2L 7s: Difference between revisions

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'''2L 7s''' is a MOS pattern with generators ranging from 533.33 cents ([[9edo]]) to 600 cents ([[2edo]]).
{{MOS intro}}
 
== Names ==
== Names ==
This scale is called '''balzano''' in [[TAMNAMS]] nomenclature.
This scale is called '''balzano''' in [[TAMNAMS]] nomenclature.


== Intervals ==
== Scale properties ==
Note: In TAMNAMS, a k-step interval class in balzano may be called a "k-step", "k-mosstep", or "k-balstep" (/bæl-/). 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
{{TAMNAMS use}}


== Modes ==
=== Intervals ===
* 8|0 LsssLssss
{{MOS intervals}}
* 7|1 LssssLsss
* 6|2 sLsssLsss
* 5|3 sLssssLss
* 4|4 ssLsssLss
* 3|5 ssLssssLs
* 2|6 sssLsssLs
* 1|7 sssLssssL
* 0|8 ssssLsssL


== Scale tree ==
=== Generator chain ===
Generator ranges:
{{MOS genchain}}
* Chroma-positive generator: 533.3333 cents (4\9) to 600 cents (1\2)
* Chroma-negative generator: 600 cents (1\2) to 666.6667 cents (5\9)


{| class="wikitable"
=== Modes ===
|-
{{MOS mode degrees}}
! colspan="5" | Generator
! | Generator
! | L
! | s
! | Comments
|-
| | 4\9
| |
| |
| |
| |
| | 533.33
| | 133.33
| | 133.33
| style="text-align:center;" |
|-
|
|
|
|
|17\39
|536.84
|157.895
|126.32
|
|-
|
|
|
|13\29
|
|537.93
|165.52
|124.14
|
|-
| |
| |
| | 9\20
| |
| |
| | 540
| | 180
| | 120
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 540.84
| | 185.86
| | 118.325
| |
|-
| |
| |
| |
| |
| | 23\51
| | 541.18
| | 188.235
| | 117.65
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 541.38
| | 189.69
| | 117.23
| |
|-
| |
| |
| |
| | 14\31
| |
| | 541.935
| | 193.55
| | 116.13
| style="text-align:center;" | Casablanca is around here.
|-
| |
| |
| |
| |
| |
| | 542.66
| | 198.63
| | 114.68
| |
|-
| |
| | 5\11
| |
| |
| |
| | 545.45
| | 218.18
| | 109.09
| style="text-align:center;" |
|-
| |
| |
| |
| | 11\24
| |
| | 550
| | 250
| | 100
| |
|-
| |
| |
| |
| |
| |
| | 550.965
| | 256.75
| | 98.07
| |
|-
| |
| |
| |
| |
| | 17\37
| | 551.35
| | 259.46
| | 97.3
| |
|-
| |
| |
| |
| |
| |
| | 551.755
| | 262.29
| | 96.49
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| | 6\13
| |
| |
| | 553.85
| | 276.92
| | 92.31
| style="text-align:center;" | L/s = 3
|-
| |
| |
| |
| |
| |
| | 554.83
| | 283.81
| | 90.34
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| |
| |
| | 13\28
| | 557.14
| | 300
| | 85.14
| style="text-align:center;" | Thuja is around here.
|-
| |
| |
| |
| | 7\15
| |
| | 560
| | 320
| | 80
| style="text-align:center;" | L/s = 4
|-
|
|
|
|
|8\17
|564.71
|352.94
|70.59
|
|-
| | 1\2
| |
| |
| |
| |
| | 600
| | 600
| | 0
| style="text-align:center;" |
|}


Around L = 300¢ and s = 85¢, thuja appears, which is a complex temperament whose generator represents 11/8.
== Scale tree ==
{{MOS tuning spectrum
| 11/3 = [[Thuja]]
| 5/3 = [[Casablanca]]
}}


[[Category:9-tone scales]]
[[Category:9-tone scales]]
[[Category:Balzano| ]]
[[Category:Balzano| ]]

Latest revision as of 18:56, 3 March 2025

↖ 1L 6s ↑ 2L 6s 3L 6s ↗
← 1L 7s 2L 7s 3L 7s →
↙ 1L 8s ↓ 2L 8s 3L 8s ↘ 
┌╥┬┬┬╥┬┬┬┬┐
│║│││║│││││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssLssss
ssssLsssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\9 to 1\2 (533.3 ¢ to 600.0 ¢)
Dark 1\2 to 5\9 (600.0 ¢ to 666.7 ¢)
TAMNAMS information
Name balzano
Prefix bal-
Abbrev. bz
Related MOS scales
Parent 2L 5s
Sister 7L 2s
Daughters 9L 2s, 2L 9s
Neutralized 4L 5s
2-Flought 11L 7s, 2L 16s
Equal tunings
Equalized (L:s = 1:1) 4\9 (533.3 ¢)
Supersoft (L:s = 4:3) 13\29 (537.9 ¢)
Soft (L:s = 3:2) 9\20 (540.0 ¢)
Semisoft (L:s = 5:3) 14\31 (541.9 ¢)
Basic (L:s = 2:1) 5\11 (545.5 ¢)
Semihard (L:s = 5:2) 11\24 (550.0 ¢)
Hard (L:s = 3:1) 6\13 (553.8 ¢)
Superhard (L:s = 4:1) 7\15 (560.0 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 7s, named balzano in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 7 small steps, repeating every octave. Generators that produce this scale range from 533.3 ¢ to 600 ¢, or from 600 ¢ to 666.7 ¢.

Names

This scale is called balzano in TAMNAMS nomenclature.

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 2L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-balstep Perfect 0-balstep P0bzs 0 0.0 ¢
1-balstep Minor 1-balstep m1bzs s 0.0 ¢ to 133.3 ¢
Major 1-balstep M1bzs L 133.3 ¢ to 600.0 ¢
2-balstep Minor 2-balstep m2bzs 2s 0.0 ¢ to 266.7 ¢
Major 2-balstep M2bzs L + s 266.7 ¢ to 600.0 ¢
3-balstep Minor 3-balstep m3bzs 3s 0.0 ¢ to 400.0 ¢
Major 3-balstep M3bzs L + 2s 400.0 ¢ to 600.0 ¢
4-balstep Diminished 4-balstep d4bzs 4s 0.0 ¢ to 533.3 ¢
Perfect 4-balstep P4bzs L + 3s 533.3 ¢ to 600.0 ¢
5-balstep Perfect 5-balstep P5bzs L + 4s 600.0 ¢ to 666.7 ¢
Augmented 5-balstep A5bzs 2L + 3s 666.7 ¢ to 1200.0 ¢
6-balstep Minor 6-balstep m6bzs L + 5s 600.0 ¢ to 800.0 ¢
Major 6-balstep M6bzs 2L + 4s 800.0 ¢ to 1200.0 ¢
7-balstep Minor 7-balstep m7bzs L + 6s 600.0 ¢ to 933.3 ¢
Major 7-balstep M7bzs 2L + 5s 933.3 ¢ to 1200.0 ¢
8-balstep Minor 8-balstep m8bzs L + 7s 600.0 ¢ to 1066.7 ¢
Major 8-balstep M8bzs 2L + 6s 1066.7 ¢ to 1200.0 ¢
9-balstep Perfect 9-balstep P9bzs 2L + 7s 1200.0 ¢

Generator chain

Generator chain of 2L 7s
Bright gens Scale degree Abbrev.
10 Augmented 4-baldegree A4bzd
9 Augmented 0-baldegree A0bzd
8 Augmented 5-baldegree A5bzd
7 Major 1-baldegree M1bzd
6 Major 6-baldegree M6bzd
5 Major 2-baldegree M2bzd
4 Major 7-baldegree M7bzd
3 Major 3-baldegree M3bzd
2 Major 8-baldegree M8bzd
1 Perfect 4-baldegree P4bzd
0 Perfect 0-baldegree
Perfect 9-baldegree		 P0bzd
P9bzd
−1 Perfect 5-baldegree P5bzd
−2 Minor 1-baldegree m1bzd
−3 Minor 6-baldegree m6bzd
−4 Minor 2-baldegree m2bzd
−5 Minor 7-baldegree m7bzd
−6 Minor 3-baldegree m3bzd
−7 Minor 8-baldegree m8bzd
−8 Diminished 4-baldegree d4bzd
−9 Diminished 9-baldegree d9bzd
−10 Diminished 5-baldegree d5bzd

Modes

Scale degrees of the modes of 2L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (baldegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LsssLssss Perf. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Perf.
7|1 5 LssssLsss Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
6|2 9 sLsssLsss Perf. Min. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
5|3 4 sLssssLss Perf. Min. Maj. Maj. Perf. Perf. Min. Maj. Maj. Perf.
4|4 8 ssLsssLss Perf. Min. Min. Maj. Perf. Perf. Min. Maj. Maj. Perf.
3|5 3 ssLssssLs Perf. Min. Min. Maj. Perf. Perf. Min. Min. Maj. Perf.
2|6 7 sssLsssLs Perf. Min. Min. Min. Perf. Perf. Min. Min. Maj. Perf.
1|7 2 sssLssssL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|8 6 ssssLsssL Perf. Min. Min. Min. Dim. Perf. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 7s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\9 533.333 666.667 1:1 1.000 Equalized 2L 7s
21\47 536.170 663.830 6:5 1.200
17\38 536.842 663.158 5:4 1.250
30\67 537.313 662.687 9:7 1.286
13\29 537.931 662.069 4:3 1.333 Supersoft 2L 7s
35\78 538.462 661.538 11:8 1.375
22\49 538.776 661.224 7:5 1.400
31\69 539.130 660.870 10:7 1.429
9\20 540.000 660.000 3:2 1.500 Soft 2L 7s
32\71 540.845 659.155 11:7 1.571
23\51 541.176 658.824 8:5 1.600
37\82 541.463 658.537 13:8 1.625
14\31 541.935 658.065 5:3 1.667 Semisoft 2L 7s
Casablanca
33\73 542.466 657.534 12:7 1.714
19\42 542.857 657.143 7:4 1.750
24\53 543.396 656.604 9:5 1.800
5\11 545.455 654.545 2:1 2.000 Basic 2L 7s
Scales with tunings softer than this are proper
21\46 547.826 652.174 9:4 2.250
16\35 548.571 651.429 7:3 2.333
27\59 549.153 650.847 12:5 2.400
11\24 550.000 650.000 5:2 2.500 Semihard 2L 7s
28\61 550.820 649.180 13:5 2.600
17\37 551.351 648.649 8:3 2.667
23\50 552.000 648.000 11:4 2.750
6\13 553.846 646.154 3:1 3.000 Hard 2L 7s
19\41 556.098 643.902 10:3 3.333
13\28 557.143 642.857 7:2 3.500
20\43 558.140 641.860 11:3 3.667 Thuja
7\15 560.000 640.000 4:1 4.000 Superhard 2L 7s
15\32 562.500 637.500 9:2 4.500
8\17 564.706 635.294 5:1 5.000
9\19 568.421 631.579 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 7s
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