1L 1s: Difference between revisions

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→Scale tree: Removed unrecognized/extension names, replaced basic locations of basic mosses with mos tuning ranges
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
Undo revision 102475 by Ganaram inukshuk (talk)
Tag: Undo
Line 49: Line 49:


== Scale tree ==
== Scale tree ==
As the mos 1L 1s is related to all single-period mosses, the scale tree shows the tuning ranges for certain mosses (5-9 notes) rather than the ranges of temperaments.
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.
{| class="wikitable"
{| class="wikitable"
! colspan="7" |Generator
|+
! colspan="6" |Generator
!Bright gen.
!Bright gen.
!Dark gen.
!Dark gen.
Line 57: Line 58:
!s
!s
!L/s
!L/s
! colspan="2" |Ranges of mosses
!Selected [[TAMNAMS|basic mosses]]
!Other comments
|-
|-
|1\2
|1\2
|
|
|
|
|
Line 73: Line 74:
|
|
|
|
|-
|
|
|
|
|
|
|7\13
|646.154
|553.846
|7
|6
|1.167
| rowspan="7" |Antidiatonic (2L 5s)
| rowspan="3" |Balzano (2L 7s)
|-
|-
|
|
Line 95: Line 81:
|
|
|6\11
|6\11
|
|654.545
|654.545
|545.455
|545.455
Line 101: Line 86:
|5
|5
|1.200
|1.200
|-
|balzano (2L 7s)
|
|
|
|
|
|
|
|11\20
|660.000
|540.000
|11
|9
|1.222
|-
|-
|
|
Line 120: Line 94:
|
|
|5\9
|5\9
|
|
|
|666.667
|666.667
Line 127: Line 100:
|4
|4
|1.250
|1.250
|antidiatonic (2L 5s)
|
|
|-
|
|
|
|
|
|
|14\25
|672.000
|528.000
|14
|11
|1.273
| rowspan="3" |Armotonic (7L 2s)
|-
|-
|
|
Line 149: Line 109:
|
|
|9\16
|9\16
|
|675.000
|675.000
|525.000
|525.000
Line 155: Line 114:
|7
|7
|1.286
|1.286
|-
|armotonic (7L 2s)
|
|
|
|
|
|
|
|13\23
|678.261
|521.739
|13
|10
|1.300
|-
|-
|
|
Line 173: Line 121:
|
|
|4\7
|4\7
|
|
|
|
|
Line 181: Line 128:
|3
|3
|1.333
|1.333
|
|pentic (2L 3s)
|
|-
|
|
|
|
|
|
|15\26
|692.308
|507.692
|15
|11
|1.364
| rowspan="7" |Diatonic (5L 2s)
|
|
|-
|-
Line 205: Line 137:
|
|
|11\19
|11\19
|
|694.737
|694.737
|505.263
|505.263
Line 211: Line 142:
|8
|8
|1.375
|1.375
|
|m-chromatic (7L 5s)
|-
|
|
|
|
|
|
|18\31
|696.774
|503.226
|18
|13
|1.385
|
|
|-
|-
Line 232: Line 150:
|
|
|7\12
|7\12
|
|
|
|700.000
|700.000
Line 239: Line 156:
|5
|5
|1.400
|1.400
|
|diatonic (5L 2s)
|-
|
|
|
|
|
|
|17\29
|703.448
|496.552
|17
|12
|1.417
|
|
|-
|-
Line 261: Line 165:
|
|
|10\17
|10\17
|
|705.882
|705.882
|494.118
|494.118
Line 267: Line 170:
|7
|7
|1.429
|1.429
|
|p-chromatic (5L 7s)
|-
|
|
|
|
|
|
|13\22
|709.091
|490.909
|13
|9
|1.444
|
|
|-
|-
Line 286: Line 176:
|
|
|3\5
|3\5
|
|
|
|
|
Line 295: Line 184:
|2
|2
|1.500
|1.500
|
|trial (2L 1s)
|
|-
|
|
|
|
|
|
|14\23
|730.435
|469.565
|14
|9
|1.556
| rowspan="7" |Oneirotonic (5L 3s)
|
|
|-
|-
Line 319: Line 193:
|
|
|11\18
|11\18
|
|733.333
|733.333
|466.667
|466.667
Line 325: Line 198:
|7
|7
|1.571
|1.571
|
|p-noble (5L 8s)
|-
|
|
|
|
|
|
|19\31
|735.484
|464.516
|19
|12
|1.583
|
|
|-
|-
Line 346: Line 206:
|
|
|8\13
|8\13
|
|
|
|738.462
|738.462
Line 353: Line 212:
|5
|5
|1.600
|1.600
|
|oneirotonic (5L 3s)
|-
|
|
|
|
|
|
|21\34
|741.176
|458.824
|21
|13
|1.615
|
|
|-
|-
Line 375: Line 221:
|
|
|13\21
|13\21
|
|742.857
|742.857
|457.143
|457.143
Line 381: Line 226:
|8
|8
|1.625
|1.625
|
|m-noble (8L 5s)
|-
|
|
|
|
|
|
|18\29
|744.828
|455.172
|18
|11
|1.636
|
|
|-
|-
Line 401: Line 233:
|
|
|5\8
|5\8
|
|
|
|
|
Line 409: Line 240:
|3
|3
|1.667
|1.667
|
|antipentic (3L 2s)
|
|-
|
|
|
|
|
|
|17\27
|755.556
|444.444
|17
|10
|1.700
| rowspan="7" |Checkertonic (3L 5s)
|
|
|-
|-
Line 433: Line 249:
|
|
|12\19
|12\19
|
|757.895
|757.895
|442.105
|442.105
Line 439: Line 254:
|7
|7
|1.714
|1.714
|
|m-chro checkertonic (8L 3s)
|-
|
|
|
|
|
|
|19\30
|760.000
|440.000
|19
|11
|1.727
|
|
|-
|-
Line 460: Line 262:
|
|
|7\11
|7\11
|
|
|
|763.636
|763.636
Line 467: Line 268:
|4
|4
|1.750
|1.750
|
|checkertonic (3L 5s)
|-
|
|
|
|
|
|
|16\25
|768.000
|432.000
|16
|9
|1.778
|
|
|-
|-
Line 489: Line 277:
|
|
|9\14
|9\14
|
|771.429
|771.429
|428.571
|428.571
Line 495: Line 282:
|5
|5
|1.800
|1.800
|
|p-chro checkertonic (3L 8s)
|-
|
|
|
|
|
|
|11\17
|776.471
|423.529
|11
|6
|1.833
|
|
|-
|-
|
|
|2\3
|2\3
|
|
|
|
|
Line 524: Line 297:
|2.000
|2.000
|
|
|
|[[2L 1s]] and [[1L 2s]] separate here.
|-
|
|
|
|
|
|
|11\16
|825.000
|375.000
|11
|5
|2.200
| rowspan="7" |Mosh (3L 4s)
| rowspan="3" |Sephiroid (3L 7s)
|-
|-
|
|
Line 547: Line 305:
|
|
|9\13
|9\13
|
|830.769
|830.769
|369.231
|369.231
Line 553: Line 310:
|4
|4
|2.250
|2.250
|-
|sephiroid (3L 7s)
|
|
|
|
|
|
|
|16\23
|834.783
|365.217
|16
|7
|2.286
|-
|-
|
|
Line 572: Line 318:
|
|
|7\10
|7\10
|
|
|
|840.000
|840.000
Line 579: Line 324:
|3
|3
|2.333
|2.333
|mosh (3L 4s)
|
|
|-
|
|
|
|
|
|
|19\27
|844.444
|355.556
|19
|8
|2.375
| rowspan="3" |Zalteritc (7L 3s)
|-
|-
|
|
Line 601: Line 333:
|
|
|12\17
|12\17
|
|847.059
|847.059
|352.941
|352.941
Line 607: Line 338:
|5
|5
|2.400
|2.400
|-
|zaltertic (7L 3s)
|
|
|
|
|
|
|
|17\24
|850.000
|350.000
|17
|7
|2.429
|-
|-
|
|
Line 625: Line 345:
|
|
|5\7
|5\7
|
|
|
|
|
Line 633: Line 352:
|2
|2
|2.500
|2.500
|
|tetric (3L 1s)
|
|-
|
|
|
|
|
|
|18\25
|864.000
|336.000
|18
|7
|2.571
| rowspan="7" |Smitonic (4L 3s)
|
|
|-
|-
Line 657: Line 361:
|
|
|13\18
|13\18
|
|866.667
|866.667
|333.333
|333.333
Line 663: Line 366:
|5
|5
|2.600
|2.600
|
|antikleismic (7L 4s)
|-
|
|
|
|
|
|
|21\29
|868.966
|331.034
|21
|8
|2.625
|
|
|-
|-
Line 684: Line 374:
|
|
|8\11
|8\11
|
|
|
|872.727
|872.727
Line 691: Line 380:
|3
|3
|2.667
|2.667
|
|smitonic (4L 3s)
|-
|
|
|
|
|
|
|19\26
|876.923
|323.077
|19
|7
|2.714
|
|
|-
|-
Line 713: Line 389:
|
|
|11\15
|11\15
|
|880.000
|880.000
|320.000
|320.000
Line 719: Line 394:
|4
|4
|2.750
|2.750
|
|kleismic (4L 7s)
|-
|
|
|
|
|
|
|14\19
|884.211
|315.789
|14
|5
|2.800
|
|
|-
|-
Line 738: Line 400:
|
|
|3\4
|3\4
|
|
|
|
|
Line 747: Line 408:
|1
|1
|3.000
|3.000
|antrial (1L 2s)
|
|
|
|-
|
|
|
|
|
|
|13\17
|917.647
|282.353
|13
|4
|3.250
| rowspan="7" |Manual (4L 1s)
| rowspan="3" |Gramitonic (4L 5s)
|-
|-
|
|
Line 771: Line 417:
|
|
|10\13
|10\13
|
|923.077
|923.077
|276.923
|276.923
Line 777: Line 422:
|3
|3
|3.333
|3.333
|-
|gramitonic (4L 5s)
|
|
|
|
|
|
|
|17\22
|927.273
|272.727
|17
|5
|3.400
|-
|-
|
|
Line 796: Line 430:
|
|
|7\9
|7\9
|
|
|
|933.333
|933.333
Line 803: Line 436:
|2
|2
|3.500
|3.500
|manual (4L 1s)
|
|
|-
|
|
|
|
|
|
|18\23
|939.130
|260.870
|18
|5
|3.600
| rowspan="3" |Semiquartal (5L 4s)
|-
|-
|
|
Line 825: Line 445:
|
|
|11\14
|11\14
|
|942.857
|942.857
|257.143
|257.143
Line 831: Line 450:
|3
|3
|3.667
|3.667
|-
|semiquartal (5L 4s)
|
|
|
|
|
|
|
|15\19
|947.368
|252.632
|15
|4
|3.750
|-
|-
|
|
Line 849: Line 457:
|
|
|4\5
|4\5
|
|
|
|
|
Line 857: Line 464:
|1
|1
|4.000
|4.000
|antetric (1L 4s)
|
|
|
|-
|
|
|
|
|
|
|13\16
|975.000
|225.000
|13
|3
|4.333
| rowspan="7" |Pedal (1L 4s)
| rowspan="3" |Machinoid (5L 1s)
|-
|-
|
|
Line 881: Line 473:
|
|
|9\11
|9\11
|
|981.818
|981.818
|218.182
|218.182
Line 887: Line 478:
|2
|2
|4.500
|4.500
|-
|machinoid (5L 1s)
|
|
|
|
|
|
|
|14\17
|988.235
|211.765
|14
|3
|4.667
|-
|-
|
|
Line 906: Line 486:
|
|
|5\6
|5\6
|
|
|
|1000.000
|1000.000
Line 913: Line 492:
|1
|1
|5.000
|5.000
|pedal (1L 4s)
|
|
|-
|
|
|
|
|
|
|11\13
|1015.385
|184.615
|11
|2
|5.500
| rowspan="3" |Antimachinoid (1L 5s)
6L 1s, 1L 6s, 7L 1s, etc. can be found here
|-
|-
|
|
Line 936: Line 501:
|
|
|6\7
|6\7
|
|1028.571
|1028.571
|171.429
|171.429
Line 942: Line 506:
|1
|1
|6.000
|6.000
|-
|antimachinoid (1L 5s)
|
|
|
|
|
|
|
|7\8
|1050.000
|150.000
|7
|1
|7.000
|-
|-
|1\1
|1\1
|
|
|
|
|

Revision as of 00:48, 7 February 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 ¢)

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 (perfect) L (major) L+s (perfect)
sL 0|1 1L 1s 0| 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 how more familiar mosses are related, rather than related temperaments.

Generator Bright gen. Dark gen. L s L/s Selected basic mosses Other comments
1\2 600.000 600.000 1 1 1.000
6\11 654.545 545.455 6 5 1.200 balzano (2L 7s)
5\9 666.667 533.333 5 4 1.250 antidiatonic (2L 5s)
9\16 675.000 525.000 9 7 1.286 armotonic (7L 2s)
4\7 685.714 514.286 4 3 1.333 pentic (2L 3s)
11\19 694.737 505.263 11 8 1.375 m-chromatic (7L 5s)
7\12 700.000 500.000 7 5 1.400 diatonic (5L 2s)
10\17 705.882 494.118 10 7 1.429 p-chromatic (5L 7s)
3\5 720.000 480.000 3 2 1.500 trial (2L 1s)
11\18 733.333 466.667 11 7 1.571 p-noble (5L 8s)
8\13 738.462 461.538 8 5 1.600 oneirotonic (5L 3s)
13\21 742.857 457.143 13 8 1.625 m-noble (8L 5s)
5\8 750.000 450.000 5 3 1.667 antipentic (3L 2s)
12\19 757.895 442.105 12 7 1.714 m-chro checkertonic (8L 3s)
7\11 763.636 436.364 7 4 1.750 checkertonic (3L 5s)
9\14 771.429 428.571 9 5 1.800 p-chro checkertonic (3L 8s)
2\3 800.000 400.000 2 1 2.000 2L 1s and 1L 2s separate here.
9\13 830.769 369.231 9 4 2.250 sephiroid (3L 7s)
7\10 840.000 360.000 7 3 2.333 mosh (3L 4s)
12\17 847.059 352.941 12 5 2.400 zaltertic (7L 3s)
5\7 857.143 342.857 5 2 2.500 tetric (3L 1s)
13\18 866.667 333.333 13 5 2.600 antikleismic (7L 4s)
8\11 872.727 327.273 8 3 2.667 smitonic (4L 3s)
11\15 880.000 320.000 11 4 2.750 kleismic (4L 7s)
3\4 900.000 300.000 3 1 3.000 antrial (1L 2s)
10\13 923.077 276.923 10 3 3.333 gramitonic (4L 5s)
7\9 933.333 266.667 7 2 3.500 manual (4L 1s)
11\14 942.857 257.143 11 3 3.667 semiquartal (5L 4s)
4\5 960.000 240.000 4 1 4.000 antetric (1L 4s)
9\11 981.818 218.182 9 2 4.500 machinoid (5L 1s)
5\6 1000.000 200.000 5 1 5.000 pedal (1L 4s)
6\7 1028.571 171.429 6 1 6.000 antimachinoid (1L 5s)
1\1 1200.000 0.000 1 0 → inf
Retrieved from "https://en.xen.wiki/index.php?title=1L_1s&oldid=102506"