2L 4s: Difference between revisions

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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>
| Name = malic
: This revision was by author [[User:guest|guest]] and made on <tt>2011-08-28 00:27:38 UTC</tt>.<br>
| Periods = 2
: The original revision id was <tt>248860749</tt>.<br>
| nLargeSteps = 2
: The revision comment was: <tt></tt><br>
| nSmallSteps = 4
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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<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">The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of harmonic entropy is [[Diaschismic family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is **half** of that (about a quartertone), so 3/2 is a period plus two generators; and [[Porcupine family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).
| Pattern = LssLss
}}
 
{{MOS intro}}
 
The only scale with this [[MOSScales|MOS]] pattern that's a really significant minimum of [[harmonic entropy]] is [[Diaschismic_family|srutal/pajara]], in which the period plus the generator is 3/2. Other scales include [[shrutar]], in which the generator is '''half''' of that (about a [[quartertone]]), so 3/2 is a period plus two generators; and [[Porcupine_family#Hedgehog|hedgehog]], in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).


In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.


Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.
||||||||||||||||||||||~ Generator ||~ Cents ||~ Comments ||
|| 0\2 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 0 ||  ||
||  ||  ||  ||  ||  ||  ||  ||  ||  || 1\24 ||  || 50 ||  ||
||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 2\46 || 52.17 || Shrutar is around here ||
||  ||  ||  ||  ||  ||  ||  ||  || 1\22 ||  ||  || 54.55 ||  ||
||  ||  ||  ||  ||  ||  ||  || 1\20 ||  ||  ||  || 60 ||  ||
||  ||  ||  ||  ||  ||  || 1\18 ||  ||  ||  ||  || 66.67 ||  ||
||  ||  ||  ||  ||  || 1\16 ||  ||  ||  ||  ||  || 75 ||  ||
||  ||  ||  ||  || 1\14 ||  ||  ||  ||  ||  ||  || 85.71 ||  ||
||  ||  ||  || 1\12 ||  ||  ||  ||  ||  ||  ||  || 100 ||  ||
||  ||  ||  ||  || 2\22 ||  ||  ||  ||  ||  ||  || 109.09 || Srutal/Pajara is around here ||
||  ||  || 1\10 ||  ||  ||  ||  ||  ||  ||  ||  || 120 ||  ||
||  || 1\8 ||  ||  ||  ||  ||  ||  ||  ||  ||  || 150 ||= Boundary of propriety (generators
larger than this are proper) ||
||  ||  ||  || 3\22 ||  ||  ||  ||  ||  ||  ||  || 163.64 || Hedgehog and echidna are both around here ||
||  ||  ||  ||  ||  || 8\58 ||  ||  ||  ||  ||  || 165.52 ||  ||
||  ||  ||  ||  ||  ||  || 13\94 ||  ||  ||  ||  || 165.96 || Golden hedgehog/echidna ||
||  ||  ||  ||  || 5\36 ||  ||  ||  ||  ||  ||  || 166.67 ||  ||
||  ||  || 2\14 ||  ||  ||  ||  ||  ||  ||  ||  || 171.43 ||  ||
|| 1\6 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  || 200 ||  ||</pre></div>
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<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 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The only scale with this &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern that's a really significant minimum of harmonic entropy is &lt;a class="wiki_link" href="/Diaschismic%20family"&gt;srutal/pajara&lt;/a&gt;, in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is &lt;strong&gt;half&lt;/strong&gt; of that (about a quartertone), so 3/2 is a period plus two generators; and &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).&lt;br /&gt;
&lt;br /&gt;
In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.&lt;br /&gt;
&lt;br /&gt;
Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.&lt;br /&gt;


== Scale properties ==
{{TAMNAMS use}}
=== Intervals ===
{{MOS intervals}}
=== Generator chain ===
{{MOS genchain}}
=== Modes ===
{{MOS mode degrees}}


&lt;table class="wiki_table"&gt;
== Scale tree ==
    &lt;tr&gt;
{{MOS tuning spectrum
        &lt;th colspan="11"&gt;Generator&lt;br /&gt;
| 9/7 = [[Unidec]]
&lt;/th&gt;
| 13/8 = Golden [[hedgehog]]/[[echidna]]
        &lt;th&gt;Cents&lt;br /&gt;
| 5/3 = Hedgehog (optimal around here)
&lt;/th&gt;
| 9/4 = [[Crepuscular]]
        &lt;th&gt;Comments&lt;br /&gt;
| 8/3 = [[Octokaidecal]]
&lt;/th&gt;
| 7/2 = [[Pajara]]
    &lt;/tr&gt;
| 9/2 = [[Injera]]
    &lt;tr&gt;
| 6/1 = [[Shrutar]]&nbsp;↓
        &lt;td&gt;0\2&lt;br /&gt;
}}
&lt;/td&gt;
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        &lt;td&gt;2\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;52.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Shrutar is around here&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;54.55&lt;br /&gt;
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        &lt;td&gt;109.09&lt;br /&gt;
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        &lt;td&gt;Srutal/Pajara is around here&lt;br /&gt;
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        &lt;td&gt;150&lt;br /&gt;
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        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators&lt;br /&gt;
larger than this are proper)&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hedgehog and echidna are both around here&lt;br /&gt;
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&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13\94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Golden hedgehog/echidna&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
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        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;166.67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2\14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;171.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:6-tone scales]]

Latest revision as of 05:29, 25 February 2026

↖ 1L 3s ↑ 2L 3s 3L 3s ↗
← 1L 4s 2L 4s 3L 4s →
↙ 1L 5s ↓ 2L 5s 3L 5s ↘
Scale structure
Step pattern LssLss
ssLssL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 2\6 to 1\2 (400.0 ¢ to 600.0 ¢)
Dark 0\2 to 1\6 (0.0 ¢ to 200.0 ¢)
TAMNAMS information
Name malic
Prefix mal-
Abbrev. mal
Related MOS scales
Parent 2L 2s
Sister 4L 2s
Daughters 6L 2s, 2L 6s
Neutralized 4L 2s
2-Flought 8L 4s, 2L 10s
Equal tunings
Equalized (L:s = 1:1) 2\6 (400.0 ¢)
Supersoft (L:s = 4:3) 7\20 (420.0 ¢)
Soft (L:s = 3:2) 5\14 (428.6 ¢)
Semisoft (L:s = 5:3) 8\22 (436.4 ¢)
Basic (L:s = 2:1) 3\8 (450.0 ¢)
Semihard (L:s = 5:2) 7\18 (466.7 ¢)
Hard (L:s = 3:1) 4\10 (480.0 ¢)
Superhard (L:s = 4:1) 5\12 (500.0 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)
View • Talk • Edit

2L 4s, named malic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 4 small steps, with a period of 1 large step and 2 small steps that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 400 ¢ to 600 ¢, or from 0 ¢ to 200 ¢.

The only scale with this MOS pattern that's a really significant minimum of harmonic entropy is srutal/pajara, in which the period plus the generator is 3/2. Other scales include shrutar, in which the generator is half of that (about a quartertone), so 3/2 is a period plus two generators; and hedgehog, in which two generators make a 6/5, and 4/3 would be three generators (except that it doesn't appear in this MOS).

In addition to the true MOS with pattern LssLss, all these scales also come in a near-MOS version, LsLsss, in which the period is the only generic interval that has more than two specific representatives.

Srutal/pajara probably has the lowest harmonic entropy of all 6-note MOS scales. The near-MOS version has even lower harmonic entropy.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 2L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-malstep Perfect 0-malstep P0mals 0 0.0 ¢
1-malstep Perfect 1-malstep P1mals s 0.0 ¢ to 200.0 ¢
Augmented 1-malstep A1mals L 200.0 ¢ to 600.0 ¢
2-malstep Diminished 2-malstep d2mals 2s 0.0 ¢ to 400.0 ¢
Perfect 2-malstep P2mals L + s 400.0 ¢ to 600.0 ¢
3-malstep Perfect 3-malstep P3mals L + 2s 600.0 ¢
4-malstep Perfect 4-malstep P4mals L + 3s 600.0 ¢ to 800.0 ¢
Augmented 4-malstep A4mals 2L + 2s 800.0 ¢ to 1200.0 ¢
5-malstep Diminished 5-malstep d5mals L + 4s 600.0 ¢ to 1000.0 ¢
Perfect 5-malstep P5mals 2L + 3s 1000.0 ¢ to 1200.0 ¢
6-malstep Perfect 6-malstep P6mals 2L + 4s 1200.0 ¢

Generator chain

Generator chain of 2L 4s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
3 Augmented 0-maldegree A0mald Augmented 3-maldegree A3mald
2 Augmented 1-maldegree A1mald Augmented 4-maldegree A4mald
1 Perfect 2-maldegree P2mald Perfect 5-maldegree P5mald
0 Perfect 0-maldegree
Perfect 3-maldegree		 P0mald
P3mald		 Perfect 3-maldegree
Perfect 6-maldegree		 P3mald
P6mald
−1 Perfect 1-maldegree P1mald Perfect 4-maldegree P4mald
−2 Diminished 2-maldegree d2mald Diminished 5-maldegree d5mald
−3 Diminished 3-maldegree d3mald Diminished 6-maldegree d6mald

Modes

Scale degrees of the modes of 2L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (maldegree)
0 1 2 3 4 5 6
4|0(2) 1 LssLss Perf. Aug. Perf. Perf. Aug. Perf. Perf.
2|2(2) 3 sLssLs Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|4(2) 2 ssLssL Perf. Perf. Dim. Perf. Perf. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\6 400.000 200.000 1:1 1.000 Equalized 2L 4s
11\32 412.500 187.500 6:5 1.200
9\26 415.385 184.615 5:4 1.250
16\46 417.391 182.609 9:7 1.286 Unidec
7\20 420.000 180.000 4:3 1.333 Supersoft 2L 4s
19\54 422.222 177.778 11:8 1.375
12\34 423.529 176.471 7:5 1.400
17\48 425.000 175.000 10:7 1.429
5\14 428.571 171.429 3:2 1.500 Soft 2L 4s
18\50 432.000 168.000 11:7 1.571
13\36 433.333 166.667 8:5 1.600
21\58 434.483 165.517 13:8 1.625 Golden hedgehog/echidna
8\22 436.364 163.636 5:3 1.667 Semisoft 2L 4s
Hedgehog (optimal around here)
19\52 438.462 161.538 12:7 1.714
11\30 440.000 160.000 7:4 1.750
14\38 442.105 157.895 9:5 1.800
3\8 450.000 150.000 2:1 2.000 Basic 2L 4s
Scales with tunings softer than this are proper
13\34 458.824 141.176 9:4 2.250 Crepuscular
10\26 461.538 138.462 7:3 2.333
17\44 463.636 136.364 12:5 2.400
7\18 466.667 133.333 5:2 2.500 Semihard 2L 4s
18\46 469.565 130.435 13:5 2.600
11\28 471.429 128.571 8:3 2.667 Octokaidecal
15\38 473.684 126.316 11:4 2.750
4\10 480.000 120.000 3:1 3.000 Hard 2L 4s
13\32 487.500 112.500 10:3 3.333
9\22 490.909 109.091 7:2 3.500 Pajara
14\34 494.118 105.882 11:3 3.667
5\12 500.000 100.000 4:1 4.000 Superhard 2L 4s
11\26 507.692 92.308 9:2 4.500 Injera
6\14 514.286 85.714 5:1 5.000
7\16 525.000 75.000 6:1 6.000 Shrutar ↓
1\2 600.000 0.000 1:0 → ∞ Collapsed 2L 4s
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