1L 1s
| 1L 1s | 2L 1s → | |
| ↓ 1L 2s | 2L 2s ↘ |
┌╥┬┐ │║││ ││││ └┴┴┘
sL
1L 1s, named monowood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 1 small step, repeating every octave. Generators that produce this scale range from 600 ¢ to 1200 ¢, or from 0 ¢ to 600 ¢. Scales of this form are always proper because there is only one small step. It is the simplest valid MOS pattern, often referred to as the trivial MOS scale.
Names
TAMNAMS uses the name "monowood" for this MOS scale, in reference to the other n-wood names (such as biwood, triwood, and tetrawood), named after blackwood and whitewood) and specifically refers to this mos with an octave period.
The name "trivial" refers to how this is a trivial MOS pattern, though the name is meant to be equave-agnostic.
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (monwddegree) | ||
|---|---|---|---|---|---|
| 0 | 1 | 2 | |||
| 1|0 | 1 | Ls | Perf. | Maj. | Perf. |
| 0|1 | 2 | sL | Perf. | Min. | Perf. |
Intervals
| Intervals | Steps subtended |
Range in cents | ||
|---|---|---|---|---|
| Generic | Specific | Abbrev. | ||
| 0-monwdstep | Perfect 0-monwdstep | P0ws | 0 | 0.0 ¢ |
| 1-monwdstep | Minor 1-monwdstep | m1ws | s | 0.0 ¢ to 600.0 ¢ |
| Major 1-monwdstep | M1ws | L | 600.0 ¢ to 1200.0 ¢ | |
| 2-monwdstep | Perfect 2-monwdstep | P2ws | L + s | 1200.0 ¢ |
Properties
All single-period mosses ultimately start with a generating interval and, for octave-equivalent scales, the generator's octave complement. Hence, this scale can also be seen as the parent of every strict moment-of-symmetry scale and is thus found as the root of various scale trees, such as the mos family tree.
This mos is also its own sister, though this property is also true of all nL ns scales.
Stacking a generating interval, or one of its two sizes of mossteps, just once produces this mos's daughter mosses of 2L 1s and 1L 2s.
Scale tree
As the mos 1L 1s is related to all single-period mosses, the scale tree depicted shows the ranges of related mosses, rather than temperaments.
| Generator(edo) | Cents | Step ratio | Comments(always proper) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 1\2 | 600.000 | 600.000 | 1:1 | 1.000 | Equalized 1L 1s | |||||
| 6\11 | 654.545 | 545.455 | 6:5 | 1.200 | ||||||
| 5\9 | 666.667 | 533.333 | 5:4 | 1.250 | 2L 5s range (includes 2L 7s and 7L 2s) | |||||
| 9\16 | 675.000 | 525.000 | 9:7 | 1.286 | ||||||
| 4\7 | 685.714 | 514.286 | 4:3 | 1.333 | Supersoft 1L 1s | |||||
| 11\19 | 694.737 | 505.263 | 11:8 | 1.375 | ||||||
| 7\12 | 700.000 | 500.000 | 7:5 | 1.400 | 5L 2s range (includes 7L 5s and 5L 7s) | |||||
| 10\17 | 705.882 | 494.118 | 10:7 | 1.429 | ||||||
| 3\5 | 720.000 | 480.000 | 3:2 | 1.500 | Soft 1L 1s | |||||
| 11\18 | 733.333 | 466.667 | 11:7 | 1.571 | ||||||
| 8\13 | 738.462 | 461.538 | 8:5 | 1.600 | 5L 3s range | |||||
| 13\21 | 742.857 | 457.143 | 13:8 | 1.625 | ||||||
| 5\8 | 750.000 | 450.000 | 5:3 | 1.667 | Semisoft 1L 1s | |||||
| 12\19 | 757.895 | 442.105 | 12:7 | 1.714 | ||||||
| 7\11 | 763.636 | 436.364 | 7:4 | 1.750 | 3L 5s range | |||||
| 9\14 | 771.429 | 428.571 | 9:5 | 1.800 | ||||||
| 2\3 | 800.000 | 400.000 | 2:1 | 2.000 | Basic 1L 1s | |||||
| 9\13 | 830.769 | 369.231 | 9:4 | 2.250 | ||||||
| 7\10 | 840.000 | 360.000 | 7:3 | 2.333 | 3L 4s range (includes 3L 7s and 7L 3s) | |||||
| 12\17 | 847.059 | 352.941 | 12:5 | 2.400 | ||||||
| 5\7 | 857.143 | 342.857 | 5:2 | 2.500 | Semihard 1L 1s | |||||
| 13\18 | 866.667 | 333.333 | 13:5 | 2.600 | ||||||
| 8\11 | 872.727 | 327.273 | 8:3 | 2.667 | 4L 3s range (includes 7L 4s and 4L 7s) | |||||
| 11\15 | 880.000 | 320.000 | 11:4 | 2.750 | ||||||
| 3\4 | 900.000 | 300.000 | 3:1 | 3.000 | Hard 1L 1s | |||||
| 10\13 | 923.077 | 276.923 | 10:3 | 3.333 | ||||||
| 7\9 | 933.333 | 266.667 | 7:2 | 3.500 | 4L 1s range (includes 4L 5s and 5L 4s) | |||||
| 11\14 | 942.857 | 257.143 | 11:3 | 3.667 | ||||||
| 4\5 | 960.000 | 240.000 | 4:1 | 4.000 | Superhard 1L 1s | |||||
| 9\11 | 981.818 | 218.182 | 9:2 | 4.500 | ||||||
| 5\6 | 1000.000 | 200.000 | 5:1 | 5.000 | 1L 4s range (includes 5L 1s and 1L 5s) | |||||
| 6\7 | 1028.571 | 171.429 | 6:1 | 6.000 | ||||||
| 1\1 | 1200.000 | 0.000 | 1:0 | → ∞ | Collapsed 1L 1s | |||||