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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | 2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo|7edo]]) and 1\2 (1 degree of [[2edo|2edo]] — the half-octave tritone that appears in every even-numbered edo). |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 11:45:52 UTC</tt>.<br>
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| : The original revision id was <tt>565154563</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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">2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of [[7edo]]) and 1\2 (1 degree of [[2edo]] — the half-octave tritone that appears in every even-numbered edo).
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| The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise. | | The word "mavila" is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of "mavila." In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic_pairs#Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise. |
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| In terms of harmonic entropy, the most significant minimum is at [[Meantone family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1. | | In terms of harmonic entropy, the most significant minimum is at [[Meantone_family|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1. |
| ||||||||||||||~ generator in degrees of an [[edo]] ||~ generator in cents ||~ tetrachord ||~ L in cents ||~ s in cents ||~ L to s ratio ||~ comments ||
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| ||= 3\7 ||= ||= ||= ||= || || ||= 514.3 ||= 1 1 1 ||= 171.4 ||= 171.4 ||= 1.00 ||= ||
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| ||= ||= ||= ||= ||= 13\30 || || ||= 520.0 ||= 4 4 5 ||= 200.0 ||= 160.0 ||= 1.25 ||= Mavila extends from here... ||
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| ||= ||= ||= ||= 10\23 ||= || || ||= 521.7 ||= 3 3 4 ||= 208.7 ||= 156.5 ||= 1.33 ||= ||
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| ||= ||= ||= ||= ||= 17\39 || || ||= 523.1 ||= 5 5 7 ||= 215.4 ||= 153.8 ||= 1.40 ||= ||
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| ||= ||= ||= 7\16 ||= ||= || || ||= 525.0 ||= 2 2 3 ||= 225.0 ||= 150.0 ||= 1.50 ||= Mavila in Armodue
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| Optimum rank range (L/s=3/2) ||
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| || || || || || || || ||= 526.3 ||= <span style="display: block; text-align: center;">2 2 pi</span> ||= 231.5 ||= 147.4 ||= <span style="display: block; text-align: center;">pi/2</span> || ||
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| ||= ||= ||= ||= ||= 18\41 || || ||= 526.8 ||= 5 5 8 ||= 234.1 ||= 146.3 ||= 1.60 ||= ||
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| || || || || || || || ||= 1200*5/(13-phi) ||= 1 1 phi ||= 235.7 ||= 145.7 ||= phi ||= Golden mavila ||
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| || || || || || || 29\66 || ||= 527.3 ||= 8 8 13 ||= 236.4 ||= 145.5 ||= 1.625 ||= ||
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| ||= ||= ||= ||= 11\25 ||= || || ||= 528.0 ||= 3 3 5 ||= 240.0 ||= 144.0 ||= 1.67 ||= ||
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| || || || || || || || ||= 529.1 ||= <span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span> ||= 245.6 ||= 141.8 ||= <span style="background-color: #ffffff; display: block; text-align: center;">√3</span> || ||
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| ||= ||= ||= ||= ||= 15\34 || || ||= 529.4 ||= 4 4 7 ||= 247.1 ||= 141.2 ||= 1.75 ||= ...to somewhere around here ||
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| ||= ||= 4\9 ||= ||= ||= || || ||= 533.3 ||= 1 1 2 ||= 266.7 ||= 133.3 ||= 2.00 ||= Boundary of propriety (generators
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| smaller than this are proper) ||
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| ||= ||= ||= ||= ||= 13\29 || || ||= 537.9 ||= 3 3 7 ||= 289.7 ||= 124.1 ||= 2.33 ||= ||
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| ||= ||= ||= ||= 9\20 ||= || || ||= 540.0 ||= 2 2 5 ||= 300.0 ||= 120.0 ||= 2.50 ||= ||
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| || || || || || || || ||= 541.4 ||= <span style="display: block; text-align: center;">1 1 phi+1</span> ||= 306.9 ||= 117.2 ||= <span style="display: block; text-align: center;">1 1 phi+1</span> || ||
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| ||= ||= ||= ||= ||= 14\31 || || ||= 541.9 ||= 3 3 8 ||= 309.7 ||= 116.1 ||= 2.66 ||= ||
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| || || || || || || || ||= 542<span style="line-height: 1.5;">.5</span> ||= 1 1 e ||= 321.55 ||= 115.0 ||= e ||= L/s = e ||
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| ||= ||= ||= 5\11 ||= ||= || || ||= 545.5 ||= 1 1 3 ||= 327.3 ||= 109.1 ||= 3.00 ||= L/s = 3 ||
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| || || || || || || || ||= 546.8 ||= 1 1 pi ||= 334.1 ||= 106.35 ||= pi ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
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| ||= ||= ||= ||= ||= 11\24 || || ||= 550.0 ||= 2 2 7 ||= 350.0 ||= 100.0 ||= 3.50 ||= ||
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| ||= ||= ||= ||= 6\13 ||= || || ||= 553.8 ||= 1 1 4 ||= 369.2 ||= 92.3 ||= 4.00 ||= Thuja is optimal around here
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| L/s = 4 ||
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| ||= ||= ||= ||= ||= 7\15 || || ||= 560.0 ||= 1 1 5 ||= 400.0 ||= 80.0 ||= 5.00 ||= ie. (11/8)^5 = 5/1 ||
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| ||= ||= ||= ||= ||= ||= 8\17 ||= ||= 564.7 ||= 1 1 6 ||= 423.5 ||= 70.6 ||= 6.00 ||= ||
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| ||= ||= ||= ||= ||= ||= ||= 9\19 ||= 568.4 ||= 1 1 7 ||= 442.1 ||= 63.2 ||= 7.00 ||= Liese/Triton is around here ||
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| ||= 1\2 ||= ||= ||= ||= || || ||= 600.0 ||= 0 0 1 ||= 600.0 ||= 0 ||= — ||= ||</pre></div>
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| <h4>Original HTML content:</h4>
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| <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>2L 5s</title></head><body>2L 5s refers to a Moment of Symmetry scale with two large steps and five small steps. Common names for such a tuning are mavila and anti-diatonic. The generator is a sharp fourth (or flat fifth), falling between 3\7 (3 degrees of <a class="wiki_link" href="/7edo">7edo</a>) and 1\2 (1 degree of <a class="wiki_link" href="/2edo">2edo</a> — the half-octave tritone that appears in every even-numbered edo).<br />
| |
| <br />
| |
| The word &quot;mavila&quot; is used in different ways by different folks. Not every user of the word would consider every 2L 5s scale an instance of &quot;mavila.&quot; In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Score">score</a>, which is not intended to be treated as having any kind of fifth, flat or otherwise.<br />
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| <br />
| |
| In terms of harmonic entropy, the most significant minimum is at <a class="wiki_link" href="/Meantone%20family">Liese</a>/Triton, in which the generator is about 7/5 and three of them make a 3/1.<br />
| |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | ! colspan="7" | generator in degrees of an [[EDO|edo]] |
| | ! | generator in cents |
| | ! | tetrachord |
| | ! | L in cents |
| | ! | s in cents |
| | ! | L to s ratio |
| | ! | comments |
| | |- |
| | | style="text-align:center;" | 3\7 |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 514.3 |
| | | style="text-align:center;" | 1 1 1 |
| | | style="text-align:center;" | 171.4 |
| | | style="text-align:center;" | 171.4 |
| | | style="text-align:center;" | 1.00 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 13\30 |
| | | | |
| | | | |
| | | style="text-align:center;" | 520.0 |
| | | style="text-align:center;" | 4 4 5 |
| | | style="text-align:center;" | 200.0 |
| | | style="text-align:center;" | 160.0 |
| | | style="text-align:center;" | 1.25 |
| | | style="text-align:center;" | Mavila extends from here... |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 10\23 |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 521.7 |
| | | style="text-align:center;" | 3 3 4 |
| | | style="text-align:center;" | 208.7 |
| | | style="text-align:center;" | 156.5 |
| | | style="text-align:center;" | 1.33 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 17\39 |
| | | | |
| | | | |
| | | style="text-align:center;" | 523.1 |
| | | style="text-align:center;" | 5 5 7 |
| | | style="text-align:center;" | 215.4 |
| | | style="text-align:center;" | 153.8 |
| | | style="text-align:center;" | 1.40 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 7\16 |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 525.0 |
| | | style="text-align:center;" | 2 2 3 |
| | | style="text-align:center;" | 225.0 |
| | | style="text-align:center;" | 150.0 |
| | | style="text-align:center;" | 1.50 |
| | | style="text-align:center;" | Mavila in Armodue |
|
| |
|
| <table class="wiki_table">
| | Optimum rank range (L/s=3/2) |
| <tr>
| | |- |
| <th colspan="7">generator in degrees of an <a class="wiki_link" href="/edo">edo</a><br />
| | | | |
| </th>
| | | | |
| <th>generator in cents<br />
| | | | |
| </th>
| | | | |
| <th>tetrachord<br />
| | | | |
| </th>
| | | | |
| <th>L in cents<br />
| | | | |
| </th>
| | | style="text-align:center;" | 526.3 |
| <th>s in cents<br />
| | | style="text-align:center;" | <span style="display: block; text-align: center;">2 2 pi</span> |
| </th>
| | | style="text-align:center;" | 231.5 |
| <th>L to s ratio<br />
| | | style="text-align:center;" | 147.4 |
| </th>
| | | style="text-align:center;" | <span style="display: block; text-align: center;">pi/2</span> |
| <th>comments<br />
| | | | |
| </th>
| | |- |
| </tr>
| | | style="text-align:center;" | |
| <tr>
| | | style="text-align:center;" | |
| <td style="text-align: center;">3\7<br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 18\41 |
| </td>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | style="text-align:center;" | 526.8 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 5 5 8 |
| </td>
| | | style="text-align:center;" | 234.1 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 146.3 |
| </td>
| | | style="text-align:center;" | 1.60 |
| <td><br />
| | | style="text-align:center;" | |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;">514.3<br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;">1 1 1<br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;">171.4<br />
| | | | |
| </td>
| | | style="text-align:center;" | 1200*5/(13-phi) |
| <td style="text-align: center;">171.4<br />
| | | style="text-align:center;" | 1 1 phi |
| </td>
| | | style="text-align:center;" | 235.7 |
| <td style="text-align: center;">1.00<br />
| | | style="text-align:center;" | 145.7 |
| </td>
| | | style="text-align:center;" | phi |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | Golden mavila |
| </td>
| | |- |
| </tr>
| | | | |
| <tr>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | 29\66 |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | style="text-align:center;" | 527.3 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 8 8 13 |
| </td>
| | | style="text-align:center;" | 236.4 |
| <td style="text-align: center;">13\30<br />
| | | style="text-align:center;" | 145.5 |
| </td>
| | | style="text-align:center;" | 1.625 |
| <td><br />
| | | style="text-align:center;" | |
| </td>
| | |- |
| <td><br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | |
| <td style="text-align: center;">520.0<br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | 11\25 |
| <td style="text-align: center;">4 4 5<br />
| | | style="text-align:center;" | |
| </td>
| | | | |
| <td style="text-align: center;">200.0<br />
| | | | |
| </td>
| | | style="text-align:center;" | 528.0 |
| <td style="text-align: center;">160.0<br />
| | | style="text-align:center;" | 3 3 5 |
| </td>
| | | style="text-align:center;" | 240.0 |
| <td style="text-align: center;">1.25<br />
| | | style="text-align:center;" | 144.0 |
| </td>
| | | style="text-align:center;" | 1.67 |
| <td style="text-align: center;">Mavila extends from here...<br />
| | | style="text-align:center;" | |
| </td>
| | |- |
| </tr>
| | | | |
| <tr>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | style="text-align:center;" | 529.1 |
| <td style="text-align: center;">10\23<br />
| | | style="text-align:center;" | <span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span> |
| </td>
| | | style="text-align:center;" | 245.6 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 141.8 |
| </td>
| | | style="text-align:center;" | <span style="background-color: #ffffff; display: block; text-align: center;">√3</span> |
| <td><br />
| | | | |
| </td>
| | |- |
| <td><br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | |
| <td style="text-align: center;">521.7<br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | |
| <td style="text-align: center;">3 3 4<br />
| | | style="text-align:center;" | 15\34 |
| </td>
| | | | |
| <td style="text-align: center;">208.7<br />
| | | | |
| </td>
| | | style="text-align:center;" | 529.4 |
| <td style="text-align: center;">156.5<br />
| | | style="text-align:center;" | 4 4 7 |
| </td>
| | | style="text-align:center;" | 247.1 |
| <td style="text-align: center;">1.33<br />
| | | style="text-align:center;" | 141.2 |
| </td>
| | | style="text-align:center;" | 1.75 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | ...to somewhere around here |
| </td>
| | |- |
| </tr>
| | | style="text-align:center;" | |
| <tr>
| | | style="text-align:center;" | 4\9 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | |
| </td>
| | | style="text-align:center;" | |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | |
| </td>
| | | | |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | style="text-align:center;" | 533.3 |
| <td style="text-align: center;"><br />
| | | style="text-align:center;" | 1 1 2 |
| </td>
| | | style="text-align:center;" | 266.7 |
| <td style="text-align: center;">17\39<br />
| | | style="text-align:center;" | 133.3 |
| </td>
| | | style="text-align:center;" | 2.00 |
| <td><br />
| | | style="text-align:center;" | Boundary of propriety (generators |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">523.1<br />
| |
| </td>
| |
| <td style="text-align: center;">5 5 7<br />
| |
| </td>
| |
| <td style="text-align: center;">215.4<br />
| |
| </td>
| |
| <td style="text-align: center;">153.8<br />
| |
| </td>
| |
| <td style="text-align: center;">1.40<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
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| </td>
| |
| <td style="text-align: center;">7\16<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">525.0<br />
| |
| </td>
| |
| <td style="text-align: center;">2 2 3<br />
| |
| </td>
| |
| <td style="text-align: center;">225.0<br />
| |
| </td>
| |
| <td style="text-align: center;">150.0<br />
| |
| </td>
| |
| <td style="text-align: center;">1.50<br />
| |
| </td>
| |
| <td style="text-align: center;">Mavila in Armodue<br />
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| Optimum rank range (L/s=3/2)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td><br />
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| </td>
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| <td style="text-align: center;">526.3<br />
| |
| </td>
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| <td style="text-align: center;"><span style="display: block; text-align: center;">2 2 pi</span><br />
| |
| </td>
| |
| <td style="text-align: center;">231.5<br />
| |
| </td>
| |
| <td style="text-align: center;">147.4<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">pi/2</span><br />
| |
| </td>
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| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;"><br />
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| </td>
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| <td style="text-align: center;"><br />
| |
| </td>
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| <td style="text-align: center;">18\41<br />
| |
| </td>
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| <td><br />
| |
| </td>
| |
| <td><br />
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| </td>
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| <td style="text-align: center;">526.8<br />
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| </td>
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| <td style="text-align: center;">5 5 8<br />
| |
| </td>
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| <td style="text-align: center;">234.1<br />
| |
| </td>
| |
| <td style="text-align: center;">146.3<br />
| |
| </td>
| |
| <td style="text-align: center;">1.60<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><br />
| |
| </td>
| |
| <td style="text-align: center;">1200*5/(13-phi)<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 phi<br />
| |
| </td>
| |
| <td style="text-align: center;">235.7<br />
| |
| </td>
| |
| <td style="text-align: center;">145.7<br />
| |
| </td>
| |
| <td style="text-align: center;">phi<br />
| |
| </td>
| |
| <td style="text-align: center;">Golden mavila<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>29\66<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">527.3<br />
| |
| </td>
| |
| <td style="text-align: center;">8 8 13<br />
| |
| </td>
| |
| <td style="text-align: center;">236.4<br />
| |
| </td>
| |
| <td style="text-align: center;">145.5<br />
| |
| </td>
| |
| <td style="text-align: center;">1.625<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11\25<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">528.0<br />
| |
| </td>
| |
| <td style="text-align: center;">3 3 5<br />
| |
| </td>
| |
| <td style="text-align: center;">240.0<br />
| |
| </td>
| |
| <td style="text-align: center;">144.0<br />
| |
| </td>
| |
| <td style="text-align: center;">1.67<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><br />
| |
| </td>
| |
| <td style="text-align: center;">529.1<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="background-color: #ffffff;"><span style="line-height: 1.5;">1 1 </span>√3 </span><br />
| |
| </td>
| |
| <td style="text-align: center;">245.6<br />
| |
| </td>
| |
| <td style="text-align: center;">141.8<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="background-color: #ffffff; display: block; text-align: center;">√3</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">15\34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">529.4<br />
| |
| </td>
| |
| <td style="text-align: center;">4 4 7<br />
| |
| </td>
| |
| <td style="text-align: center;">247.1<br />
| |
| </td>
| |
| <td style="text-align: center;">141.2<br />
| |
| </td>
| |
| <td style="text-align: center;">1.75<br />
| |
| </td>
| |
| <td style="text-align: center;">...to somewhere around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">4\9<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">533.3<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 2<br />
| |
| </td>
| |
| <td style="text-align: center;">266.7<br />
| |
| </td>
| |
| <td style="text-align: center;">133.3<br />
| |
| </td>
| |
| <td style="text-align: center;">2.00<br />
| |
| </td>
| |
| <td style="text-align: center;">Boundary of propriety (generators<br />
| |
| smaller than this are proper)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">13\29<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">537.9<br />
| |
| </td>
| |
| <td style="text-align: center;">3 3 7<br />
| |
| </td>
| |
| <td style="text-align: center;">289.7<br />
| |
| </td>
| |
| <td style="text-align: center;">124.1<br />
| |
| </td>
| |
| <td style="text-align: center;">2.33<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9\20<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">540.0<br />
| |
| </td>
| |
| <td style="text-align: center;">2 2 5<br />
| |
| </td>
| |
| <td style="text-align: center;">300.0<br />
| |
| </td>
| |
| <td style="text-align: center;">120.0<br />
| |
| </td>
| |
| <td style="text-align: center;">2.50<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><br />
| |
| </td>
| |
| <td style="text-align: center;">541.4<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">1 1 phi+1</span><br />
| |
| </td>
| |
| <td style="text-align: center;">306.9<br />
| |
| </td>
| |
| <td style="text-align: center;">117.2<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">1 1 phi+1</span><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">14\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">541.9<br />
| |
| </td>
| |
| <td style="text-align: center;">3 3 8<br />
| |
| </td>
| |
| <td style="text-align: center;">309.7<br />
| |
| </td>
| |
| <td style="text-align: center;">116.1<br />
| |
| </td>
| |
| <td style="text-align: center;">2.66<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><br />
| |
| </td>
| |
| <td style="text-align: center;">542<span style="line-height: 1.5;">.5</span><br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 e<br />
| |
| </td>
| |
| <td style="text-align: center;">321.55<br />
| |
| </td>
| |
| <td style="text-align: center;">115.0<br />
| |
| </td>
| |
| <td style="text-align: center;">e<br />
| |
| </td>
| |
| <td style="text-align: center;">L/s = e<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">5\11<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">545.5<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 3<br />
| |
| </td>
| |
| <td style="text-align: center;">327.3<br />
| |
| </td>
| |
| <td style="text-align: center;">109.1<br />
| |
| </td>
| |
| <td style="text-align: center;">3.00<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><br />
| |
| </td>
| |
| <td style="text-align: center;">546.8<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 pi<br />
| |
| </td>
| |
| <td style="text-align: center;">334.1<br />
| |
| </td>
| |
| <td style="text-align: center;">106.35<br />
| |
| </td>
| |
| <td style="text-align: center;">pi<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">11\24<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">550.0<br />
| |
| </td>
| |
| <td style="text-align: center;">2 2 7<br />
| |
| </td>
| |
| <td style="text-align: center;">350.0<br />
| |
| </td>
| |
| <td style="text-align: center;">100.0<br />
| |
| </td>
| |
| <td style="text-align: center;">3.50<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">6\13<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">553.8<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 4<br />
| |
| </td>
| |
| <td style="text-align: center;">369.2<br />
| |
| </td>
| |
| <td style="text-align: center;">92.3<br />
| |
| </td>
| |
| <td style="text-align: center;">4.00<br />
| |
| </td>
| |
| <td style="text-align: center;">Thuja is optimal around here<br />
| |
| L/s = 4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">7\15<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">560.0<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 5<br />
| |
| </td>
| |
| <td style="text-align: center;">400.0<br />
| |
| </td>
| |
| <td style="text-align: center;">80.0<br />
| |
| </td>
| |
| <td style="text-align: center;">5.00<br />
| |
| </td>
| |
| <td style="text-align: center;">ie. (11/8)^5 = 5/1<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">8\17<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">564.7<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 6<br />
| |
| </td>
| |
| <td style="text-align: center;">423.5<br />
| |
| </td>
| |
| <td style="text-align: center;">70.6<br />
| |
| </td>
| |
| <td style="text-align: center;">6.00<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;">9\19<br />
| |
| </td>
| |
| <td style="text-align: center;">568.4<br />
| |
| </td>
| |
| <td style="text-align: center;">1 1 7<br />
| |
| </td>
| |
| <td style="text-align: center;">442.1<br />
| |
| </td>
| |
| <td style="text-align: center;">63.2<br />
| |
| </td>
| |
| <td style="text-align: center;">7.00<br />
| |
| </td>
| |
| <td style="text-align: center;">Liese/Triton is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td style="text-align: center;">1\2<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td style="text-align: center;">600.0<br />
| |
| </td>
| |
| <td style="text-align: center;">0 0 1<br />
| |
| </td>
| |
| <td style="text-align: center;">600.0<br />
| |
| </td>
| |
| <td style="text-align: center;">0<br />
| |
| </td>
| |
| <td style="text-align: center;">—<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| </body></html></pre></div>
| | smaller than this are proper) |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 13\29 |
| | | | |
| | | | |
| | | style="text-align:center;" | 537.9 |
| | | style="text-align:center;" | 3 3 7 |
| | | style="text-align:center;" | 289.7 |
| | | style="text-align:center;" | 124.1 |
| | | style="text-align:center;" | 2.33 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 9\20 |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 540.0 |
| | | style="text-align:center;" | 2 2 5 |
| | | style="text-align:center;" | 300.0 |
| | | style="text-align:center;" | 120.0 |
| | | style="text-align:center;" | 2.50 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | style="text-align:center;" | 541.4 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span> |
| | | style="text-align:center;" | 306.9 |
| | | style="text-align:center;" | 117.2 |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">1 1 phi+1</span> |
| | | | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 14\31 |
| | | | |
| | | | |
| | | style="text-align:center;" | 541.9 |
| | | style="text-align:center;" | 3 3 8 |
| | | style="text-align:center;" | 309.7 |
| | | style="text-align:center;" | 116.1 |
| | | style="text-align:center;" | 2.66 |
| | | style="text-align:center;" | |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | style="text-align:center;" | 542<span style="line-height: 1.5;">.5</span> |
| | | style="text-align:center;" | 1 1 e |
| | | style="text-align:center;" | 321.55 |
| | | style="text-align:center;" | 115.0 |
| | | style="text-align:center;" | e |
| | | style="text-align:center;" | L/s = e |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 5\11 |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 545.5 |
| | | style="text-align:center;" | 1 1 3 |
| | | style="text-align:center;" | 327.3 |
| | | style="text-align:center;" | 109.1 |
| | | style="text-align:center;" | 3.00 |
| | | style="text-align:center;" | L/s = 3 |
| | |- |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | | |
| | | style="text-align:center;" | 546.8 |
| | | style="text-align:center;" | 1 1 pi |
| | | style="text-align:center;" | 334.1 |
| | | style="text-align:center;" | 106.35 |
| | | style="text-align:center;" | pi |
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span> |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 11\24 |
| | | | |
| | | | |
| | | style="text-align:center;" | 550.0 |
| | | style="text-align:center;" | 2 2 7 |
| | | style="text-align:center;" | 350.0 |
| | | style="text-align:center;" | 100.0 |
| | | style="text-align:center;" | 3.50 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 6\13 |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 553.8 |
| | | style="text-align:center;" | 1 1 4 |
| | | style="text-align:center;" | 369.2 |
| | | style="text-align:center;" | 92.3 |
| | | style="text-align:center;" | 4.00 |
| | | style="text-align:center;" | Thuja is optimal around here |
| | |
| | L/s = 4 |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 7\15 |
| | | | |
| | | | |
| | | style="text-align:center;" | 560.0 |
| | | style="text-align:center;" | 1 1 5 |
| | | style="text-align:center;" | 400.0 |
| | | style="text-align:center;" | 80.0 |
| | | style="text-align:center;" | 5.00 |
| | | style="text-align:center;" | ie. (11/8)^5 = 5/1 |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 8\17 |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 564.7 |
| | | style="text-align:center;" | 1 1 6 |
| | | style="text-align:center;" | 423.5 |
| | | style="text-align:center;" | 70.6 |
| | | style="text-align:center;" | 6.00 |
| | | style="text-align:center;" | |
| | |- |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | 9\19 |
| | | style="text-align:center;" | 568.4 |
| | | style="text-align:center;" | 1 1 7 |
| | | style="text-align:center;" | 442.1 |
| | | style="text-align:center;" | 63.2 |
| | | style="text-align:center;" | 7.00 |
| | | style="text-align:center;" | Liese/Triton is around here |
| | |- |
| | | style="text-align:center;" | 1\2 |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | style="text-align:center;" | |
| | | | |
| | | | |
| | | style="text-align:center;" | 600.0 |
| | | style="text-align:center;" | 0 0 1 |
| | | style="text-align:center;" | 600.0 |
| | | style="text-align:center;" | 0 |
| | | style="text-align:center;" | — |
| | | style="text-align:center;" | |
| | |} |