7L 1s
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There are two notable [[harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The first is [[Porcupine family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc. Scales of this form are always [[Rothenberg propriety|proper]], because there is only one small step. ||||||||||||~ [[Generator]] ||~ [[Cent]]s ||~ Scale in [[EDO]] steps ||~ Comments || || 1\7 || || || || || || 171.43 ||= 1 1 1 1 1 1 1 0 ||= || || || || || 4\29 || || || 165.52 ||= 4 4 4 4 4 4 4 1 ||= L/s = 4 || || || || || || || || 163.97 ||= pi pi pi pi pi pi pi 1 ||= <span style="display: block; text-align: center;">L/s = pi</span> || || || || 3\22 || || || || 163.64 ||= 3 3 3 3 3 3 3 1 ||= L/s = 3 || ||= ||= ||= ||= ||= ||= ||= 162.87 ||= e e e e e e e e 1 ||= <span style="display: block; text-align: center;">L/s = e</span> || || || || || || 8\59 || || 162,71 ||= <span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span> || || || || || || || || 13\96 || 162.5 ||= <span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span> || || || || || || 5\37 || || || 162.16 ||= 5 5 5 5 5 5 5 2 ||= Porcupine is in this general region || || || || || || 7\52 || || 161.54 ||= 7 7 7 7 7 7 7 3 ||= || || || 2\15 || || || || || 160 ||= 2 2 2 2 2 2 2 1 ||= Optimum rank range (L/s=2/1) porcupine || || || || || || || || 158.37 ||= <span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span> || || || || || || 5\38 || || || 157.89 ||= 5 5 5 5 5 5 5 3 ||= || || || || || || || 13\99 || 157.58 ||= 13 13 13 13 13 13 13 8 ||= Golden porcupine / golden hemikleismic || || || || || || 8\61 || || 157.38 ||= 8 8 8 8 8 8 8 5 ||= || || || || || || || (11\84) || 157.14 ||= <span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">pi pi pi pi pi pi pi 2</span> || || || || || 3\23 || || || || 156.52 ||= 3 3 3 3 3 3 3 2 ||= || || || || || || || 10\77 || 155.84 ||= 10 10 10 10 10 10 10 7 ||= Greeley is around here || || || || || || 7\54 || || 155.56 ||= 7 7 7 7 7 7 7 5 ||= || || || || || 4\31 || || || 154.84 ||= 4 4 4 4 4 4 4 3 ||= || || 1\8 || || || || || || 150 ||= 1 1 1 1 1 1 1 1 ||= ||
Original HTML content:
<html><head><title>7L 1s</title></head><body>There are two notable <a class="wiki_link" href="/harmonic%20entropy">harmonic entropy</a> minima with this <a class="wiki_link" href="/MOSScales">MOS</a> pattern. The first is <a class="wiki_link" href="/Porcupine%20family">porcupine</a>, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is <a class="wiki_link" href="/Chromatic%20pairs#Greeley">greeley</a>, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.<br />
<br />
Scales of this form are always <a class="wiki_link" href="/Rothenberg%20propriety">proper</a>, because there is only one small step.<br />
<table class="wiki_table">
<tr>
<th colspan="6"><a class="wiki_link" href="/Generator">Generator</a><br />
</th>
<th><a class="wiki_link" href="/Cent">Cent</a>s<br />
</th>
<th>Scale in <a class="wiki_link" href="/EDO">EDO</a> steps<br />
</th>
<th>Comments<br />
</th>
</tr>
<tr>
<td>1\7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>171.43<br />
</td>
<td style="text-align: center;">1 1 1 1 1 1 1 0<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\29<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>165.52<br />
</td>
<td style="text-align: center;">4 4 4 4 4 4 4 1<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><br />
</td>
<td>163.97<br />
</td>
<td style="text-align: center;">pi pi pi pi pi pi pi 1<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>3\22<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>163.64<br />
</td>
<td style="text-align: center;">3 3 3 3 3 3 3 1<br />
</td>
<td style="text-align: center;">L/s = 3<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;">162.87<br />
</td>
<td style="text-align: center;">e e e e e e e e 1<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><br />
</td>
<td><br />
</td>
<td>8\59<br />
</td>
<td><br />
</td>
<td>162,71<br />
</td>
<td style="text-align: center;"><span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>13\96<br />
</td>
<td>162.5<br />
</td>
<td style="text-align: center;"><span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\37<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>162.16<br />
</td>
<td style="text-align: center;">5 5 5 5 5 5 5 2<br />
</td>
<td style="text-align: center;">Porcupine is in this general region<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\52<br />
</td>
<td><br />
</td>
<td>161.54<br />
</td>
<td style="text-align: center;">7 7 7 7 7 7 7 3<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>2\15<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>160<br />
</td>
<td style="text-align: center;">2 2 2 2 2 2 2 1<br />
</td>
<td style="text-align: center;">Optimum rank range (L/s=2/1) porcupine<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>158.37<br />
</td>
<td style="text-align: center;"><span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>5\38<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>157.89<br />
</td>
<td style="text-align: center;">5 5 5 5 5 5 5 3<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>13\99<br />
</td>
<td>157.58<br />
</td>
<td style="text-align: center;">13 13 13 13 13 13 13 8<br />
</td>
<td style="text-align: center;">Golden porcupine / golden hemikleismic<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>8\61<br />
</td>
<td><br />
</td>
<td>157.38<br />
</td>
<td style="text-align: center;">8 8 8 8 8 8 8 5<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>(11\84)<br />
</td>
<td>157.14<br />
</td>
<td style="text-align: center;"><span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">pi pi pi pi pi pi pi 2</span><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>3\23<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>156.52<br />
</td>
<td style="text-align: center;">3 3 3 3 3 3 3 2<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>10\77<br />
</td>
<td>155.84<br />
</td>
<td style="text-align: center;">10 10 10 10 10 10 10 7<br />
</td>
<td style="text-align: center;">Greeley is around here<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>7\54<br />
</td>
<td><br />
</td>
<td>155.56<br />
</td>
<td style="text-align: center;">7 7 7 7 7 7 7 5<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>4\31<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>154.84<br />
</td>
<td style="text-align: center;">4 4 4 4 4 4 4 3<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td>1\8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>150<br />
</td>
<td style="text-align: center;">1 1 1 1 1 1 1 1<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
</body></html>