4L 5s: Difference between revisions
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==== Proposed | ==== Proposed names ==== | ||
[https://twitter.com/Lilly__Flores/status/1640779893108805632 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'. | [https://twitter.com/Lilly__Flores/status/1640779893108805632 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'. | ||
{{MOS modes|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}} | {{MOS modes|Scale Signature=4L 5s|Mode Names=Roi; Steno; Limni; Telma; Krini; Elos; Mychos; Akti; Dini}} | ||
Revision as of 00:43, 30 July 2024
- 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 interval regions.
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 |
|---|---|---|
| 8|0 | 1 | LsLsLsLss |
| 7|1 | 3 | LsLsLssLs |
| 6|2 | 5 | LsLssLsLs |
| 5|3 | 7 | LssLsLsLs |
| 4|4 | 9 | sLsLsLsLs |
| 3|5 | 2 | sLsLsLssL |
| 2|6 | 4 | sLsLssLsL |
| 1|7 | 6 | sLssLsLsL |
| 0|8 | 8 | ssLsLsLsL |
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.