1L 1s: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Moremajorthanmajor (talk | contribs)
autopatrolled
3,126 edits
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
→Scale tree: Removed unrecognized/extension names, replaced basic locations of basic mosses with mos tuning ranges
Line 49: Line 49:


== 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 shows the tuning ranges for certain mosses (5-9 notes) rather than the ranges of temperaments.
{| class="wikitable"
{| class="wikitable"
|+
! colspan="7" |Generator
! colspan="6" |Generator
!Bright gen.
!Bright gen.
!Dark gen.
!Dark gen.
Line 58: Line 57:
!s
!s
!L/s
!L/s
!Selected [[TAMNAMS|basic mosses]]
! colspan="2" |Ranges of mosses
!Other comments
|-
|-
|1\2
|1\2
|
|
|
|
|
Line 74: Line 73:
|
|
|
|
|-
|
|
|
|
|
|
|7\13
|646.154
|553.846
|7
|6
|1.167
| rowspan="7" |Antidiatonic (2L 5s)
| rowspan="3" |Balzano (2L 7s)
|-
|-
|
|
Line 81: Line 95:
|
|
|6\11
|6\11
|
|654.545
|654.545
|545.455
|545.455
Line 86: Line 101:
|5
|5
|1.200
|1.200
|balzano (2L 7s)
|-
|
|
|
|
|
|
|
|11\20
|660.000
|540.000
|11
|9
|1.222
|-
|-
|
|
Line 94: Line 120:
|
|
|5\9
|5\9
|
|
|
|666.667
|666.667
Line 100: Line 127:
|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 109: Line 149:
|
|
|9\16
|9\16
|
|675.000
|675.000
|525.000
|525.000
Line 114: Line 155:
|7
|7
|1.286
|1.286
|armotonic (7L 2s)
|-
|
|
|
|
|
|
|
|13\23
|678.261
|521.739
|13
|10
|1.300
|-
|-
|
|
Line 121: Line 173:
|
|
|4\7
|4\7
|
|
|
|
|
Line 128: Line 181:
|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 137: Line 205:
|
|
|11\19
|11\19
|
|694.737
|694.737
|505.263
|505.263
Line 142: Line 211:
|8
|8
|1.375
|1.375
|m-chromatic (7L 5s)
|
|-
|
|
|
|
|
|
|18\31
|696.774
|503.226
|18
|13
|1.385
|
|
|-
|-
Line 150: Line 232:
|
|
|7\12
|7\12
|
|
|
|700.000
|700.000
Line 156: Line 239:
|5
|5
|1.400
|1.400
|diatonic (5L 2s)
|
|-
|
|
|
|
|
|
|17\29
|703.448
|496.552
|17
|12
|1.417
|
|
|-
|-
Line 165: Line 261:
|
|
|10\17
|10\17
|
|705.882
|705.882
|494.118
|494.118
Line 170: Line 267:
|7
|7
|1.429
|1.429
|p-chromatic (5L 7s)
|
|-
|
|
|
|
|
|
|13\22
|709.091
|490.909
|13
|9
|1.444
|
|
|-
|-
Line 176: Line 286:
|
|
|3\5
|3\5
|
|
|
|
|
Line 184: Line 295:
|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 193: Line 319:
|
|
|11\18
|11\18
|
|733.333
|733.333
|466.667
|466.667
Line 198: Line 325:
|7
|7
|1.571
|1.571
|p-noble (5L 8s)
|
|-
|
|
|
|
|
|
|19\31
|735.484
|464.516
|19
|12
|1.583
|
|
|-
|-
Line 206: Line 346:
|
|
|8\13
|8\13
|
|
|
|738.462
|738.462
Line 212: Line 353:
|5
|5
|1.600
|1.600
|oneirotonic (5L 3s)
|
|-
|
|
|
|
|
|
|21\34
|741.176
|458.824
|21
|13
|1.615
|
|
|-
|-
Line 221: Line 375:
|
|
|13\21
|13\21
|
|742.857
|742.857
|457.143
|457.143
Line 226: Line 381:
|8
|8
|1.625
|1.625
|m-noble (8L 5s)
|
|-
|
|
|
|
|
|
|18\29
|744.828
|455.172
|18
|11
|1.636
|
|
|-
|-
Line 233: Line 401:
|
|
|5\8
|5\8
|
|
|
|
|
Line 240: Line 409:
|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 249: Line 433:
|
|
|12\19
|12\19
|
|757.895
|757.895
|442.105
|442.105
Line 254: Line 439:
|7
|7
|1.714
|1.714
|m-chro checkertonic (8L 3s)
|
|-
|
|
|
|
|
|
|19\30
|760.000
|440.000
|19
|11
|1.727
|
|
|-
|-
Line 262: Line 460:
|
|
|7\11
|7\11
|
|
|
|763.636
|763.636
Line 268: Line 467:
|4
|4
|1.750
|1.750
|checkertonic (3L 5s)
|
|-
|
|
|
|
|
|
|16\25
|768.000
|432.000
|16
|9
|1.778
|
|
|-
|-
Line 277: Line 489:
|
|
|9\14
|9\14
|
|771.429
|771.429
|428.571
|428.571
Line 282: Line 495:
|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 297: Line 524:
|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 305: Line 547:
|
|
|9\13
|9\13
|
|830.769
|830.769
|369.231
|369.231
Line 310: Line 553:
|4
|4
|2.250
|2.250
|sephiroid (3L 7s)
|-
|
|
|
|
|
|
|
|16\23
|834.783
|365.217
|16
|7
|2.286
|-
|-
|
|
Line 318: Line 572:
|
|
|7\10
|7\10
|
|
|
|840.000
|840.000
Line 324: Line 579:
|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 333: Line 601:
|
|
|12\17
|12\17
|
|847.059
|847.059
|352.941
|352.941
Line 338: Line 607:
|5
|5
|2.400
|2.400
|zaltertic (7L 3s)
|-
|
|
|
|
|
|
|
|17\24
|850.000
|350.000
|17
|7
|2.429
|-
|-
|
|
Line 345: Line 625:
|
|
|5\7
|5\7
|
|
|
|
|
Line 352: Line 633:
|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 361: Line 657:
|
|
|13\18
|13\18
|
|866.667
|866.667
|333.333
|333.333
Line 366: Line 663:
|5
|5
|2.600
|2.600
|antikleismic (7L 4s)
|
|-
|
|
|
|
|
|
|21\29
|868.966
|331.034
|21
|8
|2.625
|
|
|-
|-
Line 374: Line 684:
|
|
|8\11
|8\11
|
|
|
|872.727
|872.727
Line 380: Line 691:
|3
|3
|2.667
|2.667
|smitonic (4L 3s)
|
|-
|
|
|
|
|
|
|19\26
|876.923
|323.077
|19
|7
|2.714
|
|
|-
|-
Line 389: Line 713:
|
|
|11\15
|11\15
|
|880.000
|880.000
|320.000
|320.000
Line 394: Line 719:
|4
|4
|2.750
|2.750
|kleismic (4L 7s)
|
|-
|
|
|
|
|
|
|14\19
|884.211
|315.789
|14
|5
|2.800
|
|
|-
|-
Line 400: Line 738:
|
|
|3\4
|3\4
|
|
|
|
|
Line 408: Line 747:
|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 417: Line 771:
|
|
|10\13
|10\13
|
|923.077
|923.077
|276.923
|276.923
Line 422: Line 777:
|3
|3
|3.333
|3.333
|gramitonic (4L 5s)
|-
|
|
|
|
|
|
|
|17\22
|927.273
|272.727
|17
|5
|3.400
|-
|-
|
|
Line 430: Line 796:
|
|
|7\9
|7\9
|
|
|
|933.333
|933.333
Line 436: Line 803:
|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 445: Line 825:
|
|
|11\14
|11\14
|
|942.857
|942.857
|257.143
|257.143
Line 450: Line 831:
|3
|3
|3.667
|3.667
|semiquartal (5L 4s)
|-
|
|
|
|
|
|
|
|15\19
|947.368
|252.632
|15
|4
|3.750
|-
|-
|
|
Line 457: Line 849:
|
|
|4\5
|4\5
|
|
|
|
|
Line 464: Line 857:
|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 473: Line 881:
|
|
|9\11
|9\11
|
|981.818
|981.818
|218.182
|218.182
Line 478: Line 887:
|2
|2
|4.500
|4.500
|machinoid (5L 1s)
|-
|
|
|
|
|
|
|
|14\17
|988.235
|211.765
|14
|3
|4.667
|-
|-
|
|
Line 486: Line 906:
|
|
|5\6
|5\6
|
|
|
|1000.000
|1000.000
Line 492: Line 913:
|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 501: Line 936:
|
|
|6\7
|6\7
|
|1028.571
|1028.571
|171.429
|171.429
Line 506: Line 942:
|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 09:25, 6 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 shows the tuning ranges for certain mosses (5-9 notes) rather than the ranges of temperaments.

Generator Bright gen. Dark gen. L s L/s Ranges of mosses
1\2 600.000 600.000 1 1 1.000
7\13 646.154 553.846 7 6 1.167 Antidiatonic (2L 5s) Balzano (2L 7s)
6\11 654.545 545.455 6 5 1.200
11\20 660.000 540.000 11 9 1.222
5\9 666.667 533.333 5 4 1.250
14\25 672.000 528.000 14 11 1.273 Armotonic (7L 2s)
9\16 675.000 525.000 9 7 1.286
13\23 678.261 521.739 13 10 1.300
4\7 685.714 514.286 4 3 1.333
15\26 692.308 507.692 15 11 1.364 Diatonic (5L 2s)
11\19 694.737 505.263 11 8 1.375
18\31 696.774 503.226 18 13 1.385
7\12 700.000 500.000 7 5 1.400
17\29 703.448 496.552 17 12 1.417
10\17 705.882 494.118 10 7 1.429
13\22 709.091 490.909 13 9 1.444
3\5 720.000 480.000 3 2 1.500
14\23 730.435 469.565 14 9 1.556 Oneirotonic (5L 3s)
11\18 733.333 466.667 11 7 1.571
19\31 735.484 464.516 19 12 1.583
8\13 738.462 461.538 8 5 1.600
21\34 741.176 458.824 21 13 1.615
13\21 742.857 457.143 13 8 1.625
18\29 744.828 455.172 18 11 1.636
5\8 750.000 450.000 5 3 1.667
17\27 755.556 444.444 17 10 1.700 Checkertonic (3L 5s)
12\19 757.895 442.105 12 7 1.714
19\30 760.000 440.000 19 11 1.727
7\11 763.636 436.364 7 4 1.750
16\25 768.000 432.000 16 9 1.778
9\14 771.429 428.571 9 5 1.800
11\17 776.471 423.529 11 6 1.833
2\3 800.000 400.000 2 1 2.000
11\16 825.000 375.000 11 5 2.200 Mosh (3L 4s) Sephiroid (3L 7s)
9\13 830.769 369.231 9 4 2.250
16\23 834.783 365.217 16 7 2.286
7\10 840.000 360.000 7 3 2.333
19\27 844.444 355.556 19 8 2.375 Zalteritc (7L 3s)
12\17 847.059 352.941 12 5 2.400
17\24 850.000 350.000 17 7 2.429
5\7 857.143 342.857 5 2 2.500
18\25 864.000 336.000 18 7 2.571 Smitonic (4L 3s)
13\18 866.667 333.333 13 5 2.600
21\29 868.966 331.034 21 8 2.625
8\11 872.727 327.273 8 3 2.667
19\26 876.923 323.077 19 7 2.714
11\15 880.000 320.000 11 4 2.750
14\19 884.211 315.789 14 5 2.800
3\4 900.000 300.000 3 1 3.000
13\17 917.647 282.353 13 4 3.250 Manual (4L 1s) Gramitonic (4L 5s)
10\13 923.077 276.923 10 3 3.333
17\22 927.273 272.727 17 5 3.400
7\9 933.333 266.667 7 2 3.500
18\23 939.130 260.870 18 5 3.600 Semiquartal (5L 4s)
11\14 942.857 257.143 11 3 3.667
15\19 947.368 252.632 15 4 3.750
4\5 960.000 240.000 4 1 4.000
13\16 975.000 225.000 13 3 4.333 Pedal (1L 4s) Machinoid (5L 1s)
9\11 981.818 218.182 9 2 4.500
14\17 988.235 211.765 14 3 4.667
5\6 1000.000 200.000 5 1 5.000
11\13 1015.385 184.615 11 2 5.500 Antimachinoid (1L 5s)

6L 1s, 1L 6s, 7L 1s, etc. can be found here

6\7 1028.571 171.429 6 1 6.000
7\8 1050.000 150.000 7 1 7.000
1\1 1200.000 0.000 1 0 → inf
Retrieved from "https://en.xen.wiki/index.php?title=1L_1s&oldid=102475"