4L 7s

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Scale structure
Step pattern LsLssLssLss
ssLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 8\11 to 3\4 (872.7 ¢ to 900.0 ¢)
Dark 1\4 to 3\11 (300.0 ¢ to 327.3 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 4L 3s
Sister 7L 4s
Daughters 11L 4s, 4L 11s
Neutralized 8L 3s
2-Flought 15L 7s, 4L 18s
Equal tunings
Equalized (L:s = 1:1) 8\11 (872.7 ¢)
Supersoft (L:s = 4:3) 27\37 (875.7 ¢)
Soft (L:s = 3:2) 19\26 (876.9 ¢)
Semisoft (L:s = 5:3) 30\41 (878.0 ¢)
Basic (L:s = 2:1) 11\15 (880.0 ¢)
Semihard (L:s = 5:2) 25\34 (882.4 ¢)
Hard (L:s = 3:1) 14\19 (884.2 ¢)
Superhard (L:s = 4:1) 17\23 (887.0 ¢)
Collapsed (L:s = 1:0) 3\4 (900.0 ¢)

4L 7s or kleistonic klyse-TON-ik /klaɪsˈtɒnɪk/ refers to the structure of MOS scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 3\11edo (three degrees of 11edo, 327.27¢), representing approximate diatonic minor thirds (6/5). The name refers to the temperament that is one of the harmonic entropy minimums in this range (Kleismic/Hanson), itself named after the interval known as the kleisma.

4L 7s has a heptatonic subset, which is the hard end of the spectrum of the smitonic scale (4L 3s).

Notation

The notation used in this article is LssLsLssLss = А҃В҃Г҃Д҃Е҃Ѕ҃З҃И҃Ѳ҃І҃Ѫ҃А҃, based on old Cyrillic numerals 1-10 using the titlo as a numeric sign, and the addition of the big yus (Ѫ) for 11. Chromas are represented by regular sharps and flats. Thus the 15edo gamut is as follows: А҃ А҃#/В҃b В҃ Г҃ Д҃ Д҃#/Е҃b Е҃ Ѕ҃ Ѕ҃#/З҃b З҃ И҃ Ѳ҃ Ѳ҃#/І҃b І҃ Ѫ҃ А҃

Letter names

The letters can be named in English as such: Az, Vede, Glagol, Dobro, Yest, Dzelo, Zemlya, Izhe, Thita, I(Ee), Yus. They can also be named as numbers 1-11.

Intervals

Generators Notation (1/1 = А҃) Interval category name Generators Notation of 2/1 inverse Interval category name
The 11-note MOS has the following intervals (from some root):
0 А҃ perfect unison 0 А҃ dodecave (same as octave)
1 Д҃ perfect kleifourth (minor third) -1 Ѳ҃ perfect kleininth (major sixth)
2 З҃b minor kleiseventh -2 Ѕ҃ major kleisixth
3 І҃b minor kleitenth -3 Г҃ major kleithird
4 В҃b minor kleisecond -4 Ѫ҃ major kleieleventh
5 Е҃b minor kleififth -5 И҃ major kleieight
6 И҃b minor kleieight -6 Е҃ major kleififth
7 Ѫ҃b minor kleieleventh -7 В҃ major kleisecond
8 Г҃b minor kleithird -8 І҃ major kleitenth
9 Ѕ҃b minor kleisixth -9 З҃ major kleiseventh
10 Ѳ҃b diminished kleininth -10 Д҃# augmented kleithird
The chromatic 15-note MOS (either 4L 11s, 11L 4s, or 15edo) also has the following intervals (from some root):
11 А҃b diminished dodecave -11 А҃# augmented unison (mychroma, kleicomma)
12 Д҃b diminished kleifourth -12 Ѳ҃# augmented kleininth
13 З҃bb diminished kleiseventh -13 Ѕ҃# augmented kleisixth
14 І҃bb diminished kleitenth -14 Г҃# augmented kleithird

Genchain

The generator chain for this scale is as follows:

Д҃b А҃b Ѳ҃b Ѕ҃b Г҃b Ѫ҃b И҃b Е҃b В҃b І҃b З҃b Д҃ А҃ Ѳ҃ Ѕ҃ Г҃ Ѫ҃ И҃ Е҃ В҃ І҃ З҃ Д҃# А҃# Ѳ҃# Ѕ҃# Г҃# Ѫ҃# И҃# Е҃# В҃# І҃# З҃#
d4 d12 d9 m6 m3 m11 m8 m5 m2 m10 m7 P4 P1 P9 M6 M3 M11 M8 M5 M2 M10 M7 A4 A1 A9 A6 A3 A11 A8 A5 A2 A10 A7

Tuning ranges

Soft range

The soft range for tunings of mynatonic encompasses parasoft and hyposoft tunings. This implies step ratios smaller than 2/1, meaning a generator sharper than 4\15 = 320¢. This is the range associated with extensions of Orgone[7].

Hypohard

Hypohard tunings of mynatonic have step ratios between 2/1 and 3/1, implying a generator sharper than 5\19 = 315.79¢ and flatter than 4\15 = 320¢. This range represents one of the harmonic entropy minimums, where 6 generators make a just diatonic fifth (3/2), an octave above. This is the range associated with the eponymous Kleismic temperament and its extensions, such as the 5-limit Hanson.

Parahard

Parahard tunings of mynatonic have step ratios between 3/1 and 4/1, implying a generator sharper than 6\23 = 313.04¢ and flatter than 5\19 = 315.79¢. The minor third is at its purest here, but the resulting scales tend to result in intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo.

Hyperhard

Hyperhard tunings of mynatonic have step ratios between 4/1 and 6/1, implying a generator sharper than 8\31 = 309.68¢ and flatter than 6\23 = 313.04¢. The temperament known as Myna (a pun on "minor third") resides here, as this is the range where 10 generators make a just diatonic fifth (3/2), two octaves above. These scales are stacked with simple intervals, but are melodically difficult due to the extreme step size disparity.

Modes

The names are based on smitonic modes, modified with the "super-" prefix, with thematic additions, as there are an extra 4 modes available.

Mode UDP Name
LsLssLssLss 10|0 Supernerevarine
LssLsLssLss 9|1 Supervivecan
LssLssLsLss 8|2 Superbaardauan
LssLssLssLs 7|3 Superlorkhanic
sLsLssLssLs 6|4 Supervvardenic
sLssLsLssLs 5|5 Supersothic
sLssLssLsLs 4|6 Supernumidian
sLssLssLssL 3|7 Superkagrenacan
ssLsLssLssL 2|8 Supernecromic
ssLssLsLssL 1|9 Superalmalexian
ssLssLssLsL 0|10 Superdagothic

Temperaments

Scale tree

The spectrum looks like this:

1\4 300¢
10\39 307.692
9\35 308.571
8\31 309.677 Myna
23\89 310.112 Myna
15\58 310.345 Myna
7\27 311.111 Starlingtet
6\23 313.043 Skateboard
17\65 313.846
11\42 314.286
16\61 314.754
21\80 315
26\99 315.152 Parakleismic
315.332
5\19 315.789 Keemun
19\72 316.667 Catakleismic
316.785
14\53 316.981 Hanson/Marveltwintri/Cata
317.17
23\87 317.241 Countercata
9\34 317.647
4\15 320 Boundary of propriety

(generators larger than this are proper)

321.539
11\41 321.951 Superkleismic
322.268
18\67 322.388
322.585
7\26 323.068 Magicaltet/Orgone
10\37 324.324 Orgone
13\48 325 Oregon
16\59 325.424 Oregon
19\70 325.714 Oregon
22/81 325.926 Oregon
3\11 327.273 Oregon
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