6L 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>
| Periods = 2
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-05-23 16:19:42 UTC</tt>.<br>
| nLargeSteps = 6
: The original revision id was <tt>551974104</tt>.<br>
| nSmallSteps = 4
: The revision comment was: <tt></tt><br>
| Equalized = 2
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Collapsed = 1
<h4>Original Wikitext content:</h4>
| Pattern = LLsLsLLsLs
<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">[[MOSScales|MOS]] pattern with 6 large steps and 4 small steps. Good temperaments include [[antikythera]], [[lemba]], and [[echidnic]].
| Name = lemon
||||||||||~ Generator ||~ Cents ||~ Comments ||
}}
|| 1\6 ||  ||  ||  ||  || 200 ||=   ||
{{MOS intro}}
||  ||  ||  ||  || 6\34 || 211.765 ||  ||
Supported temperaments include [[antikythera]], [[lemba]], and [[echidnic]].
||  ||  ||  || 5\28 ||  || 214.29 ||=   ||
||  ||  ||  ||  ||  || 217.51 ||  ||
||  ||  || 4\22 ||  ||  || 218.18 ||= Antikythera is around here ||
||  ||  ||  ||  ||  || 219.695 ||  ||
||  ||  ||  || 7\38 ||  || 221.05 ||=   ||
||  || 3\16 ||  ||  ||  || 225 ||= Boundary of propriety (generators larger than this are proper) ||
||  ||  ||  || 8\42 ||  || 228.57 ||=   ||
||  ||  || 5\26 ||  ||  || 230.77 ||= Lemba is around here ||
||  ||  ||  || 7\36 ||  || 233.33 ||=   ||
||  ||  ||  ||  || 9\46 || 234.78 ||= Echidnic is around here ||
|| 2\10 ||  ||  ||  ||  || 240 ||=   ||</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 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt; pattern with 6 large steps and 4 small steps. Good temperaments include &lt;a class="wiki_link" href="/antikythera"&gt;antikythera&lt;/a&gt;, &lt;a class="wiki_link" href="/lemba"&gt;lemba&lt;/a&gt;, and &lt;a class="wiki_link" href="/echidnic"&gt;echidnic&lt;/a&gt;.&lt;br /&gt;


== Scale properties ==
{{TAMNAMS use}}


&lt;table class="wiki_table"&gt;
=== Intervals ===
    &lt;tr&gt;
{{MOS intervals}}
        &lt;th colspan="5"&gt;Generator&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\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;200&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;6\34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;211.765&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5\28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;214.29&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;217.51&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;4\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;218.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Antikythera 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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;219.695&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;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7\38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;221.05&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;3\16&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;225&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Boundary of propriety (generators larger than this are proper)&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;8\42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;228.57&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;5\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;230.77&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Lemba 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;7\36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;233.33&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;9\46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;234.78&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Echidnic is around here&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2\10&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;240&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>
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 5/4 = Echidnic
| 4/3 = Baladic
| 3/2 = Lemba
| 8/3 = Divination
| 3/1 = Antikythera/astrology
| 10/3 = Wizard
}}
 
{{todo|expand}}
 
[[Category:lemon| ]]
[[Category:10-tone scales]]<!-- main article -->

Latest revision as of 15:59, 10 April 2025

↖ 5L 3s ↑ 6L 3s 7L 3s ↗
← 5L 4s 6L 4s 7L 4s →
↙ 5L 5s ↓ 6L 5s 7L 5s ↘ 
┌╥╥┬╥┬╥╥┬╥┬┐
│║║│║│║║│║││
││││││││││││
└┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLLsLs
sLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 3\10 to 2\6 (360.0 ¢ to 400.0 ¢)
Dark 1\6 to 2\10 (200.0 ¢ to 240.0 ¢)
TAMNAMS information
Name lemon
Prefix lem-
Abbrev. le
Related MOS scales
Parent 4L 2s
Sister 4L 6s
Daughters 10L 6s, 6L 10s
Neutralized 2L 8s
2-Flought 16L 4s, 6L 14s
Equal tunings
Equalized (L:s = 1:1) 3\10 (360.0 ¢)
Supersoft (L:s = 4:3) 11\36 (366.7 ¢)
Soft (L:s = 3:2) 8\26 (369.2 ¢)
Semisoft (L:s = 5:3) 13\42 (371.4 ¢)
Basic (L:s = 2:1) 5\16 (375.0 ¢)
Semihard (L:s = 5:2) 12\38 (378.9 ¢)
Hard (L:s = 3:1) 7\22 (381.8 ¢)
Superhard (L:s = 4:1) 9\28 (385.7 ¢)
Collapsed (L:s = 1:0) 2\6 (400.0 ¢)

6L 4s, named lemon in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 4 small steps, with a period of 3 large steps and 2 small steps that repeats every 600.0 ¢, or twice every octave. Generators that produce this scale range from 360 ¢ to 400 ¢, or from 200 ¢ to 240 ¢. Supported temperaments include antikythera, lemba, and echidnic.

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 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-lemstep Perfect 0-lemstep P0les 0 0.0 ¢
1-lemstep Minor 1-lemstep m1les s 0.0 ¢ to 120.0 ¢
Major 1-lemstep M1les L 120.0 ¢ to 200.0 ¢
2-lemstep Perfect 2-lemstep P2les L + s 200.0 ¢ to 240.0 ¢
Augmented 2-lemstep A2les 2L 240.0 ¢ to 400.0 ¢
3-lemstep Diminished 3-lemstep d3les L + 2s 200.0 ¢ to 360.0 ¢
Perfect 3-lemstep P3les 2L + s 360.0 ¢ to 400.0 ¢
4-lemstep Minor 4-lemstep m4les 2L + 2s 400.0 ¢ to 480.0 ¢
Major 4-lemstep M4les 3L + s 480.0 ¢ to 600.0 ¢
5-lemstep Perfect 5-lemstep P5les 3L + 2s 600.0 ¢
6-lemstep Minor 6-lemstep m6les 3L + 3s 600.0 ¢ to 720.0 ¢
Major 6-lemstep M6les 4L + 2s 720.0 ¢ to 800.0 ¢
7-lemstep Perfect 7-lemstep P7les 4L + 3s 800.0 ¢ to 840.0 ¢
Augmented 7-lemstep A7les 5L + 2s 840.0 ¢ to 1000.0 ¢
8-lemstep Diminished 8-lemstep d8les 4L + 4s 800.0 ¢ to 960.0 ¢
Perfect 8-lemstep P8les 5L + 3s 960.0 ¢ to 1000.0 ¢
9-lemstep Minor 9-lemstep m9les 5L + 4s 1000.0 ¢ to 1080.0 ¢
Major 9-lemstep M9les 6L + 3s 1080.0 ¢ to 1200.0 ¢
10-lemstep Perfect 10-lemstep P10les 6L + 4s 1200.0 ¢

Generator chain

Generator chain of 6L 4s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
7 Augmented 1-lemdegree A1led Augmented 6-lemdegree A6led
6 Augmented 3-lemdegree A3led Augmented 8-lemdegree A8led
5 Augmented 0-lemdegree A0led Augmented 5-lemdegree A5led
4 Augmented 2-lemdegree A2led Augmented 7-lemdegree A7led
3 Major 4-lemdegree M4led Major 9-lemdegree M9led
2 Major 1-lemdegree M1led Major 6-lemdegree M6led
1 Perfect 3-lemdegree P3led Perfect 8-lemdegree P8led
0 Perfect 0-lemdegree
Perfect 5-lemdegree		 P0led
P5led		 Perfect 5-lemdegree
Perfect 10-lemdegree		 P5led
P10led
−1 Perfect 2-lemdegree P2led Perfect 7-lemdegree P7led
−2 Minor 4-lemdegree m4led Minor 9-lemdegree m9led
−3 Minor 1-lemdegree m1led Minor 6-lemdegree m6led
−4 Diminished 3-lemdegree d3led Diminished 8-lemdegree d8led
−5 Diminished 5-lemdegree d5led Diminished 10-lemdegree d10led
−6 Diminished 2-lemdegree d2led Diminished 7-lemdegree d7led
−7 Diminished 4-lemdegree d4led Diminished 9-lemdegree d9led

Modes

Scale degrees of the modes of 6L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (lemdegree)
0 1 2 3 4 5 6 7 8 9 10
8|0(2) 1 LLsLsLLsLs Perf. Maj. Aug. Perf. Maj. Perf. Maj. Aug. Perf. Maj. Perf.
6|2(2) 4 LsLLsLsLLs Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf.
4|4(2) 2 LsLsLLsLsL Perf. Maj. Perf. Perf. Min. Perf. Maj. Perf. Perf. Min. Perf.
2|6(2) 5 sLLsLsLLsL Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf.
0|8(2) 3 sLsLLsLsLL Perf. Min. Perf. Dim. Min. Perf. Min. Perf. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\10 360.000 240.000 1:1 1.000 Equalized 6L 4s
17\56 364.286 235.714 6:5 1.200
14\46 365.217 234.783 5:4 1.250 Echidnic
25\82 365.854 234.146 9:7 1.286
11\36 366.667 233.333 4:3 1.333 Supersoft 6L 4s
Baladic
30\98 367.347 232.653 11:8 1.375
19\62 367.742 232.258 7:5 1.400
27\88 368.182 231.818 10:7 1.429
8\26 369.231 230.769 3:2 1.500 Soft 6L 4s
Lemba
29\94 370.213 229.787 11:7 1.571
21\68 370.588 229.412 8:5 1.600
34\110 370.909 229.091 13:8 1.625
13\42 371.429 228.571 5:3 1.667 Semisoft 6L 4s
31\100 372.000 228.000 12:7 1.714
18\58 372.414 227.586 7:4 1.750
23\74 372.973 227.027 9:5 1.800
5\16 375.000 225.000 2:1 2.000 Basic 6L 4s
Scales with tunings softer than this are proper
22\70 377.143 222.857 9:4 2.250
17\54 377.778 222.222 7:3 2.333
29\92 378.261 221.739 12:5 2.400
12\38 378.947 221.053 5:2 2.500 Semihard 6L 4s
31\98 379.592 220.408 13:5 2.600
19\60 380.000 220.000 8:3 2.667 Divination
26\82 380.488 219.512 11:4 2.750
7\22 381.818 218.182 3:1 3.000 Hard 6L 4s
Antikythera/astrology
23\72 383.333 216.667 10:3 3.333 Wizard
16\50 384.000 216.000 7:2 3.500
25\78 384.615 215.385 11:3 3.667
9\28 385.714 214.286 4:1 4.000 Superhard 6L 4s
20\62 387.097 212.903 9:2 4.500
11\34 388.235 211.765 5:1 5.000
13\40 390.000 210.000 6:1 6.000
2\6 400.000 200.000 1:0 → ∞ Collapsed 6L 4s
Retrieved from "https://en.xen.wiki/index.php?title=6L_4s&oldid=190607"