6L 2s: 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>
{{MOS intro}}
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2013-01-20 16:21:18 UTC</tt>.<br>
There is only one significant (though small) harmonic entropy minimum with this MOS pattern: [[Porcupine_family#Hedgehog|hedgehog]], in which two generators are 6/5 and three are 4/3, same as [[porcupine]].
: The original revision id was <tt>399959980</tt>.<br>
: The revision comment was: <tt></tt><br>
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>
<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">There is only one significant (though small) harmonic entropy minimum with this MOS pattern: [[Porcupine family#Hedgehog|hedgehog]], in which two generators are 6/5 and three are 4/3, same as porcupine.


In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).
6L&nbsp;2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one additional large step is added to diatonic (5L&nbsp;2s).
||||||~ Generator ||~  ||~  ||~  ||~ Cents ||~ Comments ||
|| 1\8 ||  ||  ||  ||  ||  || 150 ||=  ||
||  ||  || 3\22 ||  ||  ||  || 163.64 ||= Hedgehog is around here ||
||  ||  ||  ||  || 8\58 ||  || 165.52 ||=  ||
||  ||  ||  ||  ||  || 13\94 || 165.96 ||= Golden hedgehog/echidna ||
||  ||  ||  || 5\36 ||  ||  || 166.67 ||=  ||
||  || 2\14 ||  ||  ||  ||  || 171.43 ||= Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS ||
||  ||  || 3\20 ||  ||  ||  || 180 ||= L/s = 3 ||
||  ||  ||  || 4/26 ||  ||  || 184.615 ||= L/s = 4 ||
|| 1\6 ||  ||  ||  ||  ||  || 200 ||=  ||</pre></div>
<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;6L 2s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;There is only one significant (though small) harmonic entropy minimum with this MOS pattern: &lt;a class="wiki_link" href="/Porcupine%20family#Hedgehog"&gt;hedgehog&lt;/a&gt;, in which two generators are 6/5 and three are 4/3, same as porcupine.&lt;br /&gt;
&lt;br /&gt;
In addition to the true MOS, LLLsLLLs, there is also a near-MOS, LLLLsLLs, in which the period is the only interval with more than two flavors. The true MOS is always proper, because there is only one small step per period, but the near-MOS is only proper if the generator is smaller than 2\14 (which includes hedgehog).&lt;br /&gt;


In addition to the true MOS pattern, there is a near-mos pattern, LLLLsLLs, in which the period is the only interval with more than two varieties. This near-MOS pattern is only proper if the generator is smaller than 2\14. Hedgehog is among these tunings.


&lt;table class="wiki_table"&gt;
== Scale properties ==
    &lt;tr&gt;
{{TAMNAMS use}}
        &lt;th colspan="3"&gt;Generator&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;Comments&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1\8&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;150&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&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;3\22&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;163.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Hedgehog is around here&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8\58&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&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;&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;13\94&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;165.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&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;
        &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;166.67&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&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;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;171.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety for near-MOS&lt;br /&gt;
Optimum rank range (L/s=2/1) for MOS&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;3\20&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;180&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 3&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;4/26&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;184.615&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;L/s = 4&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;200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Proposed Names ===
{{Idiosyncratic terms|Mode names proposed by [[User:Frostburn|Frostburn]] for their dreamy, yet oppressing sound especially in [[20edo]].}}
{{MOS modes
| Mode Names=
Paralysis $
Nightmare $
Succubus $
Incubus $
}}
 
== Scale tree ==
{{MOS tuning spectrum
| 6/5 = Bison
| 3/2 = [[Hedgehog]] is around here
| 11/7 = Echidna
| 13/8 = Supers, pogo
| 13/5 = Golden ekic
| 11/3 = Unidec
| 9/2 = Secant
}}
 
== Music ==
; [[User:Frostburn|Frostburn]]
* [https://youtu.be/nlF6al8MEuk ''Galloping Nightmares''] (2024) – synth metal
[[Category:Ekic| ]]
[[Category:8-tone scales]]
<!-- main article -->

Latest revision as of 14:01, 5 May 2025

↖ 5L 1s ↑ 6L 1s 7L 1s ↗
← 5L 2s 6L 2s 7L 2s →
↙ 5L 3s ↓ 6L 3s 7L 3s ↘ 
┌╥╥╥┬╥╥╥┬┐
│║║║│║║║││
││││││││││
└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLs
sLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 1\8 to 1\6 (150.0 ¢ to 200.0 ¢)
Dark 2\6 to 3\8 (400.0 ¢ to 450.0 ¢)
TAMNAMS information
Name ekic
Prefix ek-
Abbrev. ek
Related MOS scales
Parent 2L 4s
Sister 2L 6s
Daughters 8L 6s, 6L 8s
Neutralized 4L 4s
2-Flought 14L 2s, 6L 10s
Equal tunings
Equalized (L:s = 1:1) 1\8 (150.0 ¢)
Supersoft (L:s = 4:3) 4\30 (160.0 ¢)
Soft (L:s = 3:2) 3\22 (163.6 ¢)
Semisoft (L:s = 5:3) 5\36 (166.7 ¢)
Basic (L:s = 2:1) 2\14 (171.4 ¢)
Semihard (L:s = 5:2) 5\34 (176.5 ¢)
Hard (L:s = 3:1) 3\20 (180.0 ¢)
Superhard (L:s = 4:1) 4\26 (184.6 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)

6L 2s, named ekic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 2 small steps, with a period of 3 large steps and 1 small step that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 150 ¢ to 200 ¢, or from 400 ¢ to 450 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. There is only one significant (though small) harmonic entropy minimum with this MOS pattern: hedgehog, in which two generators are 6/5 and three are 4/3, same as porcupine.

6L 2s can be seen as a warped diatonic scale, where one additional large step is added to diatonic (5L 2s).

In addition to the true MOS pattern, there is a near-mos pattern, LLLLsLLs, in which the period is the only interval with more than two varieties. This near-MOS pattern is only proper if the generator is smaller than 2\14. Hedgehog is among these tunings.

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 6L 2s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-ekstep Perfect 0-ekstep P0eks 0 0.0 ¢
1-ekstep Diminished 1-ekstep d1eks s 0.0 ¢ to 150.0 ¢
Perfect 1-ekstep P1eks L 150.0 ¢ to 200.0 ¢
2-ekstep Minor 2-ekstep m2eks L + s 200.0 ¢ to 300.0 ¢
Major 2-ekstep M2eks 2L 300.0 ¢ to 400.0 ¢
3-ekstep Perfect 3-ekstep P3eks 2L + s 400.0 ¢ to 450.0 ¢
Augmented 3-ekstep A3eks 3L 450.0 ¢ to 600.0 ¢
4-ekstep Perfect 4-ekstep P4eks 3L + s 600.0 ¢
5-ekstep Diminished 5-ekstep d5eks 3L + 2s 600.0 ¢ to 750.0 ¢
Perfect 5-ekstep P5eks 4L + s 750.0 ¢ to 800.0 ¢
6-ekstep Minor 6-ekstep m6eks 4L + 2s 800.0 ¢ to 900.0 ¢
Major 6-ekstep M6eks 5L + s 900.0 ¢ to 1000.0 ¢
7-ekstep Perfect 7-ekstep P7eks 5L + 2s 1000.0 ¢ to 1050.0 ¢
Augmented 7-ekstep A7eks 6L + s 1050.0 ¢ to 1200.0 ¢
8-ekstep Perfect 8-ekstep P8eks 6L + 2s 1200.0 ¢

Generator chain

Generator chain of 6L 2s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
6 Augmented 2-ekdegree A2ekd Augmented 6-ekdegree A6ekd
5 Augmented 1-ekdegree A1ekd Augmented 5-ekdegree A5ekd
4 Augmented 0-ekdegree A0ekd Augmented 4-ekdegree A4ekd
3 Augmented 3-ekdegree A3ekd Augmented 7-ekdegree A7ekd
2 Major 2-ekdegree M2ekd Major 6-ekdegree M6ekd
1 Perfect 1-ekdegree P1ekd Perfect 5-ekdegree P5ekd
0 Perfect 0-ekdegree
Perfect 4-ekdegree		 P0ekd
P4ekd		 Perfect 4-ekdegree
Perfect 8-ekdegree		 P4ekd
P8ekd
−1 Perfect 3-ekdegree P3ekd Perfect 7-ekdegree P7ekd
−2 Minor 2-ekdegree m2ekd Minor 6-ekdegree m6ekd
−3 Diminished 1-ekdegree d1ekd Diminished 5-ekdegree d5ekd
−4 Diminished 4-ekdegree d4ekd Diminished 8-ekdegree d8ekd
−5 Diminished 3-ekdegree d3ekd Diminished 7-ekdegree d7ekd
−6 Diminished 2-ekdegree d2ekd Diminished 6-ekdegree d6ekd

Modes

Scale degrees of the modes of 6L 2s
UDP Cyclic
order 		Step
pattern 		Scale degree (ekdegree)
0 1 2 3 4 5 6 7 8
6|0(2) 1 LLLsLLLs Perf. Perf. Maj. Aug. Perf. Perf. Maj. Aug. Perf.
4|2(2) 2 LLsLLLsL Perf. Perf. Maj. Perf. Perf. Perf. Maj. Perf. Perf.
2|4(2) 3 LsLLLsLL Perf. Perf. Min. Perf. Perf. Perf. Min. Perf. Perf.
0|6(2) 4 sLLLsLLL Perf. Dim. Min. Perf. Perf. Dim. Min. Perf. Perf.

Proposed Names

This article or section contains multiple idiosyncratic terms. Such terms are used by only a few people and are not regularly used within the community.

Terms: Mode names proposed by Frostburn for their dreamy, yet oppressing sound especially in 20edo.

Modes of 6L 2s
UDP Cyclic
order		 Step
pattern		 Mode names
6|0(2) 1 LLLsLLLs Paralysis
4|2(2) 2 LLsLLLsL Nightmare
2|4(2) 3 LsLLLsLL Succubus
0|6(2) 4 sLLLsLLL Incubus

Scale tree

Scale tree and tuning spectrum of 6L 2s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\8 150.000 450.000 1:1 1.000 Equalized 6L 2s
6\46 156.522 443.478 6:5 1.200 Bison
5\38 157.895 442.105 5:4 1.250
9\68 158.824 441.176 9:7 1.286
4\30 160.000 440.000 4:3 1.333 Supersoft 6L 2s
11\82 160.976 439.024 11:8 1.375
7\52 161.538 438.462 7:5 1.400
10\74 162.162 437.838 10:7 1.429
3\22 163.636 436.364 3:2 1.500 Soft 6L 2s
Hedgehog is around here
11\80 165.000 435.000 11:7 1.571 Echidna
8\58 165.517 434.483 8:5 1.600
13\94 165.957 434.043 13:8 1.625 Supers, pogo
5\36 166.667 433.333 5:3 1.667 Semisoft 6L 2s
12\86 167.442 432.558 12:7 1.714
7\50 168.000 432.000 7:4 1.750
9\64 168.750 431.250 9:5 1.800
2\14 171.429 428.571 2:1 2.000 Basic 6L 2s
9\62 174.194 425.806 9:4 2.250
7\48 175.000 425.000 7:3 2.333
12\82 175.610 424.390 12:5 2.400
5\34 176.471 423.529 5:2 2.500 Semihard 6L 2s
13\88 177.273 422.727 13:5 2.600 Golden ekic
8\54 177.778 422.222 8:3 2.667
11\74 178.378 421.622 11:4 2.750
3\20 180.000 420.000 3:1 3.000 Hard 6L 2s
10\66 181.818 418.182 10:3 3.333
7\46 182.609 417.391 7:2 3.500
11\72 183.333 416.667 11:3 3.667 Unidec
4\26 184.615 415.385 4:1 4.000 Superhard 6L 2s
9\58 186.207 413.793 9:2 4.500 Secant
5\32 187.500 412.500 5:1 5.000
6\38 189.474 410.526 6:1 6.000
1\6 200.000 400.000 1:0 → ∞ Collapsed 6L 2s

Music

Frostburn
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