6L 7s: Difference between revisions

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{{Infobox MOS}}
{{Infobox MOS}}
{{MOS intro}}
This MOS is the chromatic scale of a family of temperaments which are index 2 [[subtemperaments]] of various [[meantone]] temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/[[Mohajira]] is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).


This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).
==Modes==
{{MOS intro}}


==Scale tree==
{| class="wikitable"
{| class="wikitable"
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Revision as of 11:08, 12 February 2024

↖ 5L 6s ↑ 6L 6s 7L 6s ↗
← 5L 7s 6L 7s 7L 7s →
↙ 5L 8s ↓ 6L 8s 7L 8s ↘
Scale structure
Step pattern LsLsLsLsLsLss
ssLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 2\13 to 1\6 (184.6 ¢ to 200.0 ¢)
Dark 5\6 to 11\13 (1000.0 ¢ to 1015.4 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 1s
Sister 7L 6s
Daughters 13L 6s, 6L 13s
Neutralized 12L 1s
2-Flought 19L 7s, 6L 20s
Equal tunings
Equalized (L:s = 1:1) 2\13 (184.6 ¢)
Supersoft (L:s = 4:3) 7\45 (186.7 ¢)
Soft (L:s = 3:2) 5\32 (187.5 ¢)
Semisoft (L:s = 5:3) 8\51 (188.2 ¢)
Basic (L:s = 2:1) 3\19 (189.5 ¢)
Semihard (L:s = 5:2) 7\44 (190.9 ¢)
Hard (L:s = 3:1) 4\25 (192.0 ¢)
Superhard (L:s = 4:1) 5\31 (193.5 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)
View • Talk • Edit

6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6 ¢ to 200 ¢, or from 1000 ¢ to 1015.4 ¢. This MOS is the chromatic scale of a family of temperaments which are index 2 subtemperaments of various meantone temperaments. It is a great early step into un-syntonic temperaments by virtue of this property, though admittedly Neutral thirds/Mohajira is greater in this respect if you don't mind essentially giving up major and minor seconds/sevenths and thirds/sixths (syntonic temperaments are index 2 subtemperaments of them) because it at least has an albitonic sized MOS which feels like a division of the octave, which cannot be said for the temperaments which this scale belongs to (Happy and Grumpy scales have a very strong period dysphoric feeling due to the common practice use of the equally divided chromatic scale, and Grumpy scales have it stronger because their small step is the the odd step out).

Modes

6L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 7 small steps, repeating every octave. 6L 7s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 184.6 ¢ to 200 ¢, or from 1000 ¢ to 1015.4 ¢.

Scale tree

Generator cents 3g 5g
2/13 184.615 553.846 923.077
9/58 186.207 558.621 931.0345
16/103 186.408 559.223 932.039
7/45 186.667 560 933.333
19/122 186.885 560.656 934.426
12/77 187.013 561.039 935.065
17/109 187.156 561.468 935.78
22/141 187.234 561.702 936.17
5/32 187.5 562.5 937.5
23/147 187.755 563.265 938.7755
187.823 563.47 939.116
18/115 187.826 563.478 939.103
13/83 187.951 563.855 939.759
188.03 564.089 940.149
8/51 188.235 564.706 941.1765
188.501 565.502 942.503
11/70 188.571 565.714 942.857
14/89 188.764 566.2921 943.82
17/108 188.889 566.667 944.444
20/127 188.976 566.929 944.882
23/146 189.041 567.123 945.2055
26/165 189.091 567.273 945.4545
29/184 189.13 567.391 945.652
32/203 189.163 567.488 945.813
35/222 189.189 567.568 945.946
38/241 189.212 567.635 946.037
3/19 189.474 568.421 947.368
31/196 189.796 568.388 948.98
28/177 189.8305 568.4915 949.1525
25/158 189.873 568.62 949.367
22/139 189.928 569.784 949.64
19/120 190 570 950
16/101 190.099 570.297 950.495
13/82 190.244 570.732 951.2195
10/63 190.476 571.429 952.381
17/107 190.654 571.963 953.271
7/44 190.909 572.727 954.5455
18/113 191.15 573.451 955.752
191.193 573.578 955.963
11/69 191.304 573.913 956.522
191.42 574.26 957.1
15/94 191.489 574.468 957.447
19/119 191.597 574.79 957.983
23/144 191.667 575 958.333
27/169 191.716 575.148 958.58
31/194 191.753 575.258 959.505
4/25 192 576 960
192.263 576.789 961.315
21/131 192.366 577.11 961.832
17/106 192.453 577.3585 962.264
13/81 192.592 577.778 962.963
22/137 192.701 578.102 963.504
9/56 192.857 578.571 964.286
14/87 193.103 579.31 965.517
19/118 193.22 579.661 966.102
5/31 193.548 580.645 967.742
26/161 193.789 581.3665 968.944
21/130 193.846 581.5385 969.231
16/99 193.94 581.818 969.697
11/68 194.118 582.353 970.588
17/105 194.286 582.857 971.143
6/37 194.595 583.784 972.973
1/6 200 600 1000
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