5L 4s: Difference between revisions
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'''5L 4s''' refers to the structure of [[MOS]] scales with generators ranging from 1\5 (one degree of [[5edo]] = 240¢) to 2\9 (two degrees of [[9edo]] = 266.7¢). In the case of 9edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). | |||
The familiar harmonic entropy minimum with this MOS pattern is [[Meantone_family#Godzilla|godzilla]], in which a generator is [[8/7|8/7]] or [[7/6|7/6]] (tempered to be the same interval, or even 37/32 if you like) so two of them make a [[4/3|4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[Chromatic_pairs#semaphore|semaphore]], there is also a weird scale called "[[Pseudo-semaphore|pseudo-semaphore]]", in which two different flavors of [[3/2|3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. | The familiar harmonic entropy minimum with this MOS pattern is [[Meantone_family#Godzilla|godzilla]], in which a generator is [[8/7|8/7]] or [[7/6|7/6]] (tempered to be the same interval, or even 37/32 if you like) so two of them make a [[4/3|4/3]]. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament [[Chromatic_pairs#semaphore|semaphore]], there is also a weird scale called "[[Pseudo-semaphore|pseudo-semaphore]]", in which two different flavors of [[3/2|3/2]] exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2. | ||
== Scale tree == | |||
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== Tuning ranges and data == | |||
=== Semaphore === | |||
=== Bug === | |||
== Notations == | |||
== Intervals == | |||
== Modes == | |||
TODO: names | |||
* LLsLsLsLs | |||
* LsLLsLsLs | |||
* LsLsLLsLs | |||
* LsLsLsLLs | |||
* LsLsLsLsL | |||
* sLLsLsLsL | |||
* sLsLLsLsL | |||
* sLsLsLLsL | |||
* sLsLsLsLL | |||
One can think of godzilla[9] modes as being built from two pentachords (division of the perfect fourth into four intervals) plus a whole tone. The possible pentachords are LsLs, sLLs, and sLsL. | |||
== Chords == | |||
== Primodal theory == | == Primodal theory == | ||
=== Nejis === | === Nejis === | ||
Revision as of 11:23, 17 March 2021
5L 4s refers to the structure of MOS scales with generators ranging from 1\5 (one degree of 5edo = 240¢) to 2\9 (two degrees of 9edo = 266.7¢). In the case of 9edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's).
The familiar harmonic entropy minimum with this MOS pattern is godzilla, in which a generator is 8/7 or 7/6 (tempered to be the same interval, or even 37/32 if you like) so two of them make a 4/3. However, in addition to godzilla (tempering out 81/80) and the 2.3.7 temperament semaphore, there is also a weird scale called "pseudo-semaphore", in which two different flavors of 3/2 exist in the same scale: an octave minus two generators makes a sharp 3/2, and two octaves minus seven generators makes a flat 3/2.
Scale tree
| Generator | Cents | Comments | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1\5 | 240 | |||||||||||
| 12\59 | 244.068 | Pseudo-semaphore is around here | ||||||||||
| 11\54 | 244.444 | |||||||||||
| 10\49 | 244.898 | |||||||||||
| 9\44 | 245.455 | |||||||||||
| 8\39 | 246.154 | |||||||||||
| 7\34 | 247.059 | |||||||||||
| 6\29 | 248.276 | |||||||||||
| 11\53 | 249.057 | Semaphore is around here | ||||||||||
| 5\24 | 250 | L/s = 4 | ||||||||||
| 9\43 | 251.163 | |||||||||||
| 4\19 | 252.632 | Godzilla is around here
L/s = 3 | ||||||||||
| 11\52 | 253.813 | |||||||||||
| 29\137 | 254.015 | |||||||||||
| 76\359 | 254.039 | |||||||||||
| 199\940 | 254.043 | |||||||||||
| 123\581 | 254.045 | |||||||||||
| 47\222 | 254.054 | |||||||||||
| 18\85 | 254.118 | |||||||||||
| 7\33 | 254.5455 | |||||||||||
| 10\47 | 255.319 | |||||||||||
| 13\61 | 255.734 | |||||||||||
| 16\75 | 256.000 | |||||||||||
| 3\14 | 257.143 | Boundary of propriety (generators
larger than this are proper) | ||||||||||
| 11\51 | 258.8235 | |||||||||||
| 258.957 | ||||||||||||
| 8\37 | 259.459 | |||||||||||
| 21\97 | 259.794 | |||||||||||
| 55\254 | 259.843 | |||||||||||
| 144\665 | 259.850 | |||||||||||
| 233\1076 | 259.851 | Golden superpelog | ||||||||||
| 89\411 | 259.854 | |||||||||||
| 34\157 | 259.873 | |||||||||||
| 13\60 | 260 | |||||||||||
| 260.246 | ||||||||||||
| 5\23 | 260.870 | Optimum rank range (L/s=3/2) superpelog | ||||||||||
| 7\32 | 262.5 | |||||||||||
| 9\41 | 263.415 | |||||||||||
| 11\50 | 264 | |||||||||||
| 13\59 | 264.407 | |||||||||||
| 15\68 | 264.706 | |||||||||||
| 17\77 | 264.935 | |||||||||||
| 19\86 | 265.116 | |||||||||||
| 21\95 | 265.263 | |||||||||||
| 2\9 | 266.667 | |||||||||||
Tuning ranges and data
Semaphore
Bug
Notations
Intervals
Modes
TODO: names
- LLsLsLsLs
- LsLLsLsLs
- LsLsLLsLs
- LsLsLsLLs
- LsLsLsLsL
- sLLsLsLsL
- sLsLLsLsL
- sLsLsLLsL
- sLsLsLsLL
One can think of godzilla[9] modes as being built from two pentachords (division of the perfect fourth into four intervals) plus a whole tone. The possible pentachords are LsLs, sLLs, and sLsL.
Chords
Primodal theory
Nejis
14nejis
- 95:100:105:110:116:122:128:135:141:148:156:164:172:180:190 (uses /19 prime family intervals while being pretty close to equal)
Samples
File:Dream EP 14edo Sketch.mp3 is a short swing ditty in 14edo semaphore[9], in the 212121221 mode.