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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 = 1 |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2012-11-25 20:46:26 UTC</tt>.<br>
| | | nLargeSteps = 1 |
| : The original revision id was <tt>385887062</tt>.<br>
| | | nSmallSteps = 8 |
| : The revision comment was: <tt></tt><br>
| | | Equalized = 8 |
| 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 = Lssssssss |
| <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, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2<L<3 s=1) and Negri (3<L<4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L<= 4 s=3).
| | }} |
| || 0/1 || || || || || 0 ||= || | |
| || || || || || 1/13 || 92 4/13 ||= ||
| |
| || || || || 1/12 || || 100 ||= L/s=4:
| |
| generators smaller than this are "impractical" ||
| |
| || || || || || 2/23 || 104.347826 ||= || | |
| || || || 1/11 || || || 109 1/11 ||= L/s=3:
| |
| generators smaller than this may be considered "impractical" ||
| |
| || || || || || 3/32 || 112.5 ||= ||
| |
| || || || || 2/21 || || 114 2/7 ||= || | |
| || || || || || 3/31 || 116.129032 ||= || | |
| || || 1/10 || || || || 120 ||= || | |
| || || || || || 4/39 || 123 1/13 ||= ||
| |
| || || || || 3/29 || || 124.137931 ||= ||
| |
| || || || || || 5/48 || 125 ||= ||
| |
| || || || 2/19 || || || 126.315789 ||= ||
| |
| || || || || || 5/47 || 127.659574 ||= ||
| |
| || || || || 3/28 || || 128 4/7 ||= ||
| |
| || || || || || 4/37 || 129 27/37 ||= ||
| |
| || 1/9 || || || || || 133 1/3 ||= ||</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>1L 8s</title></head><body>This MOS, with a generator of up to 1/9edo (133 1/3 cents), represents temperaments like Miracle (2&lt;L&lt;3 s=1) and Negri (3&lt;L&lt;4 s=2). Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval of at least 3/28edo (L&lt;= 4 s=3).<br />
| |
|
| |
|
| | {{MOS intro}} |
|
| |
|
| <table class="wiki_table">
| | This MOS represents temperaments like [[Miracle]] and [[Negri]]. Of all the temperaments it represents, the [[harmonic entropy]] minimum is the one where the scale is generated by an interval near [[28edo|3\28]] (around [[14/13]]). |
| <tr>
| |
| <td>0/1<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>1/13<br />
| |
| </td>
| |
| <td>92 4/13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1/12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>100<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s=4:<br />
| |
| generators smaller than this are &quot;impractical&quot;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2/23<br />
| |
| </td>
| |
| <td>104.347826<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1/11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>109 1/11<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s=3:<br />
| |
| generators smaller than this may be considered &quot;impractical&quot;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/32<br />
| |
| </td>
| |
| <td>112.5<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2/21<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>114 2/7<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/31<br />
| |
| </td>
| |
| <td>116.129032<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>1/10<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><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 1/13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>124.137931<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/48<br />
| |
| </td>
| |
| <td>125<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2/19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>126.315789<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/47<br />
| |
| </td>
| |
| <td>127.659574<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/28<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>128 4/7<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/37<br />
| |
| </td>
| |
| <td>129 27/37<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1/9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>133 1/3<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | == Modes == |
| | {{MOS modes}} |
| | |
| | === Degrees === |
| | {{MOS mode degrees}} |
| | |
| | == Intervals == |
| | {{MOS intervals}} |
| | |
| | == Scale tree == |
| | Generator ranges: |
| | * Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1) |
| | * Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9) |
| | |
| | {| class="wikitable center-all" |
| | ! colspan="6" | Small step <br><span style="font-size:0.85em">(chroma-negative generator)</span> |
| | ! Cents |
| | ! L |
| | ! s |
| | ! L/s |
| | ! Comments |
| | |- |
| | | 1\9 || || || || || || 133.333 || 1 || 1 || 1.000 || |
| | |- |
| | | || || || || || 5\46 || 130.435 || 6 || 5 || 1.200 || |
| | |- |
| | | || || || || 4\37 || || 129.730 || 5 || 4 || 1.250 || |
| | |- |
| | | || || || || || 7\65 || 129.231 || 9 || 7 || 1.286 || |
| | |- |
| | | || || || 3\28 || || || 128.571 || 4 || 3 || 1.333 || |
| | |- |
| | | || || || || || 8\75 || 128.000 || 11 || 8 || 1.375 || |
| | |- |
| | | || || || || 5\47 || || 127.660 || 7 || 5 || 1.400 || |
| | |- |
| | | || || || || || 7\66 || 127.273 || 10 || 7 || 1.429 || |
| | |- |
| | | || || 2\19 || || || || 126.316 || 3 || 2 || 1.500 || [[Negri]] |
| | |- |
| | | || || || || || 7\67 || 125.373 || 11 || 7 || 1.571 || |
| | |- |
| | | || || || || 5\48 || || 125.000 || 8 || 5 || 1.600 || |
| | |- |
| | | || || || || || 8\77 || 124.675 || 13 || 8 || 1.625 || Golden negri (124.7656¢) |
| | |- |
| | | || || || 3\29 || || || 124.138 || 5 || 3 || 1.667 || |
| | |- |
| | | || || || || || 7\68 || 123.529 || 12 || 7 || 1.714 || |
| | |- |
| | | || || || || 4\39 || || 123.077 || 7 || 4 || 1.750 || |
| | |- |
| | | || || || || || 5\49 || 122.449 || 9 || 5 || 1.800 || |
| | |- |
| | | || 1\10 || || || || || 120.000 || 2 || 1 || 2.000 || Basic 1L 8s <br>(small steps larger than this are proper) |
| | |- |
| | | || || || || || 4\41 || 117.073 || 9 || 4 || 2.250 || [[Miracle]] |
| | |- |
| | | || || || || 3\31 || || 116.129 || 7 || 3 || 2.333 || Miracle/[[revelation]] |
| | |- |
| | | || || || || || 5\52 || 115.385 || 12 || 5 || 2.400 || |
| | |- |
| | | || || || 2\21 || || || 114.286 || 5 || 2 || 2.500 || |
| | |- |
| | | || || || || || 5\53 || 113.208 || 13 || 5 || 2.600 || Golden [[misneb]] (113.0153¢) |
| | |- |
| | | || || || || 3\32 || || 112.500 || 8 || 3 || 2.667 || |
| | |- |
| | | || || || || || 4\43 || 111.628 || 11 || 4 || 2.750 || |
| | |- |
| | | || || 1\11 || || || || 109.091 || 3 || 1 || 3.000 || |
| | |- |
| | | || || || || || 3\34 || 105.882 || 10 || 3 || 3.333 || |
| | |- |
| | | || || || || 2\23 || || 104.348 || 7 || 2 || 3.500 || |
| | |- |
| | | || || || || || 3\35 || 102.857 || 11 || 3 || 3.667 || |
| | |- |
| | | || || || 1\12 || || || 100.000 || 4 || 1 || 4.000 || [[Ripple]] |
| | |- |
| | | || || || || || 2\25 || 96.000 || 9 || 2 || 4.500 || [[Passion]] |
| | |- |
| | | || || || || 1\13 || || 92.308 || 5 || 1 || 5.000 || |
| | |- |
| | | || || || || || 1\14 || 85.714 || 6 || 1 || 6.000 || |
| | |- |
| | | 0\1 || || || || || || 0.000 || 1 || 0 || → inf || |
| | |} |
| | |
| | {{todo|expand}} |
| | [[Category:9-tone scales]] |
1L 8s, named antisubneutralic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 8 small steps, repeating every octave. Generators that produce this scale range from 1066.7 ¢ to 1200 ¢, or from 0 ¢ to 133.3 ¢.
This MOS represents temperaments like Miracle and Negri. Of all the temperaments it represents, the harmonic entropy minimum is the one where the scale is generated by an interval near 3\28 (around 14/13).
Modes
Modes of 1L 8s
| UDP |
Cyclic order |
Step pattern
|
| 8|0 |
1 |
Lssssssss
|
| 7|1 |
9 |
sLsssssss
|
| 6|2 |
8 |
ssLssssss
|
| 5|3 |
7 |
sssLsssss
|
| 4|4 |
6 |
ssssLssss
|
| 3|5 |
5 |
sssssLsss
|
| 2|6 |
4 |
ssssssLss
|
| 1|7 |
3 |
sssssssLs
|
| 0|8 |
2 |
ssssssssL
|
Degrees
Scale degrees of the modes of 1L 8s
| UDP
|
Cyclic order
|
Step pattern
|
Scale degree (abludegree)
|
| 0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
| 8|0
|
1
|
Lssssssss
|
Perf.
|
Aug.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 7|1
|
9
|
sLsssssss
|
Perf.
|
Perf.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 6|2
|
8
|
ssLssssss
|
Perf.
|
Perf.
|
Min.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 5|3
|
7
|
sssLsssss
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Maj.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 4|4
|
6
|
ssssLssss
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Maj.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 3|5
|
5
|
sssssLsss
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Min.
|
Maj.
|
Maj.
|
Perf.
|
Perf.
|
| 2|6
|
4
|
ssssssLss
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Maj.
|
Perf.
|
Perf.
|
| 1|7
|
3
|
sssssssLs
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Perf.
|
Perf.
|
| 0|8
|
2
|
ssssssssL
|
Perf.
|
Perf.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Min.
|
Dim.
|
Perf.
|
Intervals
Intervals of 1L 8s
| Intervals
|
Steps subtended
|
Range in cents
|
| Generic
|
Specific
|
Abbrev.
|
| 0-ablustep
|
Perfect 0-ablustep
|
P0ablus
|
0
|
0.0 ¢
|
| 1-ablustep
|
Perfect 1-ablustep
|
P1ablus
|
s
|
0.0 ¢ to 133.3 ¢
|
| Augmented 1-ablustep
|
A1ablus
|
L
|
133.3 ¢ to 1200.0 ¢
|
| 2-ablustep
|
Minor 2-ablustep
|
m2ablus
|
2s
|
0.0 ¢ to 266.7 ¢
|
| Major 2-ablustep
|
M2ablus
|
L + s
|
266.7 ¢ to 1200.0 ¢
|
| 3-ablustep
|
Minor 3-ablustep
|
m3ablus
|
3s
|
0.0 ¢ to 400.0 ¢
|
| Major 3-ablustep
|
M3ablus
|
L + 2s
|
400.0 ¢ to 1200.0 ¢
|
| 4-ablustep
|
Minor 4-ablustep
|
m4ablus
|
4s
|
0.0 ¢ to 533.3 ¢
|
| Major 4-ablustep
|
M4ablus
|
L + 3s
|
533.3 ¢ to 1200.0 ¢
|
| 5-ablustep
|
Minor 5-ablustep
|
m5ablus
|
5s
|
0.0 ¢ to 666.7 ¢
|
| Major 5-ablustep
|
M5ablus
|
L + 4s
|
666.7 ¢ to 1200.0 ¢
|
| 6-ablustep
|
Minor 6-ablustep
|
m6ablus
|
6s
|
0.0 ¢ to 800.0 ¢
|
| Major 6-ablustep
|
M6ablus
|
L + 5s
|
800.0 ¢ to 1200.0 ¢
|
| 7-ablustep
|
Minor 7-ablustep
|
m7ablus
|
7s
|
0.0 ¢ to 933.3 ¢
|
| Major 7-ablustep
|
M7ablus
|
L + 6s
|
933.3 ¢ to 1200.0 ¢
|
| 8-ablustep
|
Diminished 8-ablustep
|
d8ablus
|
8s
|
0.0 ¢ to 1066.7 ¢
|
| Perfect 8-ablustep
|
P8ablus
|
L + 7s
|
1066.7 ¢ to 1200.0 ¢
|
| 9-ablustep
|
Perfect 9-ablustep
|
P9ablus
|
L + 8s
|
1200.0 ¢
|
Scale tree
Generator ranges:
- Chroma-positive generator: 1066.6667 cents (8\9) to 1200 cents (1\1)
- Chroma-negative generator: 0 cents (0\1) to 133.3333 cents (1\9)
Small step (chroma-negative generator)
|
Cents
|
L
|
s
|
L/s
|
Comments
|
| 1\9 |
|
|
|
|
|
133.333 |
1 |
1 |
1.000 |
|
|
|
|
|
|
5\46 |
130.435 |
6 |
5 |
1.200 |
|
|
|
|
|
4\37 |
|
129.730 |
5 |
4 |
1.250 |
|
|
|
|
|
|
7\65 |
129.231 |
9 |
7 |
1.286 |
|
|
|
|
3\28 |
|
|
128.571 |
4 |
3 |
1.333 |
|
|
|
|
|
|
8\75 |
128.000 |
11 |
8 |
1.375 |
|
|
|
|
|
5\47 |
|
127.660 |
7 |
5 |
1.400 |
|
|
|
|
|
|
7\66 |
127.273 |
10 |
7 |
1.429 |
|
|
|
2\19 |
|
|
|
126.316 |
3 |
2 |
1.500 |
Negri
|
|
|
|
|
|
7\67 |
125.373 |
11 |
7 |
1.571 |
|
|
|
|
|
5\48 |
|
125.000 |
8 |
5 |
1.600 |
|
|
|
|
|
|
8\77 |
124.675 |
13 |
8 |
1.625 |
Golden negri (124.7656¢)
|
|
|
|
3\29 |
|
|
124.138 |
5 |
3 |
1.667 |
|
|
|
|
|
|
7\68 |
123.529 |
12 |
7 |
1.714 |
|
|
|
|
|
4\39 |
|
123.077 |
7 |
4 |
1.750 |
|
|
|
|
|
|
5\49 |
122.449 |
9 |
5 |
1.800 |
|
|
1\10 |
|
|
|
|
120.000 |
2 |
1 |
2.000 |
Basic 1L 8s (small steps larger than this are proper)
|
|
|
|
|
|
4\41 |
117.073 |
9 |
4 |
2.250 |
Miracle
|
|
|
|
|
3\31 |
|
116.129 |
7 |
3 |
2.333 |
Miracle/revelation
|
|
|
|
|
|
5\52 |
115.385 |
12 |
5 |
2.400 |
|
|
|
|
2\21 |
|
|
114.286 |
5 |
2 |
2.500 |
|
|
|
|
|
|
5\53 |
113.208 |
13 |
5 |
2.600 |
Golden misneb (113.0153¢)
|
|
|
|
|
3\32 |
|
112.500 |
8 |
3 |
2.667 |
|
|
|
|
|
|
4\43 |
111.628 |
11 |
4 |
2.750 |
|
|
|
1\11 |
|
|
|
109.091 |
3 |
1 |
3.000 |
|
|
|
|
|
|
3\34 |
105.882 |
10 |
3 |
3.333 |
|
|
|
|
|
2\23 |
|
104.348 |
7 |
2 |
3.500 |
|
|
|
|
|
|
3\35 |
102.857 |
11 |
3 |
3.667 |
|
|
|
|
1\12 |
|
|
100.000 |
4 |
1 |
4.000 |
Ripple
|
|
|
|
|
|
2\25 |
96.000 |
9 |
2 |
4.500 |
Passion
|
|
|
|
|
1\13 |
|
92.308 |
5 |
1 |
5.000 |
|
|
|
|
|
|
1\14 |
85.714 |
6 |
1 |
6.000 |
|
| 0\1 |
|
|
|
|
|
0.000 |
1 |
0 |
→ inf |
|