2L 2s: Difference between revisions

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m == Intervals == {{MOS intervals}}
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
 
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-09-09 09:21:08 UTC</tt>.<br>
{{MOS intro}}
: The original revision id was <tt>558695857</tt>.<br>
 
: The revision comment was: <tt></tt><br>
This scale is the parent of all half-octave-repeating MOS scales.
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
== Names ==
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">This tetrad has the special property that it is the smallest collection of notes which can create the feeling of "completely representing&lt;span style="line-height: 1.5;"&gt;" a particular regular temperament in a "standard" way. However, it only works in even-numbered edxs, for it contains sqrt(x), and it becomes a very weakly "complete" representation of a regular temperament as L:s grows large.&lt;/span&gt;</pre></div>
[[TAMNAMS]] uses the name '''biwood''', based on the n-wood series.
<h4>Original HTML content:</h4>
 
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;2L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;This tetrad has the special property that it is the smallest collection of notes which can create the feeling of &amp;quot;completely representing&lt;span style="line-height: 1.5;"&gt;&amp;quot; a particular regular temperament in a &amp;quot;standard&amp;quot; way. However, it only works in even-numbered edxs, for it contains sqrt(x), and it becomes a very weakly &amp;quot;complete&amp;quot; representation of a regular temperament as L:s grows large.&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
== Modes ==
{{MOS mode degrees}}
 
== Intervals ==
{{MOS intervals}}
 
== Scale tree ==
Generator ranges:
* Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
* Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)
 
{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 1\4 || || || || || || 300.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 6\22 || 327.273 || 6 || 5 || 1.200 ||
|-
| || || || || 5\18 || || 333.333 || 5 || 4 || 1.250 ||
|-
| || || || || || 9\32 || 337.500 || 9 || 7 || 1.286 ||
|-
| || || || 4\14 || || || 342.857 || 4 || 3 || 1.333 ||
|-
| || || || || || 11\38 || 347.368 || 11 || 8 || 1.375 ||
|-
| || || || || 7\24 || || 350.000 || 7 || 5 || 1.400 ||
|-
| || || || || || 10\34 || 352.941 || 10 || 7 || 1.429 ||
|-
| || || 3\10 || || || || 360.000 || 3 || 2 || 1.500 ||
|-
| || || || || || 11\36 || 366.667 || 11 || 7 || 1.571 || [[Baladic]]
|-
| || || || || 8\26 || || 369.231 || 8 || 5 || 1.600 ||
|-
| || || || || || 13\42 || 371.429 || 13 || 8 || 1.625 || Golden [[Lemba]] (370.8204¢)
|-
| || || || 5\16 || || || 375.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 12\38 || 378.947 || 12 || 7 || 1.714 ||
|-
| || || || || 7\22 || || 381.818 || 7 || 4 || 1.750 ||
|-
| || || || || || 9\28 || 385.714 || 9 || 5 || 1.800 ||
|-
| || 2\6 || || || || || 400.000 || 2 || 1 || 2.000 || Basic 2L 2s  
|-
| || || || || || 9\26 || 415.385 || 9 || 4 || 2.250 || [[Unidec]] is around here
|-
| || || || || 7\20 || || 420.000 || 7 || 3 || 2.333 ||
|-
| || || || || || 12\34 || 423.529 || 12 || 5 || 2.400 ||
|-
| || || || 5\14 || || || 428.571 || 5 || 2 || 2.500 ||
|-
| || || || || || 13\36 || 433.333 || 13 || 5 || 2.600 || Golden [[Hedgehog]]-[[supers]] (434.1641¢)
|-
| || || || || 8\22 || || 436.364 || 8 || 3 || 2.667 ||
|-
| || || || || || 11\30 || 440.000 || 11 || 4 || 2.750 ||
|-
| || || 3\8 || || || || 450.000 || 3 || 1 || 3.000 ||
|-
| || || || || || 10\26 || 461.538 || 10 || 3 || 3.333 || [[Fifive]]
|-
| || || || || 7\18 || || 466.667 || 7 || 2 || 3.500 ||
|-
| || || || || || 11\28 || 471.429 || 11 || 3 || 3.667 ||
|-
| || || || 4\10 || || || 480.000 || 4 || 1 || 4.000 ||
|-
| || || || || || 9\22 || 490.909 || 9 || 2 || 4.500 || [[Diaschismic]] / [[Pajara]]
|-
| || || || || 5\12 || || 500.000 || 5 || 1 || 5.000 || [[Injera]] is around here
|-
| || || || || || 6\14 || 514.286 || 6 || 1 || 6.000 || [[Vishnu]]↓
|-
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
|}
 
{{todo|expand}}
[[Category:Tetrad]]
[[Category:4-tone scales]]

Latest revision as of 23:30, 15 December 2024

↖ 1L 1s ↑ 2L 1s 3L 1s ↗
← 1L 2s 2L 2s 3L 2s →
↙ 1L 3s ↓ 2L 3s 3L 3s ↘ 
┌╥┬╥┬┐
│║│║││
││││││
└┴┴┴┴┘
Scale structure
Step pattern LsLs
sLsL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\4 to 1\2 (300.0 ¢ to 600.0 ¢)
Dark 0\2 to 1\4 (0.0 ¢ to 300.0 ¢)
TAMNAMS information
Name biwood
Prefix biwd-
Abbrev. bw
Related MOS scales
Parent none
Sister 2L 2s (self)
Daughters 4L 2s, 2L 4s
Neutralized 4edo
2-Flought 6L 2s, 2L 6s
Equal tunings
Equalized (L:s = 1:1) 1\4 (300.0 ¢)
Supersoft (L:s = 4:3) 4\14 (342.9 ¢)
Soft (L:s = 3:2) 3\10 (360.0 ¢)
Semisoft (L:s = 5:3) 5\16 (375.0 ¢)
Basic (L:s = 2:1) 2\6 (400.0 ¢)
Semihard (L:s = 5:2) 5\14 (428.6 ¢)
Hard (L:s = 3:1) 3\8 (450.0 ¢)
Superhard (L:s = 4:1) 4\10 (480.0 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 2s, named biwood in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 2 small steps, with a period of 1 large step and 1 small step that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 300 ¢ to 600 ¢, or from 0 ¢ to 300 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

This scale is the parent of all half-octave-repeating MOS scales.

Names

TAMNAMS uses the name biwood, based on the n-wood series.

Modes

Scale degrees of the modes of 2L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (biwddegree)
0 1 2 3 4
2|0(2) 1 LsLs Perf. Maj. Perf. Maj. Perf.
0|2(2) 2 sLsL Perf. Min. Perf. Min. Perf.

Intervals

Intervals of 2L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-biwdstep Perfect 0-biwdstep P0bws 0 0.0 ¢
1-biwdstep Minor 1-biwdstep m1bws s 0.0 ¢ to 300.0 ¢
Major 1-biwdstep M1bws L 300.0 ¢ to 600.0 ¢
2-biwdstep Perfect 2-biwdstep P2bws L + s 600.0 ¢
3-biwdstep Minor 3-biwdstep m3bws L + 2s 600.0 ¢ to 900.0 ¢
Major 3-biwdstep M3bws 2L + s 900.0 ¢ to 1200.0 ¢
4-biwdstep Perfect 4-biwdstep P4bws 2L + 2s 1200.0 ¢

Scale tree

Generator ranges:

  • Chroma-positive generator: 300 cents (1\4) to 600 cents (1\2)
  • Chroma-negative generator: 0 cents (0\2) to 300 cents (1\4)
Generator Cents L s L/s Comments
1\4 300.000 1 1 1.000
6\22 327.273 6 5 1.200
5\18 333.333 5 4 1.250
9\32 337.500 9 7 1.286
4\14 342.857 4 3 1.333
11\38 347.368 11 8 1.375
7\24 350.000 7 5 1.400
10\34 352.941 10 7 1.429
3\10 360.000 3 2 1.500
11\36 366.667 11 7 1.571 Baladic
8\26 369.231 8 5 1.600
13\42 371.429 13 8 1.625 Golden Lemba (370.8204¢)
5\16 375.000 5 3 1.667
12\38 378.947 12 7 1.714
7\22 381.818 7 4 1.750
9\28 385.714 9 5 1.800
2\6 400.000 2 1 2.000 Basic 2L 2s
9\26 415.385 9 4 2.250 Unidec is around here
7\20 420.000 7 3 2.333
12\34 423.529 12 5 2.400
5\14 428.571 5 2 2.500
13\36 433.333 13 5 2.600 Golden Hedgehog-supers (434.1641¢)
8\22 436.364 8 3 2.667
11\30 440.000 11 4 2.750
3\8 450.000 3 1 3.000
10\26 461.538 10 3 3.333 Fifive
7\18 466.667 7 2 3.500
11\28 471.429 11 3 3.667
4\10 480.000 4 1 4.000
9\22 490.909 9 2 4.500 Diaschismic / Pajara
5\12 500.000 5 1 5.000 Injera is around here
6\14 514.286 6 1 6.000 Vishnu↓
1\2 600.000 1 0 → inf
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