User:Moremajorthanmajor/10L 3s (19/9-equivalent): Difference between revisions

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{{Infobox MOS
{{Infobox MOS
| Periods = 1
|Tuning=10L 3s<19/9>}}{{MOS intro|Scale Signature=10L 3s<19/9>}}It is the highest just tuning for greater luachoid, a scale pattern that expands on greater sephiroid ([[3L 7s (5/2-equivalent)|3L 7s]]). A tempered flat chain of 27/16 really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered in descending order so that the the tempered 27/16 is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.
| nLargeSteps = 10
| nSmallSteps = 3
| Equalized = 4
| Collapsed = 3
| Pattern = LLLLsLLLsLLLs
| Equave = 19/9}}
'''10L 3s(<19/9>)''', also known as greater luachoid is a scale pattern that expands on greater sephiroid ([[3L 7s (5/2-equivalent)|3L 7s]]). A tempered (flat) chain of the 13th harmonic or 5/3 really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered in descending order so that the the tempered 13th harmonic or 5/3 is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 66: Line 59:
| |Elul
| |Elul
|}
|}
{| class="wikitable"
{{MOS tuning spectrum|Scale Signature=10L 3s<19/9>}}
! colspan="3" |Generator
!Cents
!Normalized Cents
!Centishrutis
!''ed23\22''
|-
| |3/10
| |
|
| |360
|360
|660
|''690''
|-
| |16/53
| |
|
| |362.264
|369.231
|676.923
|''694.340''
|-
|
|45/149
|
|362.416
|369.863
|678.082
|''694.631''
|-
|
|29/96
|
|362.500
|370.213
|678.723
|''694.792''
|-
|
|42/139
|
|362.590
|370.588
|679.412
|''694.964''
|-
| |13/43
| |
|
| |362.791
|371.429
|680.952
|''695.349''
|-
|
|36/119
|
|363.025
|372.414
|682.757
|''695.798''
|-
|
|23/76
|
|363.158
|372.973
|683.784
|''696.052''
|-
|
|33/109
|
|363.303
|373.584
|684.906
|''696.330''
|-
| |
| |
|
| |363.487
|374.364
|686.335
|''696.683''
|-
| |10/33
| |
|
| |363.636
|375.000
|687.500
|''696.970''
|-
|
|47/155
|
|363.871
|376.000
|689.333
|''697.419''
|-
|
|37/122
|
|363.944
|376.271
|[[Tel:689.8305|689.8305]]
|''697.540''
|-
| |
| |
|
| |363.976
|376.448
|690.155
|''697.620''
|-
| |
| |27/89
|
| |364.045
|376.744
|690.698
|''697.753''
|-
| |
| |
|
| |364.112
|377.033
|691.227
|''697.882''
|-
| |
| |17/56
|
| |364.286
|377.778
|692.593
|''698.214''
|-
|
|
|41/135
|364.444
|[[Tel:378.4615|378.4615]]
|693.846
|''[[Tel:698.5185|698.5185]]''
|-
|
|24/79
|
|364.557
|378.947
|694.737
|''698.734''
|-
|
|31/102
|
|364.706
|379.392
|695.918
|''699.020''
|-
|
|38/125
|
|364.800
|380.000
|696.667
|''699.200''
|-
| |7/23
| |
|
| |365.217
|381.818
|700.000
|''700.000''
|-
|
|39/128
|
|365.625
|383.607
|703.279
|''700.781''
|-
|
|32/105
|
|365.714
|384.000
|704.000
|''700.952''
|-
|
|25/82
|
|365.854
|384.615
|705.182
|''[[Tel:701.2195|701.2195]]''
|-
| |
| |
|
| |365.904
|384.844
|[[Tel:705.5475|705.5475]]
|''701.319''
|-
|
|
|43/141
|[[Tel:365.9575|365.9575]]
|385.075
|705.970
|''701.418''
|-
|
|
|61/200
|366
|385.263
|706.316
|''701.500''
|-
| |
| |18/59
|
| |366.102
|385.714
|707.143
|''701.694''
|-
| |
| |
|
| |366.256
|386.402
|708.404
|''701.991''
|-
| |
| |29/95
|
| |366.316
|386.667
|708.889
|''702.105''
|-
|
|40/131
|
|366.412
|387.097
|709.677
|''702.290''
|-
| |
| |
|
| |366.414
|[[Tel:387.1065|387.1065]]
|709.695
|''702.294''
|-
|
|51/167
|
|366.467
|387.342
|710.127
|''702.395''
|-
| |11/36
| |
|
| |366.667
|388.235
|711.765
|''702.778''
|-
|
|37/121
|
|366.942
|389.474
|713.196
|''703.306''
|-
|
|
|63/206
|366.990
|389.691
|714.433
|''703.398''
|-
|
|26/85
|
|367.059
|390.000
|715.000
|''703.529''
|-
| |15/49
| |
|
| |367.347
|391.304
|717.391
|''704.082''
|-
|
|49/160
|
|367.500
|392.000
|718.667
|''704.375''
|-
|
|34/111
|
|367.568
|392.308
|719.231
|''[[Tel:704.5045|704.5045]]''
|-
| |19/62
| |
|
| |367.742
|393.103
|720.690
|''704.838''
|-
| |4/13
| |
|
| |369.231
|400.000
|733.333
|''707.692''
|}

Latest revision as of 16:51, 3 March 2025

↖ 9L 2s⟨19/9⟩ ↑ 10L 2s⟨19/9⟩ 11L 2s⟨19/9⟩ ↗
← 9L 3s⟨19/9⟩ 10L 3s (19/9-equivalent) 11L 3s⟨19/9⟩ →
↙ 9L 4s⟨19/9⟩ ↓ 10L 4s⟨19/9⟩ 11L 4s⟨19/9⟩ ↘
Scale structure
Step pattern LLLLsLLLsLLLs
sLLLsLLLsLLLL
Equave 19/9 (1293.6 ¢)
Period 19/9 (1293.6 ¢)
Generator size(ed19/9)
Bright 9\13 to 7\10 (895.6 ¢ to 905.5 ¢)
Dark 3\10 to 4\13 (388.1 ¢ to 398.0 ¢)
Related MOS scales
Parent 3L 7s⟨19/9⟩
Sister 3L 10s⟨19/9⟩
Daughters 13L 10s⟨19/9⟩, 10L 13s⟨19/9⟩
Neutralized 7L 6s⟨19/9⟩
2-Flought 23L 3s⟨19/9⟩, 10L 16s⟨19/9⟩
Equal tunings(ed19/9)
Equalized (L:s = 1:1) 9\13 (895.6 ¢)
Supersoft (L:s = 4:3) 34\49 (897.6 ¢)
Soft (L:s = 3:2) 25\36 (898.3 ¢)
Semisoft (L:s = 5:3) 41\59 (898.9 ¢)
Basic (L:s = 2:1) 16\23 (899.9 ¢)
Semihard (L:s = 5:2) 39\56 (900.9 ¢)
Hard (L:s = 3:1) 23\33 (901.6 ¢)
Superhard (L:s = 4:1) 30\43 (902.5 ¢)
Collapsed (L:s = 1:0) 7\10 (905.5 ¢)
View • Talk • Edit

10L 3s⟨19/9⟩ is a 19/9-equivalent (non-octave) moment of symmetry scale containing 10 large steps and 3 small steps, repeating every interval of 19/9 (1293.6 ¢). Generators that produce this scale range from 895.6 ¢ to 905.5 ¢, or from 388.1 ¢ to 398 ¢.It is the highest just tuning for greater luachoid, a scale pattern that expands on greater sephiroid (3L 7s). A tempered flat chain of 27/16 really comes into its own as a distinct scale when extended to 13 tones. In these "Luach" modes the degrees are to be taken as numbered in descending order so that the the tempered 27/16 is fifth rather than tenth in the scale. This inverts the meaning of major and minor so that the Ionian-like mode reaches its degrees almost exclusively by backtracking.

Circle of fifths Ascending scale Mode
I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI-X L L L L s L L L s L L L s Tishrei
x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II-VI L L L s L L L s L L L s L Cheshvan
vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI-II L L s L L L s L L L s L L Kislev
ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII-XI L s L L L s L L L s L L L Tevet
xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III-VII s L L L s L L L s L L L L Shvat
vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII-III L L L s L L L s L L L L s Adar minor
iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII-XII L L s L L L s L L L L s L Adar major
xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV-VIII L s L L L s L L L L s L L Nisan
viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII-IV s L L L s L L L L s L L L Iyar
iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX-XIII L L L s L L L L s L L L s Sivan
xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V-IX L L s L L L L s L L L s L Tammuz
ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I-V L s L L L L s L L L s L L Av
v-ix-xiii-iv-viii-xii-iii-vii-xi-ii-vi-x-I s L L L L s L L L s L L L Elul
Scale tree and tuning spectrum of 10L 3s⟨19/9⟩
Generator(ed19/9) Cents Step ratio Comments
Bright Dark L:s Hardness
9\13 895.571 398.032 1:1 1.000 Equalized 10L 3s⟨19/9⟩
52\75 896.898 396.705 6:5 1.200
43\62 897.176 396.427 5:4 1.250
77\111 897.364 396.239 9:7 1.286
34\49 897.602 396.001 4:3 1.333 Supersoft 10L 3s⟨19/9⟩
93\134 897.799 395.804 11:8 1.375
59\85 897.913 395.690 7:5 1.400
84\121 898.038 395.565 10:7 1.429
25\36 898.335 395.268 3:2 1.500 Soft 10L 3s⟨19/9⟩
91\131 898.610 394.993 11:7 1.571
66\95 898.714 394.889 8:5 1.600
107\154 898.802 394.801 13:8 1.625
41\59 898.944 394.659 5:3 1.667 Semisoft 10L 3s⟨19/9⟩
98\141 899.100 394.503 12:7 1.714
57\82 899.212 394.391 7:4 1.750
73\105 899.362 394.241 9:5 1.800
16\23 899.898 393.705 2:1 2.000 Basic 10L 3s⟨19/9⟩
Scales with tunings softer than this are proper
71\102 900.449 393.154 9:4 2.250
55\79 900.610 392.993 7:3 2.333
94\135 900.731 392.872 12:5 2.400
39\56 900.902 392.701 5:2 2.500 Semihard 10L 3s⟨19/9⟩
101\145 901.061 392.542 13:5 2.600
62\89 901.162 392.441 8:3 2.667
85\122 901.281 392.322 11:4 2.750
23\33 901.602 392.001 3:1 3.000 Hard 10L 3s⟨19/9⟩
76\109 901.962 391.641 10:3 3.333
53\76 902.118 391.485 7:2 3.500
83\119 902.261 391.342 11:3 3.667
30\43 902.514 391.089 4:1 4.000 Superhard 10L 3s⟨19/9⟩
67\96 902.827 390.776 9:2 4.500
37\53 903.081 390.522 5:1 5.000
44\63 903.469 390.134 6:1 6.000
7\10 905.522 388.081 1:0 → ∞ Collapsed 10L 3s⟨19/9⟩
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