6L 4s: Difference between revisions

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Line 4: Line 4:
| nSmallSteps = 4
| nSmallSteps = 4
| Equalized = 2
| Equalized = 2
| Paucitonic = 1
| Collapsed = 1
| Pattern = LsLsLLsLsL
| Pattern = LLsLsLLsLs
| Name = dipentic
| Name = lemon
}}
}}
{{MOS intro}}
Supported temperaments include [[antikythera]], [[lemba]], and [[echidnic]].


'''6L 4s''' is a [[MOS]] pattern with 6 large steps and 4 small steps. Good temperaments include [[antikythera]], [[lemba]], and [[echidnic]].
== Scale properties ==
{{TAMNAMS use}}
 
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}


== Scale tree ==
== Scale tree ==
{| class="wikitable center-all"
{{MOS tuning spectrum
! colspan="6" rowspan="2" | Generator
| 5/4 = Echidnic
! colspan="2" | Cents
| 4/3 = Baladic
! rowspan="2" | L
| 3/2 = Lemba
! rowspan="2" | s
| 8/3 = Divination
! rowspan="2" | L/s
| 3/1 = Antikythera/astrology
! rowspan="2" | Comments
| 10/3 = Wizard
|-
}}
! Chroma-positive
 
! Chroma-negative
{{todo|expand}}
|-
| 3\10 || || || || || || 360.000 || 240.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\56 || 364.286 || 235.714 || 6 || 5 || 1.200 ||
|-
| || || || || 14\46 || || 365.217 || 234.783 || 5 || 4 || 1.250 || Echidnic
|-
| || || || || || 25\82 || 365.854 || 234.146 || 9 || 7 || 1.286 ||
|-
| || || || 11\36 || || || 366.667 || 233.333 || 4 || 3 || 1.333 || Baladic
|-
| || || || || || 30\98 || 367.347 || 232.653 || 11 || 8 || 1.375 ||
|-
| || || || || 19\62 || || 367.742 || 232.258 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\88 || 368.182 || 231.818 || 10 || 7 || 1.428 ||
|-
| || || 8\26 || || || || 369.231 || 230.769 || 3 || 2 || 1.500 || L/s = 3/2, lemba
|-
| || || || || || 29\94 || 370.213 || 229.787 || 11 || 7 || 1.571 ||
|-
| || || || || 21\68 || || 370.588 || 229.412 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\110 || 370.909 || 229.091 || 13 || 8 || 1.625 || Unnamed golden tuning
|-
| || || || 13\42 || || || 371.429 || 228.571 || 5 || 3 || 1.667 ||
|-
| || || || || || 31\100 || 372.000 || 228.000 || 12 || 7 || 1.714 ||
|-
| || || || || 18\58 || || 372.414 || 227.586 || 7 || 4 || 1.750 ||
|-
| || || || || || 23\74 || 372.973 || 227.027 || 9 || 5 || 1.800 ||
|-
| || 5\16 || || || || || 375.000 || 225.000 || 2 || 1 || 2.000 || Basic dipentic<br>(Generators smaller than this are proper)
|-
| || || || || || 22\70 || 377.143 || 222.857 || 9 || 4 || 2.250 ||
|-
| || || || || 17\54 || || 377.778 || 222.222 || 7 || 3 || 2.333 ||
|-
| || || || || || 29\92 || 378.261 || 221.739 || 12 || 5 || 2.400 ||
|-
| || || || 12\38 || || || 378.947 || 221.053 || 5 || 2 || 2.500 ||
|-
| || || || || || 31\98 || 379.592 || 220.408 || 13 || 5 || 2.600 || Unnamed golden tuning
|-
| || || || || 19\60 || || 380.000 || 220.000 || 8 || 3 || 2.667 || Divination
|-
| || || || || || 26\82 || 380.488 || 219.512 || 11 || 4 || 2.750 || Soothsaying
|-
| || || 7\22 || || || || 381.818 || 218.182 || 3 || 1 || 3.000 || L/s = 3/1, antikythera/astrology
|-
| || || || || || 23\72 || 383.333 || 216.667 || 10 || 3 || 3.333 || Wizard
|-
| || || || || 16\50 || || 384.000 || 216.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\78 || 384.615 || 215.385 || 11 || 3 || 3.667 ||
|-
| || || || 9\28 || || || 385.714 || 214.286 || 4 || 1 || 4.000 ||
|-
| || || || || || 20\62 || 387.097 || 212.903 || 9 || 2 || 4.500 ||
|-
| || || || || 11\34 || || 388.235 || 211.765 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\40 || 390.000 || 210.000 || 6 || 1 || 6.000 ||
|-
| 2\6 || || || || || || 400.000 || 200.000 || 1 || 0 || → inf ||
|}


[[Category:Abstract MOS patterns]]
[[Category:lemon| ]]
[[Category:Dipentic| ]] <!-- main article -->
[[Category:10-tone scales]]<!-- main article -->

Latest revision as of 15:59, 10 April 2025

↖ 5L 3s ↑ 6L 3s 7L 3s ↗
← 5L 4s 6L 4s 7L 4s →
↙ 5L 5s ↓ 6L 5s 7L 5s ↘ 
┌╥╥┬╥┬╥╥┬╥┬┐
│║║│║│║║│║││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLs
sLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 3\10 to 2\6 (360.0 ¢ to 400.0 ¢)
Dark 1\6 to 2\10 (200.0 ¢ to 240.0 ¢)
TAMNAMS information
Name lemon
Prefix lem-
Abbrev. le
Related MOS scales
Parent 4L 2s
Sister 4L 6s
Daughters 10L 6s, 6L 10s
Neutralized 2L 8s
2-Flought 16L 4s, 6L 14s
Equal tunings
Equalized (L:s = 1:1) 3\10 (360.0 ¢)
Supersoft (L:s = 4:3) 11\36 (366.7 ¢)
Soft (L:s = 3:2) 8\26 (369.2 ¢)
Semisoft (L:s = 5:3) 13\42 (371.4 ¢)
Basic (L:s = 2:1) 5\16 (375.0 ¢)
Semihard (L:s = 5:2) 12\38 (378.9 ¢)
Hard (L:s = 3:1) 7\22 (381.8 ¢)
Superhard (L:s = 4:1) 9\28 (385.7 ¢)
Collapsed (L:s = 1:0) 2\6 (400.0 ¢)

6L 4s, named lemon in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 4 small steps, with a period of 3 large steps and 2 small steps that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 360 ¢ to 400 ¢, or from 200 ¢ to 240 ¢. Supported temperaments include antikythera, lemba, and echidnic.

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 6L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-lemstep Perfect 0-lemstep P0les 0 0.0 ¢
1-lemstep Minor 1-lemstep m1les s 0.0 ¢ to 120.0 ¢
Major 1-lemstep M1les L 120.0 ¢ to 200.0 ¢
2-lemstep Perfect 2-lemstep P2les L + s 200.0 ¢ to 240.0 ¢
Augmented 2-lemstep A2les 2L 240.0 ¢ to 400.0 ¢
3-lemstep Diminished 3-lemstep d3les L + 2s 200.0 ¢ to 360.0 ¢
Perfect 3-lemstep P3les 2L + s 360.0 ¢ to 400.0 ¢
4-lemstep Minor 4-lemstep m4les 2L + 2s 400.0 ¢ to 480.0 ¢
Major 4-lemstep M4les 3L + s 480.0 ¢ to 600.0 ¢
5-lemstep Perfect 5-lemstep P5les 3L + 2s 600.0 ¢
6-lemstep Minor 6-lemstep m6les 3L + 3s 600.0 ¢ to 720.0 ¢
Major 6-lemstep M6les 4L + 2s 720.0 ¢ to 800.0 ¢
7-lemstep Perfect 7-lemstep P7les 4L + 3s 800.0 ¢ to 840.0 ¢
Augmented 7-lemstep A7les 5L + 2s 840.0 ¢ to 1000.0 ¢
8-lemstep Diminished 8-lemstep d8les 4L + 4s 800.0 ¢ to 960.0 ¢
Perfect 8-lemstep P8les 5L + 3s 960.0 ¢ to 1000.0 ¢
9-lemstep Minor 9-lemstep m9les 5L + 4s 1000.0 ¢ to 1080.0 ¢
Major 9-lemstep M9les 6L + 3s 1080.0 ¢ to 1200.0 ¢
10-lemstep Perfect 10-lemstep P10les 6L + 4s 1200.0 ¢

Generator chain

Generator chain of 6L 4s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
7 Augmented 1-lemdegree A1led Augmented 6-lemdegree A6led
6 Augmented 3-lemdegree A3led Augmented 8-lemdegree A8led
5 Augmented 0-lemdegree A0led Augmented 5-lemdegree A5led
4 Augmented 2-lemdegree A2led Augmented 7-lemdegree A7led
3 Major 4-lemdegree M4led Major 9-lemdegree M9led
2 Major 1-lemdegree M1led Major 6-lemdegree M6led
1 Perfect 3-lemdegree P3led Perfect 8-lemdegree P8led
0 Perfect 0-lemdegree
Perfect 5-lemdegree		 P0led
P5led		 Perfect 5-lemdegree
Perfect 10-lemdegree		 P5led
P10led
−1 Perfect 2-lemdegree P2led Perfect 7-lemdegree P7led
−2 Minor 4-lemdegree m4led Minor 9-lemdegree m9led
−3 Minor 1-lemdegree m1led Minor 6-lemdegree m6led
−4 Diminished 3-lemdegree d3led Diminished 8-lemdegree d8led
−5 Diminished 5-lemdegree d5led Diminished 10-lemdegree d10led
−6 Diminished 2-lemdegree d2led Diminished 7-lemdegree d7led
−7 Diminished 4-lemdegree d4led Diminished 9-lemdegree d9led

Modes

Scale degrees of the modes of 6L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (lemdegree)
0 1 2 3 4 5 6 7 8 9 10
8|0(2) 1 LLsLsLLsLs Perf. Maj. Aug. Perf. Maj. Perf. Maj. Aug. Perf. Maj. Perf.
6|2(2) 4 LsLLsLsLLs Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf.
4|4(2) 2 LsLsLLsLsL Perf. Maj. Perf. Perf. Min. Perf. Maj. Perf. Perf. Min. Perf.
2|6(2) 5 sLLsLsLLsL Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf.
0|8(2) 3 sLsLLsLsLL Perf. Min. Perf. Dim. Min. Perf. Min. Perf. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\10 360.000 240.000 1:1 1.000 Equalized 6L 4s
17\56 364.286 235.714 6:5 1.200
14\46 365.217 234.783 5:4 1.250 Echidnic
25\82 365.854 234.146 9:7 1.286
11\36 366.667 233.333 4:3 1.333 Supersoft 6L 4s
Baladic
30\98 367.347 232.653 11:8 1.375
19\62 367.742 232.258 7:5 1.400
27\88 368.182 231.818 10:7 1.429
8\26 369.231 230.769 3:2 1.500 Soft 6L 4s
Lemba
29\94 370.213 229.787 11:7 1.571
21\68 370.588 229.412 8:5 1.600
34\110 370.909 229.091 13:8 1.625
13\42 371.429 228.571 5:3 1.667 Semisoft 6L 4s
31\100 372.000 228.000 12:7 1.714
18\58 372.414 227.586 7:4 1.750
23\74 372.973 227.027 9:5 1.800
5\16 375.000 225.000 2:1 2.000 Basic 6L 4s
Scales with tunings softer than this are proper
22\70 377.143 222.857 9:4 2.250
17\54 377.778 222.222 7:3 2.333
29\92 378.261 221.739 12:5 2.400
12\38 378.947 221.053 5:2 2.500 Semihard 6L 4s
31\98 379.592 220.408 13:5 2.600
19\60 380.000 220.000 8:3 2.667 Divination
26\82 380.488 219.512 11:4 2.750
7\22 381.818 218.182 3:1 3.000 Hard 6L 4s
Antikythera/astrology
23\72 383.333 216.667 10:3 3.333 Wizard
16\50 384.000 216.000 7:2 3.500
25\78 384.615 215.385 11:3 3.667
9\28 385.714 214.286 4:1 4.000 Superhard 6L 4s
20\62 387.097 212.903 9:2 4.500
11\34 388.235 211.765 5:1 5.000
13\40 390.000 210.000 6:1 6.000
2\6 400.000 200.000 1:0 → ∞ Collapsed 6L 4s
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