4L 7s
↖ 3L 6s | ↑ 4L 6s | 5L 6s ↗ |
← 3L 7s | 4L 7s | 5L 7s → |
↙ 3L 8s | ↓ 4L 8s | 5L 8s ↘ |
┌╥┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║│││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
ssLssLssLsL
4L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 7 small steps, repeating every octave. 4L 7s is a child scale of 4L 3s, expanding it by 4 tones. Generators that produce this scale range from 872.7¢ to 900¢, or from 300¢ to 327.3¢. One of the harmonic entropy minimums in this range is Kleismic/Hanson.
Name
TAMNAMS formerly used the name kleistonic for the name of this scale (prefix klei-). Other names include p-chro smitonic or smipechromic.
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-mosstep | Perfect 0-mosstep | P0ms | 0 | 0.0¢ |
1-mosstep | Minor 1-mosstep | m1ms | s | 0.0¢ to 109.1¢ |
Major 1-mosstep | M1ms | L | 109.1¢ to 300.0¢ | |
2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 218.2¢ |
Major 2-mosstep | M2ms | L + s | 218.2¢ to 300.0¢ | |
3-mosstep | Perfect 3-mosstep | P3ms | L + 2s | 300.0¢ to 327.3¢ |
Augmented 3-mosstep | A3ms | 2L + s | 327.3¢ to 600.0¢ | |
4-mosstep | Minor 4-mosstep | m4ms | L + 3s | 300.0¢ to 436.4¢ |
Major 4-mosstep | M4ms | 2L + 2s | 436.4¢ to 600.0¢ | |
5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 300.0¢ to 545.5¢ |
Major 5-mosstep | M5ms | 2L + 3s | 545.5¢ to 600.0¢ | |
6-mosstep | Minor 6-mosstep | m6ms | 2L + 4s | 600.0¢ to 654.5¢ |
Major 6-mosstep | M6ms | 3L + 3s | 654.5¢ to 900.0¢ | |
7-mosstep | Minor 7-mosstep | m7ms | 2L + 5s | 600.0¢ to 763.6¢ |
Major 7-mosstep | M7ms | 3L + 4s | 763.6¢ to 900.0¢ | |
8-mosstep | Diminished 8-mosstep | d8ms | 2L + 6s | 600.0¢ to 872.7¢ |
Perfect 8-mosstep | P8ms | 3L + 5s | 872.7¢ to 900.0¢ | |
9-mosstep | Minor 9-mosstep | m9ms | 3L + 6s | 900.0¢ to 981.8¢ |
Major 9-mosstep | M9ms | 4L + 5s | 981.8¢ to 1200.0¢ | |
10-mosstep | Minor 10-mosstep | m10ms | 3L + 7s | 900.0¢ to 1090.9¢ |
Major 10-mosstep | M10ms | 4L + 6s | 1090.9¢ to 1200.0¢ | |
11-mosstep | Perfect 11-mosstep | P11ms | 4L + 7s | 1200.0¢ |
Modes
UDP | Cyclic Order |
Step Pattern |
Scale Degree (mosdegree) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||
10|0 | 1 | LsLssLssLss | Perf. | Maj. | Maj. | Aug. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
9|1 | 9 | LssLsLssLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Maj. | Maj. | Perf. |
8|2 | 6 | LssLssLsLss | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Maj. | Maj. | Perf. |
7|3 | 3 | LssLssLssLs | Perf. | Maj. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
6|4 | 11 | sLsLssLssLs | Perf. | Min. | Maj. | Perf. | Maj. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
5|5 | 8 | sLssLsLssLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Maj. | Perf. | Min. | Maj. | Perf. |
4|6 | 5 | sLssLssLsLs | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Maj. | Perf. |
3|7 | 2 | sLssLssLssL | Perf. | Min. | Maj. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
2|8 | 10 | ssLsLssLssL | Perf. | Min. | Min. | Perf. | Min. | Maj. | Min. | Min. | Perf. | Min. | Min. | Perf. |
1|9 | 7 | ssLssLsLssL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Perf. | Min. | Min. | Perf. |
0|10 | 4 | ssLssLssLsL | Perf. | Min. | Min. | Perf. | Min. | Min. | Min. | Min. | Dim. | Min. | Min. | Perf. |
Genchain
Generators | -11 | -10 | -9 | -8 | -7 | -6 | -5 | -4 | -3 | -2 | -1 | 0 | +1 | +2 | +3 | +4 | +5 | +6 | +7 | +8 | +9 | +10 | +11 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Interval quality | d11md | d8md | m5md | m2md | m10md | m7md | m4md | m1md | m9md | m6md | P3md | P0md | P8md | M5md | M2md | M10md | M7md | M4md | M1md | M9md | M6md | A3md | A0md |
Tuning ranges
Soft range
The soft range for tunings of 4L 7s 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]. The small step is recognizable as a near diatonic semitone, while the large step is in the ambiguous area of neutral seconds.
Soft edos include 15edo and 26edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various soft tunings:
15edo (basic) | 26edo (soft) | Some JI approximations | |
---|---|---|---|
generator (g) | 4\15, 320.00 | 7\26, 323.08 | 77/64, 6/5 |
L (octave - 3g) | 2\15, 160.00 | 3\26, 138.46 | 12/11, 13/12 |
s (4g - octave) | 1\15, 80.00 | 2\19, 92.31 | 21/20, 22/21, 20/19 |
Hypohard
Hypohard tunings of 4L 7s 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 (aka Hanson) temperament and its extensions.
Hypohard edos include 15edo, 19edo, and 34edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various hypohard tunings:
15edo (basic) | 19edo (hard) | 34edo (semihard) | Some JI approximations | |
---|---|---|---|---|
generator (g) | 4\15, 320.00 | 5\19, 315.79 | 9\34, 317.65 | 6/5 |
L (octave - 3g) | 2\15, 160.00 | 3\19, 189.47 | 5\34, 176.47 | 10/9, 11/10 (in 15edo) |
s (4g - octave) | 1\15, 80.00 | 1\19, 63.16 | 2\34, 70.59 | 25/24, 26/25 (in better kleismic tunings) |
Parahard
Parahard tunings of 4L 7s 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 approximate intervals that employ a much higher limit harmony, especially in the case of the superhard 23edo. However, the large step is recognizable as a regular diatonic whole step, approximating both 10/9 and 9/8, while the small step is a slightly sharp of a quarter tone.
Parahard edos include 19edo, 23edo, and 42edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various parahard tunings:
19edo (hard) | 23edo (superhard) | 42edo (parahard) | Some JI approximations | |
---|---|---|---|---|
generator (g) | 5\19, 315.79 | 6\23, 313.04 | 11\42, 314.29 | 6/5 |
L (octave - 3g) | 3\19, 189.47 | 4\23, 208.70 | 7\42, 200.00 | 10/9, 9/8 |
s (4g - octave) | 1\19, 63.16 | 1\23, 52.17 | 2\42, 57.14 | 28/27, 33/32 |
Hyperhard
Hyperhard tunings of 4L 7s 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, where the small step is generally flat of a quarter tone.
Hyperhard edos include 23edo, 31edo, and 27edo. The sizes of the generator, large step and small step of 4L 7s are as follows in various hyperhard tunings:
23edo (superhard) | 31edo (extrahard) | 27edo (pentahard) | Some JI approximations | |
---|---|---|---|---|
generator (g) | 6\23, 313.04 | 8\31, 309.68 | 7\27, 311.11 | 6/5 |
L (octave - 3g) | 4\23, 208.70 | 6\31, 232.26 | 5\27, 222.22 | 8/7, 9/8 |
s (4g - octave) | 1\23, 52.17 | 1\31, 38.71 | 1\27, 44.44 | 36/35, 45/44 |
Temperaments
Scales
Scale tree
Generator(edo) | Cents | Step Ratio | Comments | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
8\11 | 872.727 | 327.273 | 1:1 | 1.000 | Equalized 4L 7s | |||||
43\59 | 874.576 | 325.424 | 6:5 | 1.200 | Oregon | |||||
35\48 | 875.000 | 325.000 | 5:4 | 1.250 | ||||||
62\85 | 875.294 | 324.706 | 9:7 | 1.286 | ||||||
27\37 | 875.676 | 324.324 | 4:3 | 1.333 | Supersoft 4L 7s | |||||
73\100 | 876.000 | 324.000 | 11:8 | 1.375 | ||||||
46\63 | 876.190 | 323.810 | 7:5 | 1.400 | ||||||
65\89 | 876.404 | 323.596 | 10:7 | 1.429 | Orgone | |||||
19\26 | 876.923 | 323.077 | 3:2 | 1.500 | Soft 4L 7s | |||||
68\93 | 877.419 | 322.581 | 11:7 | 1.571 | Magicaltet | |||||
49\67 | 877.612 | 322.388 | 8:5 | 1.600 | ||||||
79\108 | 877.778 | 322.222 | 13:8 | 1.625 | Golden superklesimic | |||||
30\41 | 878.049 | 321.951 | 5:3 | 1.667 | Semisoft 4L 7s Superkleismic | |||||
71\97 | 878.351 | 321.649 | 12:7 | 1.714 | ||||||
41\56 | 878.571 | 321.429 | 7:4 | 1.750 | ||||||
52\71 | 878.873 | 321.127 | 9:5 | 1.800 | ||||||
11\15 | 880.000 | 320.000 | 2:1 | 2.000 | Basic 4L 7s Scales with tunings softer than this are proper | |||||
47\64 | 881.250 | 318.750 | 9:4 | 2.250 | ||||||
36\49 | 881.633 | 318.367 | 7:3 | 2.333 | Catalan | |||||
61\83 | 881.928 | 318.072 | 12:5 | 2.400 | ||||||
25\34 | 882.353 | 317.647 | 5:2 | 2.500 | Semihard 4L 7s | |||||
64\87 | 882.759 | 317.241 | 13:5 | 2.600 | Countercata | |||||
39\53 | 883.019 | 316.981 | 8:3 | 2.667 | Hanson/cata | |||||
53\72 | 883.333 | 316.667 | 11:4 | 2.750 | ||||||
14\19 | 884.211 | 315.789 | 3:1 | 3.000 | Hard 4L 7s | |||||
45\61 | 885.246 | 314.754 | 10:3 | 3.333 | Parakleismic | |||||
31\42 | 885.714 | 314.286 | 7:2 | 3.500 | ||||||
48\65 | 886.154 | 313.846 | 11:3 | 3.667 | ||||||
17\23 | 886.957 | 313.043 | 4:1 | 4.000 | Superhard 4L 7s | |||||
37\50 | 888.000 | 312.000 | 9:2 | 4.500 | Oolong | |||||
20\27 | 888.889 | 311.111 | 5:1 | 5.000 | Starlingtet | |||||
23\31 | 890.323 | 309.677 | 6:1 | 6.000 | Myna | |||||
3\4 | 900.000 | 300.000 | 1:0 | → ∞ | Collapsed 4L 7s |