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|
(23 intermediate revisions by 10 users not shown) |
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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 = 3 |
| : This revision was by author [[User:diagonalia|diagonalia]] and made on <tt>2017-01-03 23:00:17 UTC</tt>.<br>
| | | nLargeSteps = 3 |
| : The original revision id was <tt>603054444</tt>.<br>
| | | nSmallSteps = 6 |
| : The revision comment was: <tt></tt><br>
| | | Equalized = 1 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | Collapsed = 0 |
| <h4>Original Wikitext content:</h4>
| | | Pattern = LssLssLss |
| <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 MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.
| | | Name = tcherepnin |
| | }} |
| | {{MOS intro}} |
|
| |
|
| ||||||||||~ Generator ||~ Cents ||~ Comments ||
| | == Name == |
| || 0\3 || || || || || 0 ||= ||
| | [[TAMNAMS]] suggests the temperaement-agnostic name '''tcherepnin''' for this scale. This is named after Alexander Tcherepnin's 9-note scale which, in 12edo, is notated as C Db Eb E F G Ab A B C, forming the step pattern of HWHHWHHWH in standard notation (assuming a root of C). |
| || || || || || 1\21 || 57.143 || ||
| |
| || || || || 1\18 || || 66.667 ||= L/s=4 ||
| |
| || || || || || || 400/(2+pi) || ||
| |
| || || || 1\15 || || || 80 ||= L/s=3 ||
| |
| || || || || || || 400/(2+e) || ||
| |
| || || || || || 3\42 || 85.714 || ||
| |
| || || || || || || 400/(3+phi) || ||
| |
| || || || || 2\27 || || 88.889 ||= Augene is around here ||
| |
| || || 1\12 || || || || 100 ||= Boundary of propriety (generators
| |
| larger than this are proper) ||
| |
| || || || || || || 400/(2+sqrt(3)) || ||
| |
| || || || || 3\33 || || 109.091 ||= August is around here ||
| |
| || || || || || || 400/(2+phi) || ||
| |
| || || || || || 5\54 || 111.111 || ||
| |
| || || || || || || 400/(2+pi/2) || ||
| |
| || || || 2\21 || || || 114.286 ||= ||
| |
| || || || || 3\30 || || 120 ||= ||
| |
| || || || || || 4\39 || 123.077 || ||
| |
| || 1\9 || || || || || 133.333 ||= ||
| |
| .</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>3L 6s</title></head><body>This MOS has generators which range between 0 and 133.333 cents and three periods per octave and runs Lss Lss Lss.<br />
| |
| <br />
| |
|
| |
|
| | == Scale properties == |
| | {{TAMNAMS use}} |
|
| |
|
| <table class="wiki_table">
| | === Intervals === |
| <tr>
| | {{MOS intervals}} |
| <th colspan="5">Generator<br />
| |
| </th>
| |
| <th>Cents<br />
| |
| </th>
| |
| <th>Comments<br />
| |
| </th>
| |
| </tr>
| |
| <tr>
| |
| <td>0\3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>0<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1\21<br />
| |
| </td>
| |
| <td>57.143<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1\18<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>66.667<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s=4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400/(2+pi)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1\15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>80<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>400/(2+e)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\42<br />
| |
| </td>
| |
| <td>85.714<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400/(3+phi)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2\27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>88.889<br />
| |
| </td>
| |
| <td style="text-align: center;">Augene is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>1\12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>100<br />
| |
| </td>
| |
| <td style="text-align: center;">Boundary of propriety (generators<br />
| |
| larger than this are proper)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400/(2+sqrt(3))<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\33<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>109.091<br />
| |
| </td>
| |
| <td style="text-align: center;">August is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400/(2+phi)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\54<br />
| |
| </td>
| |
| <td>111.111<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>400/(2+pi/2)<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2\21<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>114.286<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\30<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>120<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4\39<br />
| |
| </td>
| |
| <td>123.077<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>133.333<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| .</body></html></pre></div>
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 9/5 = August |
| | | 12/5 = Augene |
| | | 11/4 = August |
| | | 10/3 = Inflated |
| | | 6/1 = Hemiug, hemiaug ↓ |
| | }} |
| | |
| | == External links == |
| | * Piano Encyclopedia, on Tcherepnin's 9-note scale: https://pianoencyclopedia.com/scales/tcherepnin-nine-note-mode-i/ |
| | |
| | [[Category:Tcherepnin| ]] |
| | [[Category:9-tone scales]] |
| | <!--main article--> |
3L 6s, named tcherepnin in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 6 small steps, with a period of 1 large step and 2 small steps that repeats every 400.0 ¢, or 3 times every octave. Generators that produce this scale range from 266.7 ¢ to 400 ¢, or from 0 ¢ to 133.3 ¢.
Name
TAMNAMS suggests the temperaement-agnostic name tcherepnin for this scale. This is named after Alexander Tcherepnin's 9-note scale which, in 12edo, is notated as C Db Eb E F G Ab A B C, forming the step pattern of HWHHWHHWH in standard notation (assuming a root of C).
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 3L 6s
Intervals
|
Steps subtended
|
Range in cents
|
Generic
|
Specific
|
Abbrev.
|
0-cherstep
|
Perfect 0-cherstep
|
P0chs
|
0
|
0.0 ¢
|
1-cherstep
|
Perfect 1-cherstep
|
P1chs
|
s
|
0.0 ¢ to 133.3 ¢
|
Augmented 1-cherstep
|
A1chs
|
L
|
133.3 ¢ to 400.0 ¢
|
2-cherstep
|
Diminished 2-cherstep
|
d2chs
|
2s
|
0.0 ¢ to 266.7 ¢
|
Perfect 2-cherstep
|
P2chs
|
L + s
|
266.7 ¢ to 400.0 ¢
|
3-cherstep
|
Perfect 3-cherstep
|
P3chs
|
L + 2s
|
400.0 ¢
|
4-cherstep
|
Perfect 4-cherstep
|
P4chs
|
L + 3s
|
400.0 ¢ to 533.3 ¢
|
Augmented 4-cherstep
|
A4chs
|
2L + 2s
|
533.3 ¢ to 800.0 ¢
|
5-cherstep
|
Diminished 5-cherstep
|
d5chs
|
L + 4s
|
400.0 ¢ to 666.7 ¢
|
Perfect 5-cherstep
|
P5chs
|
2L + 3s
|
666.7 ¢ to 800.0 ¢
|
6-cherstep
|
Perfect 6-cherstep
|
P6chs
|
2L + 4s
|
800.0 ¢
|
7-cherstep
|
Perfect 7-cherstep
|
P7chs
|
2L + 5s
|
800.0 ¢ to 933.3 ¢
|
Augmented 7-cherstep
|
A7chs
|
3L + 4s
|
933.3 ¢ to 1200.0 ¢
|
8-cherstep
|
Diminished 8-cherstep
|
d8chs
|
2L + 6s
|
800.0 ¢ to 1066.7 ¢
|
Perfect 8-cherstep
|
P8chs
|
3L + 5s
|
1066.7 ¢ to 1200.0 ¢
|
9-cherstep
|
Perfect 9-cherstep
|
P9chs
|
3L + 6s
|
1200.0 ¢
|
Generator chain
Generator chain of 3L 6s
Bright gens |
Scale degree |
Abbrev. |
Scale degree |
Abbrev. |
Scale degree |
Abbrev.
|
3 |
Augmented 0-cherdegree |
A0chd |
Augmented 3-cherdegree |
A3chd |
Augmented 6-cherdegree |
A6chd
|
2 |
Augmented 1-cherdegree |
A1chd |
Augmented 4-cherdegree |
A4chd |
Augmented 7-cherdegree |
A7chd
|
1 |
Perfect 2-cherdegree |
P2chd |
Perfect 5-cherdegree |
P5chd |
Perfect 8-cherdegree |
P8chd
|
0 |
Perfect 0-cherdegree Perfect 3-cherdegree |
P0chd P3chd |
Perfect 3-cherdegree Perfect 6-cherdegree |
P3chd P6chd |
Perfect 6-cherdegree Perfect 9-cherdegree |
P6chd P9chd
|
−1 |
Perfect 1-cherdegree |
P1chd |
Perfect 4-cherdegree |
P4chd |
Perfect 7-cherdegree |
P7chd
|
−2 |
Diminished 2-cherdegree |
d2chd |
Diminished 5-cherdegree |
d5chd |
Diminished 8-cherdegree |
d8chd
|
−3 |
Diminished 3-cherdegree |
d3chd |
Diminished 6-cherdegree |
d6chd |
Diminished 9-cherdegree |
d9chd
|
Modes
Scale degrees of the modes of 3L 6s
UDP
|
Cyclic order
|
Step pattern
|
Scale degree (cherdegree)
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
6|0(3)
|
1
|
LssLssLss
|
Perf.
|
Aug.
|
Perf.
|
Perf.
|
Aug.
|
Perf.
|
Perf.
|
Aug.
|
Perf.
|
Perf.
|
3|3(3)
|
3
|
sLssLssLs
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
Perf.
|
0|6(3)
|
2
|
ssLssLssL
|
Perf.
|
Perf.
|
Dim.
|
Perf.
|
Perf.
|
Dim.
|
Perf.
|
Perf.
|
Dim.
|
Perf.
|
Scale tree
Scale tree and tuning spectrum of 3L 6s
Generator(edo)
|
Cents
|
Step ratio
|
Comments
|
Bright
|
Dark
|
L:s
|
Hardness
|
2\9
|
|
|
|
|
|
266.667
|
133.333
|
1:1
|
1.000
|
Equalized 3L 6s
|
|
|
|
|
|
11\48
|
275.000
|
125.000
|
6:5
|
1.200
|
|
|
|
|
|
9\39
|
|
276.923
|
123.077
|
5:4
|
1.250
|
|
|
|
|
|
|
16\69
|
278.261
|
121.739
|
9:7
|
1.286
|
|
|
|
|
7\30
|
|
|
280.000
|
120.000
|
4:3
|
1.333
|
Supersoft 3L 6s
|
|
|
|
|
|
19\81
|
281.481
|
118.519
|
11:8
|
1.375
|
|
|
|
|
|
12\51
|
|
282.353
|
117.647
|
7:5
|
1.400
|
|
|
|
|
|
|
17\72
|
283.333
|
116.667
|
10:7
|
1.429
|
|
|
|
5\21
|
|
|
|
285.714
|
114.286
|
3:2
|
1.500
|
Soft 3L 6s
|
|
|
|
|
|
18\75
|
288.000
|
112.000
|
11:7
|
1.571
|
|
|
|
|
|
13\54
|
|
288.889
|
111.111
|
8:5
|
1.600
|
|
|
|
|
|
|
21\87
|
289.655
|
110.345
|
13:8
|
1.625
|
|
|
|
|
8\33
|
|
|
290.909
|
109.091
|
5:3
|
1.667
|
Semisoft 3L 6s
|
|
|
|
|
|
19\78
|
292.308
|
107.692
|
12:7
|
1.714
|
|
|
|
|
|
11\45
|
|
293.333
|
106.667
|
7:4
|
1.750
|
|
|
|
|
|
|
14\57
|
294.737
|
105.263
|
9:5
|
1.800
|
August
|
|
3\12
|
|
|
|
|
300.000
|
100.000
|
2:1
|
2.000
|
Basic 3L 6s Scales with tunings softer than this are proper
|
|
|
|
|
|
13\51
|
305.882
|
94.118
|
9:4
|
2.250
|
|
|
|
|
|
10\39
|
|
307.692
|
92.308
|
7:3
|
2.333
|
|
|
|
|
|
|
17\66
|
309.091
|
90.909
|
12:5
|
2.400
|
Augene
|
|
|
|
7\27
|
|
|
311.111
|
88.889
|
5:2
|
2.500
|
Semihard 3L 6s
|
|
|
|
|
|
18\69
|
313.043
|
86.957
|
13:5
|
2.600
|
|
|
|
|
|
11\42
|
|
314.286
|
85.714
|
8:3
|
2.667
|
|
|
|
|
|
|
15\57
|
315.789
|
84.211
|
11:4
|
2.750
|
August
|
|
|
4\15
|
|
|
|
320.000
|
80.000
|
3:1
|
3.000
|
Hard 3L 6s
|
|
|
|
|
|
13\48
|
325.000
|
75.000
|
10:3
|
3.333
|
Inflated
|
|
|
|
|
9\33
|
|
327.273
|
72.727
|
7:2
|
3.500
|
|
|
|
|
|
|
14\51
|
329.412
|
70.588
|
11:3
|
3.667
|
|
|
|
|
5\18
|
|
|
333.333
|
66.667
|
4:1
|
4.000
|
Superhard 3L 6s
|
|
|
|
|
|
11\39
|
338.462
|
61.538
|
9:2
|
4.500
|
|
|
|
|
|
6\21
|
|
342.857
|
57.143
|
5:1
|
5.000
|
|
|
|
|
|
|
7\24
|
350.000
|
50.000
|
6:1
|
6.000
|
Hemiug, hemiaug ↓
|
1\3
|
|
|
|
|
|
400.000
|
0.000
|
1:0
|
→ ∞
|
Collapsed 3L 6s
|
External links