2L 10s: Difference between revisions

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The '''2L 10s''' (or '''1L 5s<1\2>''') [[MOS scale]] contains two [[1L 5s]] patterns per octave.
The '''2L 10s''' (or '''1L 5s<1\2>''') [[MOS scale]] contains two [[1L 5s]] patterns per octave.


It is always proper. Its [[chroma-positive]] generator is between 5\[[12edo|12]] (500{{cent}}) and 1\[[2edo|2]] (600{{cent}}). It 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'''.
Its [[chroma-positive]] generator is between 5\[[12edo|12]] (500{{cent}}) and 1\[[2edo|2]] (600{{cent}}). It 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'''.


== Scale tree ==
== Scale tree ==
''Note: the following table uses the chroma-negative generator.''
''Note: the following table uses the dark generator.''
{| class="wikitable"
 
Generator ranges:
* Bright generator: 500 cents (5\12) to 600 cents (1\2)
* Dark generator: 0 cents (0\2) to 100 cents (1\12)
 
{| 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 ||
|-
|-
| | 0/2
| || || || || || 7\90 || 93.333 || 10 || 7 || 1.429 ||  
| |  
| |  
| |  
| |  
| |  
| | 0
|-
|-
|
| || || 2\26 || || || || 92.308 || 3 || 2 || 1.500 || [[Injera]]
|
|
|
|
|1\22
|54.5455
|-
|-
| |  
| || || || || || 7\92 || 91.304 || 11 || 7 || 1.571 ||  
| |  
| |  
| |  
| | 1/20
| |  
| | 60
|-
|-
| |  
| || || || || 5\66 || || 90.909 || 8 || 5 || 1.600 ||
| |  
| |  
| | 1/18
| |  
| |  
| | 66.667
|-
|-
| |  
| || || || || || 8\106 || 90.566 || 13 || 8 || 1.625 || Unnamed golden tuning (90.6614¢)
| |  
| |  
| |  
| | 2/34
| |  
| | 70.588
|-
|-
| |  
| || || || 3\40 || || || 90.000 || 5 || 3 || 1.667 ||
| |  
| |  
| |  
| |  
| |  
| | 600/(5+pi)
|-
|-
| |  
| || || || || || 7\94 || 89.362 || 12 || 7 || 1.714 ||  
| |  
| | 1/16
| |  
| |  
| |  
| | 75
|-
|-
| |  
| || || || || 4\54 || || 88.889 || 7 || 4 || 1.750 ||  
| |  
| |  
| |  
| |  
| |  
| | 600/(5+e)
|-
|-
| |  
| || || || || || 5\68 || 88.235 || 9 || 5 || 1.800 ||
| |  
| |  
| |  
| | 3/46
| |  
| | 78.261
|-
|-
| |  
| || 1\14 || || || || || 85.714 || 2 || 1 || 2.000 || Basic 2L 10s <br>(Generators larger than this are proper)
| |  
| |  
| |  
| |  
| |  
| | 600/(6+phi)
|-
|-
| |  
| || || || || || 4\58 || 82.759 || 9 || 4 || 2.250 ||  
| |  
| |  
| | 2/30
| |  
| |  
| | 80
|-
|-
| |  
| || || || || 3\44 || || 81.818 || 7 || 3 || 2.333 ||
| |  
| |  
| |
| | 3/44
| |  
| | 81.818
|-
|-
| |  
| || || || || || 5\74 || 81.081 || 12 || 5 || 2.400 ||
| | 1/14
| |  
| |  
| |  
| |  
| | 85.714
|-
|-
| |  
| || || || 2\30 || || || 80.000 || 5 || 2 || 2.500 ||
| |  
| |  
| |  
| | 4/54
| |  
| | 88.889
|-
|-
| |  
| || || || || || 5\76 || 78.947 || 13 || 5 || 2.600 || Unnamed golden tuning (78.7605¢)
| |  
| |  
| |  
| |  
| |  
| | 600/(5+sqrt(3))
|-
|-
| |  
| || || || || 3\46 || || 78.261 || 8 || 3 || 2.667 ||  
| |  
| |  
| | 3/40
| |  
| |  
| | 90
|-
|-
| |  
| || || || || || 4\62 || 77.419 || 11 || 4 || 2.750 ||  
| |  
| |  
| |  
| |  
| |  
| | 600/(5+phi)
|-
|-
| |  
| || || 1\16 || || || || 75.000 || 3 || 1 || 3.000 ||
| |  
| |  
| |  
| | 5/66
| |  
| | 90.909
|-
|-
| |  
| || || || || || 3\50 || 72.000 || 10 || 3 || 3.333 || [[Vishnu]]/[[vishnean]]
| |  
| |  
| |  
| |  
| |  
| | 600/(5+pi/2)
|-
|-
| |  
| || || || || 2\34 || || 70.588 || 7 || 2 || 3.500 ||
| |  
| |  
| |  
| |  
| | 7/92
| | 91.304
|-
|-
| |  
| || || || || || 3\52 || 69.231 || 11 || 3 || 3.667 ||
| |  
| | 2/26
| |  
| |  
| |  
| | 92.308
|-
|-
| |  
| || || || 1\18 || || || 66.667 || 4 || 1 || 4.000 ||
| |  
| |  
| |  
| | 5/64
| |  
| | 93.75
|-
|-
| |  
| || || || || || 2\38 || 63.158 || 9 || 2 || 4.500 ||
| |  
| |  
| | 3/38
| |  
| |  
| | 94.737
|-
|-
| |  
| || || || || 1\20 || || 60.000 || 5 || 1 || 5.000 ||  
| |  
| |  
| |  
| | 4/50
| |  
| | 96
|-
|-
|
| || || || || || 1\22 || 54.545 || 6 || 1 || 6.000 || [[Shrutar]]
|
|
|
|
|5\62
|96.774
|-
|-
| | 1/12
| 0\2 || || || || || || 0 || 1 || 0 || → inf ||  
| |  
| |  
| |  
| |  
| |  
| | 100
|}
|}


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

Revision as of 08:21, 17 May 2023

↖ 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 ¢)
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The 2L 10s (or 1L 5s<1\2>) MOS scale contains two 1L 5s patterns per octave.

Its chroma-positive generator is between 5\12 (500 ¢) and 1\2 (600 ¢). It 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.

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)
Small step
(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
(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
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