2L 7s

From Xenharmonic Wiki
Jump to navigation Jump to search
↖ 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 diatonic interval categories.

Intervals

The intervals of 2L 7s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-balstep and perfect 9-balstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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

A chain of bright generators, each a perfect 4-balstep, produces the following scale degrees. A chain of 9 bright generators contains the scale degrees of one of the modes of 2L 7s. Expanding the chain to 11 scale degrees produces the modes of either 9L 2s (for soft-of-basic tunings) or 2L 9s (for hard-of-basic tunings).

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
Retrieved from "https://en.xen.wiki/index.php?title=2L_7s&oldid=183779"