7L 6s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
ArrowHead294 (talk | contribs)
15,213 edits
mNo edit summary
 
(11 intermediate revisions by 6 users not shown)
Line 1: Line 1:
For most of its generator range, this MOS is the chromatic scale of the family of temperaments which divide the perfect fifth into four equal parts, thus representing 81:80 (the syntonic comma) by +7 or -13 generators. In fact, this comma, which may be exaggerated until the point where it is 60¢, appears as the difference between the generator and the disjunct tone and as the small step when the generator is flatter than 3/20edo.
{{Infobox MOS}}
{{MOS intro}}


{| class="wikitable"
== Scale properties ==
|-
{{TAMNAMS use}}
! colspan="3" | Generator
 
! | cents
=== Intervals ===
! colspan="2" | Syntonic comma
{{MOS intervals}}
! | cents
 
! colspan="3" | <span style="font-size: 12.8000001907349px;">Generator</span>
=== Generator chain ===
|-
{{MOS genchain}}
| | 1/7
 
| |
=== Modes ===
| |
{{MOS mode degrees}}
| | 171 3/7
 
| colspan="2" style="text-align:center;" | 0
== Theory ==
| | 184 8/13
The only notable harmonic entropy minimum corresponds to [[Tetracot]] temperament, where 1 generator is a "minor whole tone" that approximates [[10/9]] and [[11/10]], and 4 generators stack to a perfect fifth (~[[3/2]]).
| |
 
| |
== Tuning spectrum ==
| | 2/13
Enipucrop range. See also [[7L&nbsp;6s, 7L&nbsp;13s, and 13L&nbsp;7s]].
|-
{{MOS tuning spectrum
| | 6/41
| 4/3 = Mitonic
| |
| 10/3 = Wollemia, Ponens
| |
| 7/2 = Modus
| | 175 25/41
| 4/1 = [[Tetracot]] is in this range
| | 29 11/41
| 5/1 = Sesquiquartififths, Monkey, Bunya
| | 20 20/59
}}
| | 183 3/59
 
| |
{{stub}}
| |
| | 9/59
|-
| |
| | 23/157
| |
| | 175.796
| | 30.573
| | 21.525
| | 182.96
| |
| | 34/223
| |
|-
| |
| | 17/116
| |
| | 175 25/29
| | 31 1/29
| | 21 39/41
| | 182 38/41
| |
| | 25/164
| |
|-
| |
| | 11/75
| |
| | 176
| | 32
| | 22 6/7
| | 182 6/7
| |
| | 16/105
| |
|-
| |
| | 16/109
| |
| | 176.147
| | 33.0275
| | 23.841
| | 182.7815
| |
| | 23/151
| |
|-
| |
| | 21/143
| |
| | 176.224
| | 33.5665
| | 24.3655
| | 182.721
| |
| | 30/197
| |
|-
| |
| | 26/177
| |
| | 176 16/59
| | 33 53/59
| | 24 56/81
| | 182 20/27
| |
| | 37/243
| |
|-
| |
| | 31/211
| |
| | 176.303
| | 34.171
| | 24.9135
| | 182.72
| |
| | 44/289
| |
|-
| |
| | 36/245
| |
| | 176 16/49
| | 34 2/7
| | 25 5/67
| | 182 46/67
| |
| | 51/335
| |
|-
| | 5/34
| |
| |
| | 176 8/17
| | 35 5/17
| | 26 1/23
| | 182 14/23
| |
| |
| | 7/46
|-
| |
| | 24/163
| |
| | 176.687
| | 36.872
| | 27.843
| | 182.4885
| |
| | 33/217
| |
|-
| |
| | 19/129
| |
| | 176 32/43
| | 37 9/43
| | 28 4/57
| | 182 26/57
| |
| | 26/171
| |
|-
| |
| | 14/95
| |
| | 176 16/19
| | 37 17/19
| | 28.8
| | 182.4
| |
| | 19/125
| |
|-
| |
| |
| | 23/156
| | 176 12/13
| | 38 6/13
| | 29 7/17
| | 182 6/17
| | 31/204
| |
| |
|-
| |
| | 9/61
| |
| | 177 3/61
| | 39 21/61
| | 30 30/79
| | 182 22/79
| |
| | 12/79
| |
|-
| |
| |
| | 22/149
| | 177.181
| | 40.2685
| | 31.414
| | 182.199
| | 29/191
| |
| |
|-
| |
| | 13/88
| |
| | 177 3/11
| | 40 10/11
| | 32 1/7
| | 182 1/7
| |
| | 17/112
| |
|-
| |
| | 17/115
| |
| | 177 9/23
| | 41 17/23
| | 33 3/29
| | 182 2/29
| |
| | 22/145
| |
|-
| |
| | 21/142
| |
| | 177 33/71
| | 42 18/71
| | 33 63/89
| | 182 2/89
| |
| | 27/178
| |
|-
| |
| | 25/169
| |
| | 177.515
| | 42.604
| | 33.825
| | 181.9905
| |
| | 32/211
| |
|-
| |
| | 29/196
| |
| | 177 27/49
| | 42 6/7
| | 34 26/61
| | 181 59/61
| |
| | 37/244
| |
|-
| |
| |
| |
| | 177.553
| | 42.871
| | 34.542
| | 181.958
| |
| |
| |
|-
| |
| | 33/223
| |
| | 177.5785
| | 43.049
| | 34.657
| | 181.9495
| |
| | 42/277
| |
|-
| |
| | 37/250
| |
| | 177.6
| | 43.2
| | 34 26/31
| | 181 29/31
| |
| | 47/310
| |
|-
| |
| | 41/277
| |
| | 177.617
| | 43.321
| | 34.985
| | 181.924
| |
| | 52/343
| |
|-
| |
| | 45/304
| |
| | 177 12/19
| | 43 8/19
| | 35 5/47
| | 181 43/47
| |
| | 57/376
| |
|-
| | 4/27
| |
| |
| | 177 7/9
| | 44 4/9
| | 36 4/11
| | 181 9/11
| |
| |
| | 5/33
|-
| |
| | 39/263
| |
| | 177.947
| | 45.585
| | 37.539
| | 181.7035
| |
| | 48/317
| |
|-
| |
| | 35/236
| |
| | 177 57/59
| | 45 45/59
| | 38 2/71
| | 181 49/71
| |
| | 43/284
| |
|-
| |
| | 31/209
| |
| | 177.99
| | 45.933
| | 38.247
| | 181.673
| |
| | 38/251
| |
|-
| |
| | 27/182
| |
| | 178 2/91
| | 46 2/13
| | 38.514
| | 181.651
| |
| | 33/218
| |
|-
| |
| | 23/155
| |
| | 178 2/31
| | 46 14/31
| | 38 34/37
| | 181 23/37
| |
| | 28/185
| |
|-
| |
| | 19/128
| |
| | 178.125
| | 46.875
| | 39 9/19
| | 181 11/19
| |
| | 23/152
| |
|-
| |
| | 15/101
| |
| | 178.218
| | 47.525
| | 40.336
| | 181.513
| |
| | 18/119
| |
|-
| |
| |
| |
| | 178.278
| | 47.946
| | 41.099
| | 181.453
| |
| |
| |
|-
| |
| | 11/74
| |
| | 178 14/37
| | 48 24/37
| | 41 37/43
| | 181 17/43
| |
| | 13/86
| |
|-
| |
| |
| | 29/195
| | 178 6/13
| | 49 3/13
| | 42 2/3
| | 181 1/3
| | 34/225
| |
| |
|-
| |
| | 18/121
| |
| | 178.512
| | 49.587
| | 43.1655
| | 181.295
| |
| | 21/139
| |
|-
| |
| | 25/168
| |
| | 178 4/7
| | 50
| | 43.75
| | 181.25
| |
| | 29/192
| |
|-
| |
| | 32/215
| |
| | 178.605
| | 50.233
| | 44 4/49
| | 181 11/49
| |
| | 37/245
| |
|-
| | 7/47
| |
| |
| | 178 34/47
| | 51 3/47
| | 45 15/53
| | 181 7/53
| |
| |
| | 8/53
|-
| |
| | 24/161
| |
| | 178.882
| | 52.174
| | 46.927
| | 181.006
| |
| | 27/179
| |
|-
| |
| | 17/114
| |
| | 178 18/19
| | 52 12/19
| | 47 13/21
| | 180 20/21
| |
| | 19/126
| |
|-
| |
| | 27/181
| |
| | 179 1/181
| | 53 7/181
| | 48.241
| | 180.814
| |
| | 30/199
| |
|-
| | 10/67
| |
| |
| | 179 7/67
| | 53 49/67
| | 49 23/73
| | 180 42/73
| |
| |
| | 11/73
|-
| |
| | 23/154
| |
| | 179 17/77
| | 54 6/11
| | 50 50/83
| | 180 42/83
| |
| | 25/166
| |
|-
| | 13/87
| |
| |
| | 179 9/29
| | 55 5/29
| | 51 19/31
| | 180 14/31
| |
| |
| | 14/93
|-
| | 3/20
| |
| |
| | 180
| colspan="2" style="text-align:center;" | 60
| | 180
| |
| |
| | 3/20
|}

Latest revision as of 22:51, 20 January 2026

↖ 6L 5s ↑ 7L 5s 8L 5s ↗
← 6L 6s 7L 6s 8L 6s →
↙ 6L 7s ↓ 7L 7s 8L 7s ↘
Scale structure
Step pattern LLsLsLsLsLsLs
sLsLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 11\13 to 6\7 (1015.4 ¢ to 1028.6 ¢)
Dark 1\7 to 2\13 (171.4 ¢ to 184.6 ¢)
TAMNAMS information
Related to 6L 1s (archaeotonic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 6L 1s
Sister 6L 7s
Daughters 13L 7s, 7L 13s
Neutralized 1L 12s
2-Flought 20L 6s, 7L 19s
Equal tunings
Equalized (L:s = 1:1) 11\13 (1015.4 ¢)
Supersoft (L:s = 4:3) 39\46 (1017.4 ¢)
Soft (L:s = 3:2) 28\33 (1018.2 ¢)
Semisoft (L:s = 5:3) 45\53 (1018.9 ¢)
Basic (L:s = 2:1) 17\20 (1020.0 ¢)
Semihard (L:s = 5:2) 40\47 (1021.3 ¢)
Hard (L:s = 3:1) 23\27 (1022.2 ¢)
Superhard (L:s = 4:1) 29\34 (1023.5 ¢)
Collapsed (L:s = 1:0) 6\7 (1028.6 ¢)
View • Talk • Edit

7L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 6 small steps, repeating every octave. 7L 6s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 1015.4 ¢ to 1028.6 ¢, or from 171.4 ¢ to 184.6 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 7L 6s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 92.3 ¢
Major 1-mosstep M1ms L 92.3 ¢ to 171.4 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 171.4 ¢ to 184.6 ¢
Augmented 2-mosstep A2ms 2L 184.6 ¢ to 342.9 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 276.9 ¢
Major 3-mosstep M3ms 2L + s 276.9 ¢ to 342.9 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 342.9 ¢ to 369.2 ¢
Major 4-mosstep M4ms 3L + s 369.2 ¢ to 514.3 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 342.9 ¢ to 461.5 ¢
Major 5-mosstep M5ms 3L + 2s 461.5 ¢ to 514.3 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 514.3 ¢ to 553.8 ¢
Major 6-mosstep M6ms 4L + 2s 553.8 ¢ to 685.7 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 514.3 ¢ to 646.2 ¢
Major 7-mosstep M7ms 4L + 3s 646.2 ¢ to 685.7 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 685.7 ¢ to 738.5 ¢
Major 8-mosstep M8ms 5L + 3s 738.5 ¢ to 857.1 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 685.7 ¢ to 830.8 ¢
Major 9-mosstep M9ms 5L + 4s 830.8 ¢ to 857.1 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 857.1 ¢ to 923.1 ¢
Major 10-mosstep M10ms 6L + 4s 923.1 ¢ to 1028.6 ¢
11-mosstep Diminished 11-mosstep d11ms 5L + 6s 857.1 ¢ to 1015.4 ¢
Perfect 11-mosstep P11ms 6L + 5s 1015.4 ¢ to 1028.6 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 1028.6 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 7L + 5s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 7L + 6s 1200.0 ¢

Generator chain

Generator chain of 7L 6s
Bright gens Scale degree Abbrev.
19 Augmented 1-mosdegree A1md
18 Augmented 3-mosdegree A3md
17 Augmented 5-mosdegree A5md
16 Augmented 7-mosdegree A7md
15 Augmented 9-mosdegree A9md
14 Augmented 11-mosdegree A11md
13 Augmented 0-mosdegree A0md
12 Augmented 2-mosdegree A2md
11 Major 4-mosdegree M4md
10 Major 6-mosdegree M6md
9 Major 8-mosdegree M8md
8 Major 10-mosdegree M10md
7 Major 12-mosdegree M12md
6 Major 1-mosdegree M1md
5 Major 3-mosdegree M3md
4 Major 5-mosdegree M5md
3 Major 7-mosdegree M7md
2 Major 9-mosdegree M9md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 2-mosdegree P2md
−2 Minor 4-mosdegree m4md
−3 Minor 6-mosdegree m6md
−4 Minor 8-mosdegree m8md
−5 Minor 10-mosdegree m10md
−6 Minor 12-mosdegree m12md
−7 Minor 1-mosdegree m1md
−8 Minor 3-mosdegree m3md
−9 Minor 5-mosdegree m5md
−10 Minor 7-mosdegree m7md
−11 Minor 9-mosdegree m9md
−12 Diminished 11-mosdegree d11md
−13 Diminished 13-mosdegree d13md
−14 Diminished 2-mosdegree d2md
−15 Diminished 4-mosdegree d4md
−16 Diminished 6-mosdegree d6md
−17 Diminished 8-mosdegree d8md
−18 Diminished 10-mosdegree d10md
−19 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 7L 6s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LLsLsLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
11|1 12 LsLLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
10|2 10 LsLsLLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
9|3 8 LsLsLsLLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
8|4 6 LsLsLsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf.
7|5 4 LsLsLsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf.
6|6 2 LsLsLsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
5|7 13 sLLsLsLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
4|8 11 sLsLLsLsLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
3|9 9 sLsLsLLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
2|10 7 sLsLsLsLLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf.
1|11 5 sLsLsLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|12 3 sLsLsLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Perf.

Theory

The only notable harmonic entropy minimum corresponds to Tetracot temperament, where 1 generator is a "minor whole tone" that approximates 10/9 and 11/10, and 4 generators stack to a perfect fifth (~3/2).

Tuning spectrum

Enipucrop range. See also 7L 6s, 7L 13s, and 13L 7s.

Scale tree and tuning spectrum of 7L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\13 1015.385 184.615 1:1 1.000 Equalized 7L 6s
61\72 1016.667 183.333 6:5 1.200
50\59 1016.949 183.051 5:4 1.250
89\105 1017.143 182.857 9:7 1.286
39\46 1017.391 182.609 4:3 1.333 Supersoft 7L 6s
Mitonic
106\125 1017.600 182.400 11:8 1.375
67\79 1017.722 182.278 7:5 1.400
95\112 1017.857 182.143 10:7 1.429
28\33 1018.182 181.818 3:2 1.500 Soft 7L 6s
101\119 1018.487 181.513 11:7 1.571
73\86 1018.605 181.395 8:5 1.600
118\139 1018.705 181.295 13:8 1.625
45\53 1018.868 181.132 5:3 1.667 Semisoft 7L 6s
107\126 1019.048 180.952 12:7 1.714
62\73 1019.178 180.822 7:4 1.750
79\93 1019.355 180.645 9:5 1.800
17\20 1020.000 180.000 2:1 2.000 Basic 7L 6s
Scales with tunings softer than this are proper
74\87 1020.690 179.310 9:4 2.250
57\67 1020.896 179.104 7:3 2.333
97\114 1021.053 178.947 12:5 2.400
40\47 1021.277 178.723 5:2 2.500 Semihard 7L 6s
103\121 1021.488 178.512 13:5 2.600
63\74 1021.622 178.378 8:3 2.667
86\101 1021.782 178.218 11:4 2.750
23\27 1022.222 177.778 3:1 3.000 Hard 7L 6s
75\88 1022.727 177.273 10:3 3.333 Wollemia, Ponens
52\61 1022.951 177.049 7:2 3.500 Modus
81\95 1023.158 176.842 11:3 3.667
29\34 1023.529 176.471 4:1 4.000 Superhard 7L 6s
Tetracot is in this range
64\75 1024.000 176.000 9:2 4.500
35\41 1024.390 175.610 5:1 5.000 Sesquiquartififths, Monkey, Bunya
41\48 1025.000 175.000 6:1 6.000
6\7 1028.571 171.429 1:0 → ∞ Collapsed 7L 6s
This page is a stub. You can help the Xenharmonic Wiki by expanding it.
Retrieved from "https://en.xen.wiki/index.php?title=7L_6s&oldid=222058"