User:Moremajorthanmajor/Greater Luachoid: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
No edit summary
No edit summary
 
(2 intermediate revisions by the same user not shown)
Line 59: Line 59:
|}
|}
{| class="wikitable"
{| class="wikitable"
! colspan="3" |Generator
!Generator
!Cents
!Cents
!Normalized Cents
!Normalized Cents
!Centishrutis
|-
|-
| |3/10
| |3/10
| |
| |360.000
|
|360.000
| |360
|360
|660
|-
|-
| |16/53
| |16/53
| |
|
| |362.264
| |362.264
|369.231
|369.231
|676.923
|-
|-
|
|45/149
|
|362.416
|369.863
|678.082
|-
|
|29/96
|29/96
|
|362.500
|362.500
|370.213
|370.213
|678.723
|-
|
|42/139
|
|362.590
|370.588
|679.412
|-
|-
| |13/43
| |13/43
| |
|
| |362.791
| |362.791
|371.429
|371.429
|680.952
|-
|-
|
|36/119
|
|363.025
|372.414
|682.757
|-
|
|23/76
|23/76
|
|363.158
|363.158
|372.973
|372.973
|683.784
|-
|-
|
|33/109
|33/109
|
|363.303
|363.303
|373.584
|373.584
|684.906
|-
|43/142
|363.380
|373.913
|-
|53/175
|363.429
|374.118
|-
|-
| |
| |
| |
|
| |363.487
| |363.487
|374.364
|374.364
|686.335
|-
|-
| |10/33
| |10/33
| |
|
| |363.636
| |363.636
|375.000
|375.000
|687.500
|-
|-
|
|57/188
|363.830
|375.824
|-
|47/155
|47/155
|
|363.871
|363.871
|376.000
|376.000
|689.333
|-
|-
|
|37/122
|37/122
|
|363.944
|363.944
|376.271
|376.271
|689.8305
|-
|-
| |
| |
| |
|
| |363.976
| |363.976
|376.448
|376.448
|690.155
|-
|-
| |
| |27/89
| |27/89
|
| |364.045
| |364.045
|376.744
|376.744
|690.698
|-
|-
| |
| |
| |
|
| |364.112
| |364.112
|377.033
|377.033
|691.227
|-
|-
| |
| |17/56
| |17/56
|
| |364.286
| |364.286
|377.778
|377.778
|692.593
|-
|
|
|41/135
|364.444
|378.4615
|693.846
|-
|-
|
|24/79
|24/79
|
|364.557
|364.557
|378.947
|378.947
|694.737
|-
|-
|
|31/102
|31/102
|
|364.706
|364.706
|379.392
|379.392
|695.918
|-
|-
|
|38/125
|38/125
|
|364.800
|364.800
|380.000
|380.000
|696.667
|-
|-
| |7/23
| |7/23
| |
|
| |365.217
| |365.217
|381.818
|381.818
|700.000
|-
|-
|
|60/197
|365.482
|382.978
|-
|53/174
|365.517
|383.132
|-
|46/151
|365.563
|383.333
|-
|39/128
|39/128
|
|365.625
|365.625
|383.607
|383.607
|703.279
|-
|-
|
|32/105
|32/105
|
|365.714
|365.714
|384.000
|384.000
|704.000
|-
|-
|
|25/82
|25/82
|
|365.854
|365.854
|384.615
|384.615
|705.182
|-
|-
| |
| |
| |
|
| |365.904
| |365.904
|384.844
|384.844
|705.5475
|-
|-
|
|68/223
|
|365.919
|384.906
|-
|43/141
|43/141
|365.9575
|365.957
|385.075
|385.075
|705.970
|-
|-
|
|
|61/200
|61/200
|366
|366.000
|385.263
|385.263
|706.316
|-
|-
| |
| |18/59
| |18/59
|
| |366.102
| |366.102
|385.714
|385.714
|707.143
|-
|-
| |
| |
| |
|
| |366.256
| |366.256
|386.402
|386.402
|708.404
|-
|-
| |
| |29/95
| |29/95
|
| |366.316
| |366.316
|386.667
|386.667
|708.889
|-
|-
|
|40/131
|40/131
|
|366.412
|366.412
|387.097
|387.097
|709.677
|-
|-
| |
| |
| |
|
| |366.414
| |366.414
|387.1065
|387.106
|709.695
|-
|-
|
|51/167
|51/167
|
|366.467
|366.467
|387.342
|387.342
|710.127
|-
|-
| |11/36
| |11/36
| |
|
| |366.667
| |366.667
|388.235
|388.235
|711.765
|-
|-
|
|37/121
|37/121
|
|366.942
|366.942
|389.474
|389.474
|713.196
|-
|
|
|63/206
|366.990
|389.691
|714.433
|-
|-
|
|26/85
|26/85
|
|367.059
|367.059
|390.000
|390.000
|715.000
|-
|-
| |15/49
| |15/49
| |
|
| |367.347
| |367.347
|391.304
|391.304
|717.391
|-
|
|49/160
|
|367.500
|392.000
|718.667
|-
|-
|
|34/111
|34/111
|
|367.568
|367.568
|392.308
|392.308
|719.231
|-
|-
| |19/62
| |19/62
| |
|
| |367.742
| |367.742
|393.103
|393.103
|720.690
|-
|-
| |4/13
| |4/13
| |
|
| |369.231
| |369.231
|400.000
|400.000
|733.333
|}
|}


== See also ==
== See also ==
[[10L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[10L 3s (33/16-equivalent)]] - harmonic subminor ninth tuning
[[10L 3s (44/21-equivalent)]] - Neogothic minor ninth tuning


[[10L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning
[[10L 3s (21/10-equivalent)]] - septimal chromatic minor ninth tuning


[[10L 3s (19/9-equivalent)]] - highest tuning
[[10L 3s (19/9-equivalent)]] - highest tuning

Latest revision as of 03:30, 27 July 2023

10L 3s(<19/9>), also known as greater luachoid is a scale pattern that expands on greater sephiroid (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.

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
Generator Cents Normalized Cents
3/10 360.000 360.000
16/53 362.264 369.231
29/96 362.500 370.213
13/43 362.791 371.429
23/76 363.158 372.973
33/109 363.303 373.584
43/142 363.380 373.913
53/175 363.429 374.118
363.487 374.364
10/33 363.636 375.000
57/188 363.830 375.824
47/155 363.871 376.000
37/122 363.944 376.271
363.976 376.448
27/89 364.045 376.744
364.112 377.033
17/56 364.286 377.778
24/79 364.557 378.947
31/102 364.706 379.392
38/125 364.800 380.000
7/23 365.217 381.818
60/197 365.482 382.978
53/174 365.517 383.132
46/151 365.563 383.333
39/128 365.625 383.607
32/105 365.714 384.000
25/82 365.854 384.615
365.904 384.844
68/223 365.919 384.906
43/141 365.957 385.075
61/200 366.000 385.263
18/59 366.102 385.714
366.256 386.402
29/95 366.316 386.667
40/131 366.412 387.097
366.414 387.106
51/167 366.467 387.342
11/36 366.667 388.235
37/121 366.942 389.474
26/85 367.059 390.000
15/49 367.347 391.304
34/111 367.568 392.308
19/62 367.742 393.103
4/13 369.231 400.000

See also

10L 3s (33/16-equivalent) - harmonic subminor ninth tuning

10L 3s (44/21-equivalent) - Neogothic minor ninth tuning

10L 3s (21/10-equivalent) - septimal chromatic minor ninth tuning

10L 3s (19/9-equivalent) - highest tuning

Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/Greater_Luachoid&oldid=121111"