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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 = sinatonic |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-06 12:26:43 UTC</tt>.<br>
| | | Periods = 1 |
| : The original revision id was <tt>565466599</tt>.<br>
| | | nLargeSteps = 9 |
| : The revision comment was: <tt></tt><br>
| | | nSmallSteps = 1 |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| | | Equalized = 1 |
| <h4>Original Wikitext content:</h4>
| | | Collapsed = 1 |
| <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, generated by a two-third tone or small "trienthird" of 1/10edo (120 cents) to 1/9 (133.333), is called the "Grumpy" decatonic scale. It appears as the diatonic scale in temperaments such as Negri and Twothirdtonic.
| | | Pattern = LLLLLLLLLs |
| || 1/10 || || || || || 120 || | | }} |
| || || || || || 5/49 || 122.449 || | | {{MOS intro}} It appears as the [[albitonic scale]] in temperaments such as [[Negri]] and [[Twothirdtonic]]. |
| || || || || 4/39 || || 123.077 || | |
| || || || || || 7/68 || 123.529 || | |
| || || || 3/29 || || || 124.138 || | |
| || || || || || || 124.525 || | |
| || || || || || 8/77 || 124.675 ||
| |
| || || || || || || 124.766 ||
| |
| || || || || 5/48 || || 125 ||
| |
| || || || || || || 125.296 ||
| |
| || || || || || 7/67 || 125.373 ||
| |
| || || 2/19 || || || || 126.316 ||
| |
| || || || || || 7/66 || 127.273 ||
| |
| || || || || 5/47 || || 127.66 ||
| |
| || || || || || || 127.905 ||
| |
| || || || || || 8/75 || 128 ||
| |
| || || || || || || 128.097 ||
| |
| || || || 3/28 || || || 128.571 ||
| |
| || || || || || || 128.779 ||
| |
| || || || || || 7/65 || 129.231 ||
| |
| || || || || 4/37 || || 129.73 ||
| |
| || || || || || 5/46 || 130.435 ||
| |
| || 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>9L 1s</title></head><body>This MOS, generated by a two-third tone or small &quot;trienthird&quot; of 1/10edo (120 cents) to 1/9 (133.333), is called the &quot;Grumpy&quot; decatonic scale. It appears as the diatonic scale in temperaments such as Negri and Twothirdtonic.<br />
| |
|
| |
|
| | == Names == |
| | The [[TAMNAMS]] system calls this scale pattern '''sinatonic''' after [[sinaic]], a proposed interval category name for [[14/13]]-like intervals that generate the scale. Graham Breed's [[MOS naming]] calls this the "Grumpy" decatonic scale. |
|
| |
|
| <table class="wiki_table">
| | == Scale properties == |
| <tr>
| | {{TAMNAMS use}} |
| <td>1/10<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>120<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/49<br />
| |
| </td>
| |
| <td>122.449<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/39<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>123.077<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7/68<br />
| |
| </td>
| |
| <td>123.529<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>124.138<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>124.525<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8/77<br />
| |
| </td>
| |
| <td>124.675<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>124.766<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/48<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>125<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>125.296<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7/67<br />
| |
| </td>
| |
| <td>125.373<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>2/19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>126.316<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7/66<br />
| |
| </td>
| |
| <td>127.273<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/47<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>127.66<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>127.905<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8/75<br />
| |
| </td>
| |
| <td>128<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>128.097<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/28<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>128.571<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>128.779<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7/65<br />
| |
| </td>
| |
| <td>129.231<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/37<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>129.73<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/46<br />
| |
| </td>
| |
| <td>130.435<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>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | === Intervals === |
| | {{MOS intervals}} |
| | |
| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
| | |
| | == Scale tree == |
| | {{MOS tuning spectrum}} |
| | |
| | {{Todo|complete table|add examples|improve synopsis|inline=1|text=Populate scale tree}} |
| | |
| | [[Category:10-tone scales]] |
9L 1s, named sinatonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 120 ¢ to 133.3 ¢, or from 1066.7 ¢ to 1080 ¢. Scales of this form are always proper because there is only one small step. It appears as the albitonic scale in temperaments such as Negri and Twothirdtonic.
Names
The TAMNAMS system calls this scale pattern sinatonic after sinaic, a proposed interval category name for 14/13-like intervals that generate the scale. Graham Breed's MOS naming calls this the "Grumpy" decatonic scale.
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 9L 1s
Intervals
|
Steps subtended
|
Range in cents
|
Generic
|
Specific
|
Abbrev.
|
0-sinastep
|
Perfect 0-sinastep
|
P0sis
|
0
|
0.0 ¢
|
1-sinastep
|
Diminished 1-sinastep
|
d1sis
|
s
|
0.0 ¢ to 120.0 ¢
|
Perfect 1-sinastep
|
P1sis
|
L
|
120.0 ¢ to 133.3 ¢
|
2-sinastep
|
Minor 2-sinastep
|
m2sis
|
L + s
|
133.3 ¢ to 240.0 ¢
|
Major 2-sinastep
|
M2sis
|
2L
|
240.0 ¢ to 266.7 ¢
|
3-sinastep
|
Minor 3-sinastep
|
m3sis
|
2L + s
|
266.7 ¢ to 360.0 ¢
|
Major 3-sinastep
|
M3sis
|
3L
|
360.0 ¢ to 400.0 ¢
|
4-sinastep
|
Minor 4-sinastep
|
m4sis
|
3L + s
|
400.0 ¢ to 480.0 ¢
|
Major 4-sinastep
|
M4sis
|
4L
|
480.0 ¢ to 533.3 ¢
|
5-sinastep
|
Minor 5-sinastep
|
m5sis
|
4L + s
|
533.3 ¢ to 600.0 ¢
|
Major 5-sinastep
|
M5sis
|
5L
|
600.0 ¢ to 666.7 ¢
|
6-sinastep
|
Minor 6-sinastep
|
m6sis
|
5L + s
|
666.7 ¢ to 720.0 ¢
|
Major 6-sinastep
|
M6sis
|
6L
|
720.0 ¢ to 800.0 ¢
|
7-sinastep
|
Minor 7-sinastep
|
m7sis
|
6L + s
|
800.0 ¢ to 840.0 ¢
|
Major 7-sinastep
|
M7sis
|
7L
|
840.0 ¢ to 933.3 ¢
|
8-sinastep
|
Minor 8-sinastep
|
m8sis
|
7L + s
|
933.3 ¢ to 960.0 ¢
|
Major 8-sinastep
|
M8sis
|
8L
|
960.0 ¢ to 1066.7 ¢
|
9-sinastep
|
Perfect 9-sinastep
|
P9sis
|
8L + s
|
1066.7 ¢ to 1080.0 ¢
|
Augmented 9-sinastep
|
A9sis
|
9L
|
1080.0 ¢ to 1200.0 ¢
|
10-sinastep
|
Perfect 10-sinastep
|
P10sis
|
9L + s
|
1200.0 ¢
|
Generator chain
Generator chain of 9L 1s
Bright gens |
Scale degree |
Abbrev.
|
18 |
Augmented 8-sinadegree |
A8sid
|
17 |
Augmented 7-sinadegree |
A7sid
|
16 |
Augmented 6-sinadegree |
A6sid
|
15 |
Augmented 5-sinadegree |
A5sid
|
14 |
Augmented 4-sinadegree |
A4sid
|
13 |
Augmented 3-sinadegree |
A3sid
|
12 |
Augmented 2-sinadegree |
A2sid
|
11 |
Augmented 1-sinadegree |
A1sid
|
10 |
Augmented 0-sinadegree |
A0sid
|
9 |
Augmented 9-sinadegree |
A9sid
|
8 |
Major 8-sinadegree |
M8sid
|
7 |
Major 7-sinadegree |
M7sid
|
6 |
Major 6-sinadegree |
M6sid
|
5 |
Major 5-sinadegree |
M5sid
|
4 |
Major 4-sinadegree |
M4sid
|
3 |
Major 3-sinadegree |
M3sid
|
2 |
Major 2-sinadegree |
M2sid
|
1 |
Perfect 1-sinadegree |
P1sid
|
0 |
Perfect 0-sinadegree Perfect 10-sinadegree |
P0sid P10sid
|
−1 |
Perfect 9-sinadegree |
P9sid
|
−2 |
Minor 8-sinadegree |
m8sid
|
−3 |
Minor 7-sinadegree |
m7sid
|
−4 |
Minor 6-sinadegree |
m6sid
|
−5 |
Minor 5-sinadegree |
m5sid
|
−6 |
Minor 4-sinadegree |
m4sid
|
−7 |
Minor 3-sinadegree |
m3sid
|
−8 |
Minor 2-sinadegree |
m2sid
|
−9 |
Diminished 1-sinadegree |
d1sid
|
−10 |
Diminished 10-sinadegree |
d10sid
|
−11 |
Diminished 9-sinadegree |
d9sid
|
−12 |
Diminished 8-sinadegree |
d8sid
|
−13 |
Diminished 7-sinadegree |
d7sid
|
−14 |
Diminished 6-sinadegree |
d6sid
|
−15 |
Diminished 5-sinadegree |
d5sid
|
−16 |
Diminished 4-sinadegree |
d4sid
|
−17 |
Diminished 3-sinadegree |
d3sid
|
−18 |
Diminished 2-sinadegree |
d2sid
|
Modes
Scale degrees of the modes of 9L 1s
UDP
|
Cyclic order
|
Step pattern
|
Scale degree (sinadegree)
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
9|0
|
1
|
LLLLLLLLLs
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Aug.
|
Perf.
|
8|1
|
2
|
LLLLLLLLsL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
7|2
|
3
|
LLLLLLLsLL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Min.
|
Perf.
|
Perf.
|
6|3
|
4
|
LLLLLLsLLL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
5|4
|
5
|
LLLLLsLLLL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
4|5
|
6
|
LLLLsLLLLL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
3|6
|
7
|
LLLsLLLLLL
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
2|7
|
8
|
LLsLLLLLLL
|
Perf.
|
Perf.
|
Maj.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
1|8
|
9
|
LsLLLLLLLL
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
0|9
|
10
|
sLLLLLLLLL
|
Perf.
|
Dim.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
Scale tree
Scale tree and tuning spectrum of 9L 1s
Generator(edo)
|
Cents
|
Step ratio
|
Comments(always proper)
|
Bright
|
Dark
|
L:s
|
Hardness
|
1\10
|
|
|
|
|
|
120.000
|
1080.000
|
1:1
|
1.000
|
Equalized 9L 1s
|
|
|
|
|
|
6\59
|
122.034
|
1077.966
|
6:5
|
1.200
|
|
|
|
|
|
5\49
|
|
122.449
|
1077.551
|
5:4
|
1.250
|
|
|
|
|
|
|
9\88
|
122.727
|
1077.273
|
9:7
|
1.286
|
|
|
|
|
4\39
|
|
|
123.077
|
1076.923
|
4:3
|
1.333
|
Supersoft 9L 1s
|
|
|
|
|
|
11\107
|
123.364
|
1076.636
|
11:8
|
1.375
|
|
|
|
|
|
7\68
|
|
123.529
|
1076.471
|
7:5
|
1.400
|
|
|
|
|
|
|
10\97
|
123.711
|
1076.289
|
10:7
|
1.429
|
|
|
|
3\29
|
|
|
|
124.138
|
1075.862
|
3:2
|
1.500
|
Soft 9L 1s
|
|
|
|
|
|
11\106
|
124.528
|
1075.472
|
11:7
|
1.571
|
|
|
|
|
|
8\77
|
|
124.675
|
1075.325
|
8:5
|
1.600
|
|
|
|
|
|
|
13\125
|
124.800
|
1075.200
|
13:8
|
1.625
|
|
|
|
|
5\48
|
|
|
125.000
|
1075.000
|
5:3
|
1.667
|
Semisoft 9L 1s
|
|
|
|
|
|
12\115
|
125.217
|
1074.783
|
12:7
|
1.714
|
|
|
|
|
|
7\67
|
|
125.373
|
1074.627
|
7:4
|
1.750
|
|
|
|
|
|
|
9\86
|
125.581
|
1074.419
|
9:5
|
1.800
|
|
|
2\19
|
|
|
|
|
126.316
|
1073.684
|
2:1
|
2.000
|
Basic 9L 1s
|
|
|
|
|
|
9\85
|
127.059
|
1072.941
|
9:4
|
2.250
|
|
|
|
|
|
7\66
|
|
127.273
|
1072.727
|
7:3
|
2.333
|
|
|
|
|
|
|
12\113
|
127.434
|
1072.566
|
12:5
|
2.400
|
|
|
|
|
5\47
|
|
|
127.660
|
1072.340
|
5:2
|
2.500
|
Semihard 9L 1s
|
|
|
|
|
|
13\122
|
127.869
|
1072.131
|
13:5
|
2.600
|
|
|
|
|
|
8\75
|
|
128.000
|
1072.000
|
8:3
|
2.667
|
|
|
|
|
|
|
11\103
|
128.155
|
1071.845
|
11:4
|
2.750
|
|
|
|
3\28
|
|
|
|
128.571
|
1071.429
|
3:1
|
3.000
|
Hard 9L 1s
|
|
|
|
|
|
10\93
|
129.032
|
1070.968
|
10:3
|
3.333
|
|
|
|
|
|
7\65
|
|
129.231
|
1070.769
|
7:2
|
3.500
|
|
|
|
|
|
|
11\102
|
129.412
|
1070.588
|
11:3
|
3.667
|
|
|
|
|
4\37
|
|
|
129.730
|
1070.270
|
4:1
|
4.000
|
Superhard 9L 1s
|
|
|
|
|
|
9\83
|
130.120
|
1069.880
|
9:2
|
4.500
|
|
|
|
|
|
5\46
|
|
130.435
|
1069.565
|
5:1
|
5.000
|
|
|
|
|
|
|
6\55
|
130.909
|
1069.091
|
6:1
|
6.000
|
|
1\9
|
|
|
|
|
|
133.333
|
1066.667
|
1:0
|
→ ∞
|
Collapsed 9L 1s
|
|
Todo: complete table , add examples, improve synopsis
Populate scale tree
|