1L 1s: Difference between revisions

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→Scale tree: Simplified names based on suggestions by fredg
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== Scale tree ==
== Scale tree ==
As the mos 1L 1s is related to all single-period mosses, the scale tree depicted shows how more familiar mosses are related, rather than related temperaments.
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.
{| class="wikitable"
{| class="wikitable"
|+
! colspan="6" |Generator
! colspan="6" |Generator
!Bright gen.
!Bright gen.
Line 58: Line 57:
!s
!s
!L/s
!L/s
!Selected [[TAMNAMS|basic mosses]]
!Ranges of mosses
|-
|-
|1\2
|1\2
Line 84: Line 83:
|5
|5
|1.200
|1.200
|balzano (2L 7s)
| rowspan="3" |[[2L 5s]] range (includes [[2L 7s]] and [[7L 2s]])
|-
|-
|
|
Line 97: Line 96:
|4
|4
|1.250
|1.250
|antidiatonic (2L 5s)
|-
|-
|
|
Line 110: Line 108:
|7
|7
|1.286
|1.286
|armotonic (7L 2s)
|-
|-
|
|
Line 123: Line 120:
|3
|3
|1.333
|1.333
|pentic (2L 3s)
|Basic [[2L 3s]]
|-
|-
|
|
Line 136: Line 133:
|8
|8
|1.375
|1.375
|m-chromatic (7L 5s)
| rowspan="3" |[[5L 2s]] range (includes [[7L 5s]] and [[5L 7s]])
|-
|-
|
|
Line 149: Line 146:
|5
|5
|1.400
|1.400
|diatonic (5L 2s)
|-
|-
|
|
Line 162: Line 158:
|7
|7
|1.429
|1.429
|p-chromatic (5L 7s)
|-
|-
|
|
Line 175: Line 170:
|2
|2
|1.500
|1.500
|trial (2L 1s)
|Basic [[2L 1s]]
|-
|-
|
|
Line 188: Line 183:
|7
|7
|1.571
|1.571
|p-noble (5L 8s)
| rowspan="3" |[[5L 3s]] range
|-
|-
|
|
Line 201: Line 196:
|5
|5
|1.600
|1.600
|oneirotonic (5L 3s)
|-
|-
|
|
Line 214: Line 208:
|8
|8
|1.625
|1.625
|m-noble (8L 5s)
|-
|-
|
|
Line 227: Line 220:
|3
|3
|1.667
|1.667
|antipentic (3L 2s)
|Basic [[3L 2s]]
|-
|-
|
|
Line 240: Line 233:
|7
|7
|1.714
|1.714
|sensitonic (8L 3s)
| rowspan="3" |[[3L 5s]] range
|-
|-
|
|
Line 253: Line 246:
|4
|4
|1.750
|1.750
|checkertonic (3L 5s)
|-
|-
|
|
Line 266: Line 258:
|5
|5
|1.800
|1.800
|quadroid (3L 8s)
|-
|-
|
|
Line 279: Line 270:
|1
|1
|2.000
|2.000
|Dividing line between 2L 1s (upper half) and 1L 2s (lower half)
|Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
|-
|-
|
|
Line 292: Line 283:
|4
|4
|2.250
|2.250
|sephiroid (3L 7s)
| rowspan="3" |[[3L 4s]] range (includes [[3L 7s]] and [[7L 3s]])
|-
|-
|
|
Line 305: Line 296:
|3
|3
|2.333
|2.333
|mosh (3L 4s)
|-
|-
|
|
Line 318: Line 308:
|5
|5
|2.400
|2.400
|dicoid (7L 3s)
|-
|-
|
|
Line 331: Line 320:
|2
|2
|2.500
|2.500
|tetric (3L 1s)
|Basic [[3L 1s]]
|-
|-
|
|
Line 344: Line 333:
|5
|5
|2.600
|2.600
|antikleismic (7L 4s)
| rowspan="3" |[[4L 3s]] range (includes [[7L 4s]] and [[4L 7s]])
|-
|-
|
|
Line 357: Line 346:
|3
|3
|2.667
|2.667
|smitonic (4L 3s)
|-
|-
|
|
Line 370: Line 358:
|4
|4
|2.750
|2.750
|kleismic (4L 7s)
|-
|-
|
|
Line 383: Line 370:
|1
|1
|3.000
|3.000
|antrial (1L 2s)
|Basic [[1L 2s]]
|-
|-
|
|
Line 396: Line 383:
|3
|3
|3.333
|3.333
|gramitonic (4L 5s)
| rowspan="3" |Range of [[4L 1s]] (includes [[4L 5s]] and [[5L 4s]])
|-
|-
|
|
Line 409: Line 396:
|2
|2
|3.500
|3.500
|manual (4L 1s)
|-
|-
|
|
Line 422: Line 408:
|3
|3
|3.667
|3.667
|semiquartal (5L 4s)
|-
|-
|
|
Line 435: Line 420:
|1
|1
|4.000
|4.000
|antetric (1L 4s)
|Basic [[1L 3s]]
|-
|-
|
|
Line 448: Line 433:
|2
|2
|4.500
|4.500
|machinoid (5L 1s)
| rowspan="3" |Range of [[1L 4s]] (includes [[5L 1s]] and [[1L 5s]])
|-
|-
|
|
Line 461: Line 446:
|1
|1
|5.000
|5.000
|pedal (1L 4s)
|-
|-
|
|
Line 474: Line 458:
|1
|1
|6.000
|6.000
|antimachinoid (1L 5s)
|-
|-
|1\1
|1\1

Revision as of 05:39, 31 March 2023

1L 1s 2L 1s →
↓ 1L 2s 2L 2s ↘
Scale structure
Step pattern Ls
sL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\2 to 1\1 (600.0 ¢ to 1200.0 ¢)
Dark 0\1 to 1\2 (0.0 ¢ to 600.0 ¢)
TAMNAMS information
Name monowood
Prefix monwd-
Abbrev. w
Related MOS scales
Parent none
Sister 1L 1s (self)
Daughters 2L 1s, 1L 2s
Neutralized 2edo
2-Flought 3L 1s, 1L 3s
Equal tunings
Equalized (L:s = 1:1) 1\2 (600.0 ¢)
Supersoft (L:s = 4:3) 4\7 (685.7 ¢)
Soft (L:s = 3:2) 3\5 (720.0 ¢)
Semisoft (L:s = 5:3) 5\8 (750.0 ¢)
Basic (L:s = 2:1) 2\3 (800.0 ¢)
Semihard (L:s = 5:2) 5\7 (857.1 ¢)
Hard (L:s = 3:1) 3\4 (900.0 ¢)
Superhard (L:s = 4:1) 4\5 (960.0 ¢)
Collapsed (L:s = 1:0) 1\1 (1200.0 ¢)
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1L 1s is the simplest valid MOS pattern, often referred to as the trivial MOS scale.

Names

TAMNAMS uses two names for this mos: trivial and monowood. The name "trivial" references how this is the simplest possible mos pattern and is used to refer to this mos with any period, and the name "monowood" is an extension of 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.

Modes and intervals

Mode UDP Mode name Rotational order mosunison 1-mosstep mosoctave
Ls 1|0 1L 1s 1|0 0 0 (perfect) L (major) L+s (perfect)
sL 0|1 1L 1s 0|1 1 0 (perfect) s (minor) L+s (perfect)

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 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 Bright gen. Dark gen. L s L/s Ranges of mosses
1\2 600.000 600.000 1 1 1.000
6\11 654.545 545.455 6 5 1.200 2L 5s range (includes 2L 7s and 7L 2s)
5\9 666.667 533.333 5 4 1.250
9\16 675.000 525.000 9 7 1.286
4\7 685.714 514.286 4 3 1.333 Basic 2L 3s
11\19 694.737 505.263 11 8 1.375 5L 2s range (includes 7L 5s and 5L 7s)
7\12 700.000 500.000 7 5 1.400
10\17 705.882 494.118 10 7 1.429
3\5 720.000 480.000 3 2 1.500 Basic 2L 1s
11\18 733.333 466.667 11 7 1.571 5L 3s range
8\13 738.462 461.538 8 5 1.600
13\21 742.857 457.143 13 8 1.625
5\8 750.000 450.000 5 3 1.667 Basic 3L 2s
12\19 757.895 442.105 12 7 1.714 3L 5s range
7\11 763.636 436.364 7 4 1.750
9\14 771.429 428.571 9 5 1.800
2\3 800.000 400.000 2 1 2.000 Basic 1L 1s (dividing line between 2L 1s and 1L 2s)
9\13 830.769 369.231 9 4 2.250 3L 4s range (includes 3L 7s and 7L 3s)
7\10 840.000 360.000 7 3 2.333
12\17 847.059 352.941 12 5 2.400
5\7 857.143 342.857 5 2 2.500 Basic 3L 1s
13\18 866.667 333.333 13 5 2.600 4L 3s range (includes 7L 4s and 4L 7s)
8\11 872.727 327.273 8 3 2.667
11\15 880.000 320.000 11 4 2.750
3\4 900.000 300.000 3 1 3.000 Basic 1L 2s
10\13 923.077 276.923 10 3 3.333 Range of 4L 1s (includes 4L 5s and 5L 4s)
7\9 933.333 266.667 7 2 3.500
11\14 942.857 257.143 11 3 3.667
4\5 960.000 240.000 4 1 4.000 Basic 1L 3s
9\11 981.818 218.182 9 2 4.500 Range of 1L 4s (includes 5L 1s and 1L 5s)
5\6 1000.000 200.000 5 1 5.000
6\7 1028.571 171.429 6 1 6.000
1\1 1200.000 0.000 1 0 → inf
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