4L 5s
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Scale structure
Step pattern
LsLsLsLss
ssLsLsLsL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
2\9 to 1\4 (266.7¢ to 300.0¢)
Dark
3\4 to 7\9 (900.0¢ to 933.3¢)
TAMNAMS information
Name
gramitonic
Prefix
gram-
Abbrev.
gm
Related MOS scales
Parent
4L 1s
Sister
5L 4s
Daughters
9L 4s, 4L 9s
Neutralized
8L 1s
2-Flought
13L 5s, 4L 14s
Equal tunings
Equalized (L:s = 1:1)
2\9 (266.7¢)
Supersoft (L:s = 4:3)
7\31 (271.0¢)
Soft (L:s = 3:2)
5\22 (272.7¢)
Semisoft (L:s = 5:3)
8\35 (274.3¢)
Basic (L:s = 2:1)
3\13 (276.9¢)
Semihard (L:s = 5:2)
7\30 (280.0¢)
Hard (L:s = 3:1)
4\17 (282.4¢)
Superhard (L:s = 4:1)
5\21 (285.7¢)
Collapsed (L:s = 1:0)
1\4 (300.0¢)
- For the tritave-equivalent 4L 5s pattern, see 4L 5s (3/1-equivalent).
| ↖ 3L 4s | ↑ 4L 4s | 5L 4s ↗ |
| ← 3L 5s | 4L 5s | 5L 5s → |
| ↙ 3L 6s | ↓ 4L 6s | 5L 6s ↘ |
┌╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
ssLsLsLsL
4L 5s, named gramitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 5 small steps, repeating every octave. Generators that produce this scale range from 266.7¢ to 300¢, or from 900¢ to 933.3¢.
Names
The TAMNAMS name for this pattern is gramitonic (from grave minor third).
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
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-gramstep | Perfect 0-gramstep | P0gms | 0 | 0.0¢ |
| 1-gramstep | Minor 1-gramstep | m1gms | s | 0.0¢ to 133.3¢ |
| Major 1-gramstep | M1gms | L | 133.3¢ to 300.0¢ | |
| 2-gramstep | Diminished 2-gramstep | d2gms | 2s | 0.0¢ to 266.7¢ |
| Perfect 2-gramstep | P2gms | L + s | 266.7¢ to 300.0¢ | |
| 3-gramstep | Minor 3-gramstep | m3gms | L + 2s | 300.0¢ to 400.0¢ |
| Major 3-gramstep | M3gms | 2L + s | 400.0¢ to 600.0¢ | |
| 4-gramstep | Minor 4-gramstep | m4gms | L + 3s | 300.0¢ to 533.3¢ |
| Major 4-gramstep | M4gms | 2L + 2s | 533.3¢ to 600.0¢ | |
| 5-gramstep | Minor 5-gramstep | m5gms | 2L + 3s | 600.0¢ to 666.7¢ |
| Major 5-gramstep | M5gms | 3L + 2s | 666.7¢ to 900.0¢ | |
| 6-gramstep | Minor 6-gramstep | m6gms | 2L + 4s | 600.0¢ to 800.0¢ |
| Major 6-gramstep | M6gms | 3L + 3s | 800.0¢ to 900.0¢ | |
| 7-gramstep | Perfect 7-gramstep | P7gms | 3L + 4s | 900.0¢ to 933.3¢ |
| Augmented 7-gramstep | A7gms | 4L + 3s | 933.3¢ to 1200.0¢ | |
| 8-gramstep | Minor 8-gramstep | m8gms | 3L + 5s | 900.0¢ to 1066.7¢ |
| Major 8-gramstep | M8gms | 4L + 4s | 1066.7¢ to 1200.0¢ | |
| 9-gramstep | Perfect 9-gramstep | P9gms | 4L + 5s | 1200.0¢ |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (gramdegree) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||
| 8|0 | 1 | LsLsLsLss | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Maj. | Perf. |
| 7|1 | 3 | LsLsLssLs | Perf. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Perf. |
| 6|2 | 5 | LsLssLsLs | Perf. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 5|3 | 7 | LssLsLsLs | Perf. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 4|4 | 9 | sLsLsLsLs | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Maj. | Perf. |
| 3|5 | 2 | sLsLsLssL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Perf. |
| 2|6 | 4 | sLsLssLsL | Perf. | Min. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Perf. |
| 1|7 | 6 | sLssLsLsL | Perf. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
| 0|8 | 8 | ssLsLsLsL | Perf. | Min. | Dim. | Min. | Min. | Min. | Min. | Perf. | Min. | Perf. |
Proposed names
Lilly Flores proposed using the Greek name relating to water as mode names. The names are in reference to the scale's former name orwelloid because the word Orwell comes from 'a spring situated near a promontory'.
| UDP | Cyclic order |
Step pattern |
Mode names |
|---|---|---|---|
| 8|0 | 1 | LsLsLsLss | Roi |
| 7|1 | 3 | LsLsLssLs | Steno |
| 6|2 | 5 | LsLssLsLs | Limni |
| 5|3 | 7 | LssLsLsLs | Telma |
| 4|4 | 9 | sLsLsLsLs | Krini |
| 3|5 | 2 | sLsLsLssL | Elos |
| 2|6 | 4 | sLsLssLsL | Mychos |
| 1|7 | 6 | sLssLsLsL | Akti |
| 0|8 | 8 | ssLsLsLsL | Dini |
Theory
The only low harmonic entropy minimum corresponds to orwell temperament, where 1 generator approximates 7/6, 2 generators approximate 11/8, and 3 generators approximate 8/5.
Tuning ranges
Parasoft
Parasoft tunings of 4L 5s have a step ratio between 4/3 and 3/2, implying a generator sharper than 7\31 = 270.97¢ and flatter than 5\22 = 272.73¢.
Parasoft 4L 5s EDOs include 22edo, 31edo, 53edo, and 84edo.
- 22edo can be used to make large and small steps more distinct (the step ratio is 3/2).
- 31edo can be used for its nearly pure 5/4.
- 53edo can be used for its nearly pure 3/2 and good 5/4.
The sizes of the generator, large step and small step of 4L 5s are as follows in various parasoft 4L 5s tunings.
| 22edo | 31edo | 53edo | 84edo | JI intervals represented | |
|---|---|---|---|---|---|
| generator (g) | 5\22, 272.73 | 7\31, 270.97 | 12\53, 271.70 | 19\84, 271.43 | 7/6 |
| L (5g - octave) | 3\22, 163.64 | 4\31, 154.84 | 7\53, 158.49 | 11\84, 157.14 | 12/11, 11/10 |
| s (octave - 4g) | 2\22, 109.09 | 3\31, 116.13 | 5\53, 113.21 | 8\84, 114.29 | 16/15, 15/14 |
This set of JI interpretations (g = 7/6, 2g = 11/8, 3g = 8/5, 7g = 3/2) is called 11-limit orwell temperament in regular temperament theory.
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 2\9 | 266.667 | 933.333 | 1:1 | 1.000 | Equalized 4L 5s | |||||
| 11\49 | 269.388 | 930.612 | 6:5 | 1.200 | Lower range of orwell | |||||
| 9\40 | 270.000 | 930.000 | 5:4 | 1.250 | ||||||
| 16\71 | 270.423 | 929.577 | 9:7 | 1.286 | ||||||
| 7\31 | 270.968 | 929.032 | 4:3 | 1.333 | Supersoft 4L 5s | |||||
| 19\84 | 271.429 | 928.571 | 11:8 | 1.375 | ||||||
| 12\53 | 271.698 | 928.302 | 7:5 | 1.400 | ||||||
| 17\75 | 272.000 | 928.000 | 10:7 | 1.429 | ||||||
| 5\22 | 272.727 | 927.273 | 3:2 | 1.500 | Soft 4L 5s | |||||
| 18\79 | 273.418 | 926.582 | 11:7 | 1.571 | ||||||
| 13\57 | 273.684 | 926.316 | 8:5 | 1.600 | ||||||
| 21\92 | 273.913 | 926.087 | 13:8 | 1.625 | Unnamed golden tuning | |||||
| 8\35 | 274.286 | 925.714 | 5:3 | 1.667 | Semisoft 4L 5s Upper range of orwell | |||||
| 19\83 | 274.699 | 925.301 | 12:7 | 1.714 | ||||||
| 11\48 | 275.000 | 925.000 | 7:4 | 1.750 | ||||||
| 14\61 | 275.410 | 924.590 | 9:5 | 1.800 | ||||||
| 3\13 | 276.923 | 923.077 | 2:1 | 2.000 | Basic 4L 5s Scales with tunings softer than this are proper | |||||
| 13\56 | 278.571 | 921.429 | 9:4 | 2.250 | ||||||
| 10\43 | 279.070 | 920.930 | 7:3 | 2.333 | ||||||
| 17\73 | 279.452 | 920.548 | 12:5 | 2.400 | Lovecraft | |||||
| 7\30 | 280.000 | 920.000 | 5:2 | 2.500 | Semihard 4L 5s | |||||
| 18\77 | 280.519 | 919.481 | 13:5 | 2.600 | Golden lovecraft | |||||
| 11\47 | 280.851 | 919.149 | 8:3 | 2.667 | ||||||
| 15\64 | 281.250 | 918.750 | 11:4 | 2.750 | ||||||
| 4\17 | 282.353 | 917.647 | 3:1 | 3.000 | Hard 4L 5s | |||||
| 13\55 | 283.636 | 916.364 | 10:3 | 3.333 | ||||||
| 9\38 | 284.211 | 915.789 | 7:2 | 3.500 | ||||||
| 14\59 | 284.746 | 915.254 | 11:3 | 3.667 | ||||||
| 5\21 | 285.714 | 914.286 | 4:1 | 4.000 | Superhard 4L 5s | |||||
| 11\46 | 286.957 | 913.043 | 9:2 | 4.500 | ||||||
| 6\25 | 288.000 | 912.000 | 5:1 | 5.000 | ||||||
| 7\29 | 289.655 | 910.345 | 6:1 | 6.000 | ||||||
| 1\4 | 300.000 | 900.000 | 1:0 | → ∞ | Collapsed 4L 5s | |||||