.667 || 4 || 1 || 4.000 ||
|-
| || || || || || 2\38 || 63.158 || 9 || 2 || 4.500 ||
|-
| || || || || 1\20 || || 60.000 || 5 || 1 || 5.000 ||
|-
| || || || || || 1\22 || 54.545 || 6 || 1 || 6.000 || [[Shrutar]]
|-
| 0\2 || || || || || || 0 || 1 || 0 || → inf ||
|}


[[Category:12-tone scales]]
[[Category:12-tone scales]]

Revision as of 20:42, 22 September 2024

↖ 1L 9s ↑ 2L 9s 3L 9s ↗
← 1L 10s 2L 10s 3L 10s →
↙ 1L 11s ↓ 2L 11s 3L 11s ↘
Scale structure
Step pattern LsssssLsssss
sssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 5\12 to 1\2 (500.0 ¢ to 600.0 ¢)
Dark 0\2 to 1\12 (0.0 ¢ to 100.0 ¢)
TAMNAMS information
Related to 2L 8s (jaric)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 2L 8s
Sister 10L 2s
Daughters 12L 2s, 2L 12s
Neutralized 4L 8s
2-Flought 14L 10s, 2L 22s
Equal tunings
Equalized (L:s = 1:1) 5\12 (500.0 ¢)
Supersoft (L:s = 4:3) 16\38 (505.3 ¢)
Soft (L:s = 3:2) 11\26 (507.7 ¢)
Semisoft (L:s = 5:3) 17\40 (510.0 ¢)
Basic (L:s = 2:1) 6\14 (514.3 ¢)
Semihard (L:s = 5:2) 13\30 (520.0 ¢)
Hard (L:s = 3:1) 7\16 (525.0 ¢)
Superhard (L:s = 4:1) 8\18 (533.3 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)
View • Talk • Edit

2L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 10 small steps, with a period of 1 large step and 5 small steps that repeats every 600.0 ¢, or twice every octave. 2L 10s is a child scale of 2L 8s, expanding it by 2 tones. Generators that produce this scale range from 500 ¢ to 600 ¢, or from 0 ¢ to 100 ¢. 2L 10s appears as the chromatic scale of injera and shrutar temperaments, among others. Injera is the harmonic entropy minimum for this pattern, generating 5/4 by moving up four generators from the root. The name for this MOS scale is p-chro jaric.

Modes

Scale degrees of the modes of 2L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12
10|0(2) 1 LsssssLsssss Perf. Aug. Maj. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Maj. Perf. Perf.
8|2(2) 6 sLsssssLssss Perf. Perf. Maj. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Maj. Perf. Perf.
6|4(2) 5 ssLsssssLsss Perf. Perf. Min. Maj. Maj. Perf. Perf. Perf. Min. Maj. Maj. Perf. Perf.
4|6(2) 4 sssLsssssLss Perf. Perf. Min. Min. Maj. Perf. Perf. Perf. Min. Min. Maj. Perf. Perf.
2|8(2) 3 ssssLsssssLs Perf. Perf. Min. Min. Min. Perf. Perf. Perf. Min. Min. Min. Perf. Perf.
0|10(2) 2 sssssLsssssL Perf. Perf. Min. Min. Min. Dim. Perf. Perf. Min. Min. Min. Dim. Perf.

Scale tree

Note: The following table uses the dark generator.

Generator ranges:

  • Bright generator: 500 cents (5\12) to 600 cents (1\2)
  • Dark generator: 0 cents (0\2) to 100 cents (1\12)
Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 2L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\12 500.000 100.000 1:1 1.000 Equalized 2L 10s
26\62 503.226 96.774 6:5 1.200
21\50 504.000 96.000 5:4 1.250
37\88 504.545 95.455 9:7 1.286
16\38 505.263 94.737 4:3 1.333 Supersoft 2L 10s
43\102 505.882 94.118 11:8 1.375
27\64 506.250 93.750 7:5 1.400
38\90 506.667 93.333 10:7 1.429
11\26 507.692 92.308 3:2 1.500 Soft 2L 10s
39\92 508.696 91.304 11:7 1.571
28\66 509.091 90.909 8:5 1.600
45\106 509.434 90.566 13:8 1.625
17\40 510.000 90.000 5:3 1.667 Semisoft 2L 10s
40\94 510.638 89.362 12:7 1.714
23\54 511.111 88.889 7:4 1.750
29\68 511.765 88.235 9:5 1.800
6\14 514.286 85.714 2:1 2.000 Basic 2L 10s
Scales with tunings softer than this are proper
25\58 517.241 82.759 9:4 2.250
19\44 518.182 81.818 7:3 2.333
32\74 518.919 81.081 12:5 2.400
13\30 520.000 80.000 5:2 2.500 Semihard 2L 10s
33\76 521.053 78.947 13:5 2.600
20\46 521.739 78.261 8:3 2.667
27\62 522.581 77.419 11:4 2.750
7\16 525.000 75.000 3:1 3.000 Hard 2L 10s
22\50 528.000 72.000 10:3 3.333
15\34 529.412 70.588 7:2 3.500
23\52 530.769 69.231 11:3 3.667
8\18 533.333 66.667 4:1 4.000 Superhard 2L 10s
17\38 536.842 63.158 9:2 4.500
9\20 540.000 60.000 5:1 5.000
10\22 545.455 54.545 6:1 6.000
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 10s
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