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| Line 1: |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot_family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7|roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic_pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.) |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-04 15:39:59 UTC</tt>.<br>
| |
| : The original revision id was <tt>565207855</tt>.<br>
| |
| : The revision comment was: <tt></tt><br>
| |
| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| |
| <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">There are two notable harmonic entropy minima with this [[MOSScales|MOS]] pattern. The first is [[Tetracot family|tetracot]], in which four generators make a 3/2, and the second is known as [[roulette7]], the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament [[Chromatic pairs#Roulette|roulette]]. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)
| |
|
| |
|
| The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale. | | The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale. |
| Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step.
| |
| ||||||||||||~ Generator ||~ Cents ||~ Comments ||
| |
| || 1\7 || || || || || || 171.43 ||= ||
| |
| || || || || || || 6\41 || 175.61 ||= Enipucrop is between here and 1\7 ||
| |
| || || || || || 5\34 || || 176.47 ||= Tetracot is around here ||
| |
| || || || || 4\27 || || || 177.78 ||= ||
| |
| || || || 3\20 || || || || 180 ||= ||
| |
| || || || || || || || 180.815 || ||
| |
| || || || || || 8\53 || || 181.13 ||= ||
| |
| || || || || || || || 1200/(5+phi) ||= Unnamed golden temperament (discussed in [[http://launch.groups.yahoo.com/group/tuning/message/100254|this thread]]) ||
| |
| || || || || 5\33 || || || 181.82 ||= ||
| |
| || || || || || || || 182.44 || ||
| |
| || || || || || 7\46 || || 182.61 || ||
| |
| || || 2\13 || || || || || 184.62 ||= Optimum rank range glacial (L/s=2/1) ||
| |
| || || || || 5\32 || || || 187.5 || ||
| |
| || || || || || || || 188.03 || ||
| |
| || || || || || 8\51 || || 188.235 || ||
| |
| || || || || || || || 188.45 ||= <span style="display: block; text-align: center;">L/s = e</span> ||
| |
| || || || 3\19 || || || || 189.47 ||= L/s = 3 ||
| |
| || || || || || || || 189.92 ||= <span style="display: block; text-align: center;">L/s = pi</span> ||
| |
| || || || || 4\25 || || || 192 ||= L/s = 4 ||
| |
| || || || || || 5\31 || || 193.55 ||= Luna/hemithird/roulette is around here ||
| |
| || 1\6 || || || || || || 200 ||= ||</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>6L 1s</title></head><body>There are two notable harmonic entropy minima with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern. The first is <a class="wiki_link" href="/Tetracot%20family">tetracot</a>, in which four generators make a 3/2, and the second is known as <a class="wiki_link" href="/roulette7">roulette7</a>, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament <a class="wiki_link" href="/Chromatic%20pairs#Roulette">roulette</a>. (Other temperaments like &quot;luna&quot;, &quot;hemithird&quot;, and &quot;hemiwürschmidt&quot; have very similar 7-note MOSes.)<br />
| |
| <br />
| |
| The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.<br />
| |
| Scales of this form are always <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>, because there is only one small step.<br />
| |
|
| |
|
| | Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step. |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th colspan="6">Generator<br />
| | ! colspan="6" | Generator |
| </th>
| | ! | Cents |
| <th>Cents<br />
| | ! | Comments |
| </th>
| | |- |
| <th>Comments<br />
| | | | 1\7 |
| </th>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td>1\7<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 171.43 |
| </td>
| | | style="text-align:center;" | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 6\41 |
| </td>
| | | | 175.61 |
| <td>171.43<br />
| | | style="text-align:center;" | Enipucrop is between here and 1\7 |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td><br />
| | | | 5\34 |
| </td>
| | | | |
| <td><br />
| | | | 176.47 |
| </td>
| | | style="text-align:center;" | Tetracot is around here |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 4\27 |
| </td>
| | | | |
| <td>6\41<br />
| | | | |
| </td>
| | | | 177.78 |
| <td>175.61<br />
| | | style="text-align:center;" | |
| </td>
| | |- |
| <td style="text-align: center;">Enipucrop is between here and 1\7<br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | 3\20 |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 180 |
| </td>
| | | style="text-align:center;" | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>5\34<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 180.815 |
| <td>176.47<br />
| | | | |
| </td>
| | |- |
| <td style="text-align: center;">Tetracot is around here<br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td><br />
| | | | 8\53 |
| </td>
| | | | |
| <td><br />
| | | | 181.13 |
| </td>
| | | style="text-align:center;" | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td>4\27<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(5+phi) |
| <td>177.78<br />
| | | style="text-align:center;" | Unnamed golden temperament (discussed in [http://launch.groups.yahoo.com/group/tuning/message/100254 this thread]) |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | 5\33 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 181.82 |
| </td>
| | | style="text-align:center;" | |
| <td>3\20<br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 182.44 |
| <td>180<br />
| | | | |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td><br />
| | | | 7\46 |
| </td>
| | | | |
| <td><br />
| | | | 182.61 |
| </td>
| | | | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | 2\13 |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 184.62 |
| <td>180.815<br />
| | | style="text-align:center;" | Optimum rank range glacial (L/s=2/1) |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | 5\32 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 187.5 |
| </td>
| | | | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>8\53<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 188.03 |
| <td>181.13<br />
| | | | |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td><br />
| | | | 8\51 |
| </td>
| | | | |
| <td><br />
| | | | 188.235 |
| </td>
| | | | |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 188.45 |
| <td>1200/(5+phi)<br />
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span> |
| </td>
| | |- |
| <td style="text-align: center;">Unnamed golden temperament (discussed in <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/100254" rel="nofollow">this thread</a>)<br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | 3\19 |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 189.47 |
| </td>
| | | style="text-align:center;" | L/s = 3 |
| <td><br />
| | |- |
| </td>
| | | | |
| <td>5\33<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 189.92 |
| <td>181.82<br />
| | | style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span> |
| </td>
| | |- |
| <td style="text-align: center;"><br />
| | | | |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | 4\25 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 192 |
| </td>
| | | style="text-align:center;" | L/s = 4 |
| <td><br />
| | |- |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 5\31 |
| <td><br />
| | | | |
| </td>
| | | | 193.55 |
| <td>182.44<br />
| | | style="text-align:center;" | Luna/hemithird/roulette is around here |
| </td>
| | |- |
| <td><br />
| | | | 1\6 |
| </td>
| | | | |
| </tr>
| | | | |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 200 |
| </td>
| | | style="text-align:center;" | |
| <td><br />
| | |} |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>7\46<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>182.61<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>2\13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>184.62<br />
| |
| </td>
| |
| <td style="text-align: center;">Optimum rank range glacial (L/s=2/1)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5\32<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>187.5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>188.03<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8\51<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>188.235<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>188.45<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = e</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3\19<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>189.47<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>189.92<br />
| |
| </td>
| |
| <td style="text-align: center;"><span style="display: block; text-align: center;">L/s = pi</span><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4\25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>192<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>5\31<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>193.55<br />
| |
| </td>
| |
| <td style="text-align: center;">Luna/hemithird/roulette is around here<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1\6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>200<br />
| |
| </td>
| |
| <td style="text-align: center;"><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
There are two notable harmonic entropy minima with this MOS pattern. The first is tetracot, in which four generators make a 3/2, and the second is known as roulette7, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament roulette. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.
Scales of this form are always proper, because there is only one small step.
| Generator
|
Cents
|
Comments
|
| 1\7
|
|
|
|
|
|
171.43
|
|
|
|
|
|
|
|
6\41
|
175.61
|
Enipucrop is between here and 1\7
|
|
|
|
|
|
5\34
|
|
176.47
|
Tetracot is around here
|
|
|
|
|
4\27
|
|
|
177.78
|
|
|
|
|
3\20
|
|
|
|
180
|
|
|
|
|
|
|
|
|
180.815
|
|
|
|
|
|
|
8\53
|
|
181.13
|
|
|
|
|
|
|
|
|
1200/(5+phi)
|
Unnamed golden temperament (discussed in this thread)
|
|
|
|
|
5\33
|
|
|
181.82
|
|
|
|
|
|
|
|
|
182.44
|
|
|
|
|
|
|
7\46
|
|
182.61
|
|
|
|
2\13
|
|
|
|
|
184.62
|
Optimum rank range glacial (L/s=2/1)
|
|
|
|
|
5\32
|
|
|
187.5
|
|
|
|
|
|
|
|
|
188.03
|
|
|
|
|
|
|
8\51
|
|
188.235
|
|
|
|
|
|
|
|
|
188.45
|
L/s = e
|
|
|
|
3\19
|
|
|
|
189.47
|
L/s = 3
|
|
|
|
|
|
|
|
189.92
|
L/s = pi
|
|
|
|
|
4\25
|
|
|
192
|
L/s = 4
|
|
|
|
|
|
5\31
|
|
193.55
|
Luna/hemithird/roulette is around here
|
| 1\6
|
|
|
|
|
|
200
|
|