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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]]
Retrieved from "https://en.xen.wiki/w/2L_10s"