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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:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-05 12:32:58 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>565332775</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 2s can be seen as a [[Warped diatonic|warped diatonic scale]], where one additional large step is added to diatonic (5L 2s). |
| ||||||~ Generator ||~ ||~ ||~ ||~ Cents ||~ Comments ||
| |
| || 1\8 || || || || || || 150 ||= ||
| |
| || || || 3\22 || || || || 163.64 ||= Hedgehog is around here ||
| |
| || || || || || || || 164.99 || ||
| |
| || || || || || 8\58 || || 165.52 ||= ||
| |
| || || || || || || 13\94 || 165.96 ||= Golden hedgehog/echidna ||
| |
| || || || || 5\36 || || || 166.67 ||= ||
| |
| || || || || || || || 167.72 || ||
| |
| || || 2\14 || || || || || 171.43 ||= Boundary of propriety for near-MOS
| |
| Optimum rank range (L/s=2/1) for MOS ||
| |
| || || || || 5\34 || || || 176.47 || ||
| |
| || || || || || || 13\88 || 177.27 || ||
| |
| || || || || || 8\54 || || 177.78 || ||
| |
| || || || || || || || 178.15 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
| |
| || || || 3\20 || || || || 180 ||= L/s = 3 ||
| |
| || || || || || || || 180.815 || <span style="display: block; text-align: center;">L/s = pi</span> ||
| |
| || || || || 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"><html><head><title>6L 2s</title></head><body>There is only one significant (though small) harmonic entropy minimum with this MOS pattern: <a class="wiki_link" href="/Porcupine%20family#Hedgehog">hedgehog</a>, in which two generators are 6/5 and three are 4/3, same as porcupine.<br />
| |
| <br />
| |
| 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).<br />
| |
|
| |
|
| | 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. |
|
| |
|
| <table class="wiki_table">
| | == Scale properties == |
| <tr>
| | {{TAMNAMS use}} |
| <th colspan="3">Generator<br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th><br />
| |
| </th>
| |
| <th>Cents<br />
| |
| </th>
| |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>1\8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>150<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\22<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>163.64<br />
| |
| </td>
| |
| <td style="text-align: center;">Hedgehog is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>164.99<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\58<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>165.52<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\94<br />
| |
| </td>
| |
| <td>165.96<br />
| |
| </td>
| |
| <td style="text-align: center;">Golden hedgehog/echidna<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\36<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>166.67<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>167.72<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>2\14<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>171.43<br />
| |
| </td>
| |
| <td style="text-align: center;">Boundary of propriety for near-MOS<br />
| |
| Optimum rank range (L/s=2/1) for MOS<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>176.47<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13\88<br />
| |
| </td>
| |
| <td>177.27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\54<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>177.78<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>178.15<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\20<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>180<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = 3<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>180.815<br />
| |
| </td>
| |
| <td><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/26<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>184.615<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = 4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>200<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></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 --> |
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