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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | In the theory of [[Margo_Schulter|Margo Schulter]], ''interseptimal'' is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8/7|8/7]] and [[7/6|7/6]], or [[12/7|12/7]] and [[7/4|7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt Regions of the Interval Spectrum]: |
| 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-05-03 01:23:45 UTC</tt>.<br>
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| : The original revision id was <tt>581952677</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">In the theory of [[Margo Schulter]], //interseptimal// is a category of intervals which occupy regions intermediate between two septimal ratios such as [[8_7|8/7]] and [[7_6|7/6]], or [[12_7|12/7]] and [[7_4|7/4]]. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article [[http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt|Regions of the Interval Spectrum]]:
| |
| # Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢
| |
| # Maj3-4 -- intermediate between [[9_7|9/7]] and [[21_16|21/16]] -- 440¢-468¢
| |
| # 5-min6 -- intermediate between [[32_21|32/21]] and [[14_9|14/9]] -- 732¢-760¢
| |
| # Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢
| |
|
| |
|
| Interseptimal intervals are well-represented in [[24edo]] at 250¢, 450¢, 750¢ and 950¢. They also appear in [[19edo]] and [[29edo]].
| | <ol><li>Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢</li><li>Maj3-4 -- intermediate between [[9/7|9/7]] and [[21/16|21/16]] -- 440¢-468¢</li><li>5-min6 -- intermediate between [[32/21|32/21]] and [[14/9|14/9]] -- 732¢-760¢</li><li>Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢</li></ol> |
|
| |
|
| As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word //tritone// rather than diminished fifth or augmented fourth). Possible names that could be used are:
| | Interseptimal intervals are well-represented in [[24edo|24edo]] at 250¢, 450¢, 750¢ and 950¢. They also appear in [[19edo|19edo]] and [[29edo|29edo]]. |
|
| |
|
| # 240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.
| | As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word ''tritone'' rather than diminished fifth or augmented fourth). Possible names that could be used are: |
| # 440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.
| | |
| # 732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).
| | <ol><li>240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.</li><li>440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.</li><li>732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).</li><li>940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even [[edt|edts]] have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.</li></ol> |
| # 940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even [[edt|edts]] have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.
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| This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". | | This makes notating these intervals very easy as long as we have an agreed-upon symbol for "semi". |
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| By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma (50:49), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis (49:48). | | By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma (50:49), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis (49:48). |
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| |
|
| | | ==Examples== |
| ==Examples== | |
| Some interseptimal intervals in all four ranges, both just and tempered, are listed below. | | Some interseptimal intervals in all four ranges, both just and tempered, are listed below. |
|
| |
|
| ===Maj2-min3 - 240¢-260¢=== | | ===Maj2-min3 - 240¢-260¢=== |
| ||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
| |
| || 147/128 || 239.607 || 7 ||
| |
| || 1\[[5edo]] || 240.000 || - ||
| |
| || 54/47 || 240.358 || 47 ||
| |
| || 23/20 || 241.961 || 23 ||
| |
| || 1152/1001 || 243.238 || 13 ||
| |
| || 38/33 || 244.240 || 19 ||
| |
| || 144/125 || 244.969 || 5 ||
| |
| || [[15_13|15/13]] || 247.741 || 13 ||
| |
| || 6\[[29edo]] || 248.276 || - ||
| |
| || 5\[[24edo]] || 250.000 || - ||
| |
| || 52/45 || 250.304 || 13 ||
| |
| || 37/32 || 251.344 || 37 ||
| |
| || 81/70 || 252.680 || 7 ||
| |
| || 4\[[19edo]] || 252.632 || - ||
| |
| || [[22_19|22/19]] || 253.805 || 19 ||
| |
| || 29/25 || 256.950 || 29 ||
| |
| || 3\[[14edo]] || 257.143 || - ||
| |
| || 297/256 || 257.183 || 11 ||
| |
| || 36/31 || 258.874 || 31 ||
| |
| || 5\[[23edo]] || 260.870 || - ||
| |
| | |
| ===Maj3-4 - 440-468===
| |
| ||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
| |
| || 5\[[88cET]] or 11\[[30edo]] || 440.000 || - ||
| |
| || 40/31 || 441.278 || 31 ||
| |
| || 7\[[19edo]] || 442.015 || - ||
| |
| || 31/24 || 443.081 || 31 ||
| |
| || 10\[[27edo]] || 444.444 || - ||
| |
| || [[22_17|22/17]] || 446.363 || 17 ||
| |
| || [[35_27|35/27]] || 449.275 || 7 ||
| |
| || 3\[[8edo]] || 450.000 || - ||
| |
| || 48/37 || 450.611 || 37 ||
| |
| || [[13_10|13/10]] || 454.214 || 13 ||
| |
| || 11\[[29edo]] || 455.172 || - ||
| |
| || 125/96 || 456.986 || 5 ||
| |
| || 8\[[21edo]] || 457.143 || - ||
| |
| || 56/43 || 457.308 || 43 ||
| |
| || 43/33 || 458.245 || 43 ||
| |
| || 30/23 || 459.994 || 23 ||
| |
| || 5\[[13edo]] || 461.538 || - ||
| |
| || 47/36 || 461.597 || 47 ||
| |
| || [[64_49|64/49]] || 462.348 || 7 ||
| |
| || 98/75 || 463.069 || 7 ||
| |
| || [[17_13|17/13]] || 464.428 || 17 ||
| |
| || 12\[[31edo]] || 464.516 || - ||
| |
| || 7\[[18edo]] || 466.667 || - ||
| |
| || 38/29 || 467.936 || 29 ||
| |
| | |
| ===5-min6 - 732¢-760¢===
| |
| ||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
| |
| || 5\[[Bohlen-Pierce]] || 731.521 || - ||
| |
| || 29/19 || 732.064 || 29 ||
| |
| || 11\[[18edo]] || 733.333 || - ||
| |
| || 19\[[31edo]] || 735.484 || - ||
| |
| || [[26_17|26/17]] || 735.572 || 17 ||
| |
| || 49/75 || 736.931 || 7 ||
| |
| || [[49_32|49/32]] || 737.652 || 7 ||
| |
| || 72/47 || 738.403 || 47 ||
| |
| || 23/15 || 740.006 || 23 ||
| |
| || 66/43 || 741.755 || 43 ||
| |
| || 43/28 || 742.692 || 43 ||
| |
| || 13\[[21edo]] || 742.857 || - ||
| |
| || 182/125 || 743.014 || 5 ||
| |
| || 18\[[29edo]] || 744.828 || - ||
| |
| || [[20_13|20/13]] || 745.786 || 13 ||
| |
| || 37/24 || 749.389 || 37 ||
| |
| || 5\[[8edo]] || 750.000 || - ||
| |
| || 54/35 || 750.725 || 7 ||
| |
| || [[17_11|17/11]] || 753.637 || 17 ||
| |
| || 17\[[27edo]] || 755.556 || - ||
| |
| || 48/31 || 756.919 || 31 ||
| |
| || 12\[[19edo]] || 757.895 || - ||
| |
| || 31/20 || 758.722 || 31 ||
| |
| || 19\[[30edo]] || 760.000 || - ||
| |
| | |
| ===Maj6-min7 - 940-960===
| |
| ||~ Interval ||~ Cents Value ||~ Prime Limit (if applicable) ||
| |
| || 18\[[23edo]] || 939.130 || - ||
| |
| || 31/18 || 941.126 || 31 ||
| |
| || 512/297 || 942.817 || 11 ||
| |
| || 11\[[14edo]] || 942.857 || - ||
| |
| || 50/29 || 943.050 || 29 ||
| |
| || [[19_11|19/11]] || 946.195 || 19 ||
| |
| || 140/81 || 947.320 || 7 ||
| |
| || 15\[[19edo]] || 947.368 || - ||
| |
| || 64/37 || 948.656 || 37 ||
| |
| || 45/26 || 949.696 || 13 ||
| |
| || 19\[[24edo]] || 950.000 || - ||
| |
| || 23\[[29edo]] || 951.724 || - ||
| |
| || [[26_15|26/15]] || 952.259 || 13 ||
| |
| || 125/72 || 955.031 || 5 ||
| |
| || 33/19 || 955.760 || 19 ||
| |
| || 1001/576 || 956.762 || 13 ||
| |
| || 40/23 || 958.039 || 23 ||
| |
| || 47/27 || 959.642 || 47 ||
| |
| || 4\[[5edo]] || 960.000 || - ||
| |
| || 256/147 || 960.393 || 7 ||
| |
| | |
| | |
| See: [[Interval Category]], [[Gallery of Just Intervals]]</pre></div>
| |
| <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>Interseptimal</title></head><body>In the theory of <a class="wiki_link" href="/Margo%20Schulter">Margo Schulter</a>, <em>interseptimal</em> is a category of intervals which occupy regions intermediate between two septimal ratios such as <a class="wiki_link" href="/8_7">8/7</a> and <a class="wiki_link" href="/7_6">7/6</a>, or <a class="wiki_link" href="/12_7">12/7</a> and <a class="wiki_link" href="/7_4">7/4</a>. There are four interseptimal regions given below, with approximate cents ranges from Schulter's article <a class="wiki_link_ext" href="http://www.bestii.com/%7Emschulter/IntervalSpectrumRegions.txt" rel="nofollow">Regions of the Interval Spectrum</a>:<br />
| |
| <ol><li>Maj2-min3 -- intermediate between 8/7 and 7/6 -- 240¢-260¢</li><li>Maj3-4 -- intermediate between <a class="wiki_link" href="/9_7">9/7</a> and <a class="wiki_link" href="/21_16">21/16</a> -- 440¢-468¢</li><li>5-min6 -- intermediate between <a class="wiki_link" href="/32_21">32/21</a> and <a class="wiki_link" href="/14_9">14/9</a> -- 732¢-760¢</li><li>Maj6-min7 -- intermediate between 12/7 and 7/4 -- 940¢-960¢</li></ol><br />
| |
| Interseptimal intervals are well-represented in <a class="wiki_link" href="/24edo">24edo</a> at 250¢, 450¢, 750¢ and 950¢. They also appear in <a class="wiki_link" href="/19edo">19edo</a> and <a class="wiki_link" href="/29edo">29edo</a>.<br />
| |
| <br />
| |
| As they fall in ambiguous zones between simpler categories, they are inevitably xenharmonic. This also makes them difficult to name: do we classify a 250-cent interval as a second, a third, both, or neither? One option is to give each region a distinct name (analogous to using the word <em>tritone</em> rather than diminished fifth or augmented fourth). Possible names that could be used are:<br />
| |
| <br />
| |
| <ol><li>240¢-260¢ -- semifourth -- an interval of this size is around half the size of a perfect fourth.</li><li>440¢-468¢ -- semisixth -- an interval of this size is around half the size of a major sixth.</li><li>732¢-760¢ -- semitenth -- an interval of this size is around half the size of a major tenth (i. e., compound major third). Another possible name is sesquifourth (since this is also about one and a half times the size of a perfect fourth).</li><li>940¢-960¢ -- semitwelfth -- an interval of this size is around half the size of a perfect twelfth (i e., a compound perfect fifth, or tritave). All even <a class="wiki_link" href="/edt">edts</a> have a semitwelfth of approximately 951 cents, analogous to the 600 cent tritone shared by all even edos.</li></ol><br />
| |
| This makes notating these intervals very easy as long as we have an agreed-upon symbol for &quot;semi&quot;.<br />
| |
| <br />
| |
| By analogy the tritone could also be called a semioctave, although the term tritone is so well-established that seems is little reason to change it now. A key difference is that the tritone is intermediate between two septimal ratios separated by a jubilisma (50:49), whereas the other interseptimal ranges listed above are between two septimal ratios separated by a slendro diesis (49:48).<br />
| |
| <br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h2>
| |
| Some interseptimal intervals in all four ranges, both just and tempered, are listed below.<br />
| |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x-Examples-Maj2-min3 - 240¢-260¢"></a><!-- ws:end:WikiTextHeadingRule:2 -->Maj2-min3 - 240¢-260¢</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Interval<br />
| | ! | Interval |
| </th>
| | ! | Cents Value |
| <th>Cents Value<br />
| | ! | Prime Limit (if applicable) |
| </th>
| | |- |
| <th>Prime Limit (if applicable)<br />
| | | | 147/128 |
| </th>
| | | | 239.607 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td>147/128<br />
| | | | 1\[[5edo|5edo]] |
| </td>
| | | | 240.000 |
| <td>239.607<br />
| | | | - |
| </td>
| | |- |
| <td>7<br />
| | | | 54/47 |
| </td>
| | | | 240.358 |
| </tr>
| | | | 47 |
| <tr>
| | |- |
| <td>1\<a class="wiki_link" href="/5edo">5edo</a><br />
| | | | 23/20 |
| </td>
| | | | 241.961 |
| <td>240.000<br />
| | | | 23 |
| </td>
| | |- |
| <td>-<br />
| | | | 1152/1001 |
| </td>
| | | | 243.238 |
| </tr>
| | | | 13 |
| <tr>
| | |- |
| <td>54/47<br />
| | | | 38/33 |
| </td>
| | | | 244.240 |
| <td>240.358<br />
| | | | 19 |
| </td>
| | |- |
| <td>47<br />
| | | | 144/125 |
| </td>
| | | | 244.969 |
| </tr>
| | | | 5 |
| <tr>
| | |- |
| <td>23/20<br />
| | | | [[15/13|15/13]] |
| </td>
| | | | 247.741 |
| <td>241.961<br />
| | | | 13 |
| </td>
| | |- |
| <td>23<br />
| | | | 6\[[29edo|29edo]] |
| </td>
| | | | 248.276 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>1152/1001<br />
| | | | 5\[[24edo|24edo]] |
| </td>
| | | | 250.000 |
| <td>243.238<br />
| | | | - |
| </td>
| | |- |
| <td>13<br />
| | | | 52/45 |
| </td>
| | | | 250.304 |
| </tr>
| | | | 13 |
| <tr>
| | |- |
| <td>38/33<br />
| | | | 37/32 |
| </td>
| | | | 251.344 |
| <td>244.240<br />
| | | | 37 |
| </td>
| | |- |
| <td>19<br />
| | | | 81/70 |
| </td>
| | | | 252.680 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td>144/125<br />
| | | | 4\[[19edo|19edo]] |
| </td>
| | | | 252.632 |
| <td>244.969<br />
| | | | - |
| </td>
| | |- |
| <td>5<br />
| | | | [[22/19|22/19]] |
| </td>
| | | | 253.805 |
| </tr>
| | | | 19 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/15_13">15/13</a><br />
| | | | 29/25 |
| </td>
| | | | 256.950 |
| <td>247.741<br />
| | | | 29 |
| </td>
| | |- |
| <td>13<br />
| | | | 3\[[14edo|14edo]] |
| </td>
| | | | 257.143 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>6\<a class="wiki_link" href="/29edo">29edo</a><br />
| | | | 297/256 |
| </td>
| | | | 257.183 |
| <td>248.276<br />
| | | | 11 |
| </td>
| | |- |
| <td>-<br />
| | | | 36/31 |
| </td>
| | | | 258.874 |
| </tr>
| | | | 31 |
| <tr>
| | |- |
| <td>5\<a class="wiki_link" href="/24edo">24edo</a><br />
| | | | 5\[[23edo|23edo]] |
| </td>
| | | | 260.870 |
| <td>250.000<br />
| | | | - |
| </td>
| | |} |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>52/45<br />
| |
| </td>
| |
| <td>250.304<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/32<br />
| |
| </td>
| |
| <td>251.344<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>81/70<br />
| |
| </td>
| |
| <td>252.680<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4\<a class="wiki_link" href="/19edo">19edo</a><br />
| |
| </td>
| |
| <td>252.632<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/22_19">22/19</a><br />
| |
| </td>
| |
| <td>253.805<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>29/25<br />
| |
| </td>
| |
| <td>256.950<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3\<a class="wiki_link" href="/14edo">14edo</a><br />
| |
| </td>
| |
| <td>257.143<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>297/256<br />
| |
| </td>
| |
| <td>257.183<br />
| |
| </td>
| |
| <td>11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>36/31<br />
| |
| </td>
| |
| <td>258.874<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5\<a class="wiki_link" href="/23edo">23edo</a><br />
| |
| </td>
| |
| <td>260.870<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ===Maj3-4 - 440-468=== |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="x-Examples-Maj3-4 - 440-468"></a><!-- ws:end:WikiTextHeadingRule:4 -->Maj3-4 - 440-468</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Interval<br />
| | ! | Interval |
| </th>
| | ! | Cents Value |
| <th>Cents Value<br />
| | ! | Prime Limit (if applicable) |
| </th>
| | |- |
| <th>Prime Limit (if applicable)<br />
| | | | 5\[[88cET|88cET]] or 11\[[30edo|30edo]] |
| </th>
| | | | 440.000 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>5\<a class="wiki_link" href="/88cET">88cET</a> or 11\<a class="wiki_link" href="/30edo">30edo</a><br />
| | | | 40/31 |
| </td>
| | | | 441.278 |
| <td>440.000<br />
| | | | 31 |
| </td>
| | |- |
| <td>-<br />
| | | | 7\[[19edo|19edo]] |
| </td>
| | | | 442.015 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>40/31<br />
| | | | 31/24 |
| </td>
| | | | 443.081 |
| <td>441.278<br />
| | | | 31 |
| </td>
| | |- |
| <td>31<br />
| | | | 10\[[27edo|27edo]] |
| </td>
| | | | 444.444 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>7\<a class="wiki_link" href="/19edo">19edo</a><br />
| | | | [[22/17|22/17]] |
| </td>
| | | | 446.363 |
| <td>442.015<br />
| | | | 17 |
| </td>
| | |- |
| <td>-<br />
| | | | [[35/27|35/27]] |
| </td>
| | | | 449.275 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td>31/24<br />
| | | | 3\[[8edo|8edo]] |
| </td>
| | | | 450.000 |
| <td>443.081<br />
| | | | - |
| </td>
| | |- |
| <td>31<br />
| | | | 48/37 |
| </td>
| | | | 450.611 |
| </tr>
| | | | 37 |
| <tr>
| | |- |
| <td>10\<a class="wiki_link" href="/27edo">27edo</a><br />
| | | | [[13/10|13/10]] |
| </td>
| | | | 454.214 |
| <td>444.444<br />
| | | | 13 |
| </td>
| | |- |
| <td>-<br />
| | | | 11\[[29edo|29edo]] |
| </td>
| | | | 455.172 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/22_17">22/17</a><br />
| | | | 125/96 |
| </td>
| | | | 456.986 |
| <td>446.363<br />
| | | | 5 |
| </td>
| | |- |
| <td>17<br />
| | | | 8\[[21edo|21edo]] |
| </td>
| | | | 457.143 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/35_27">35/27</a><br />
| | | | 56/43 |
| </td>
| | | | 457.308 |
| <td>449.275<br />
| | | | 43 |
| </td>
| | |- |
| <td>7<br />
| | | | 43/33 |
| </td>
| | | | 458.245 |
| </tr>
| | | | 43 |
| <tr>
| | |- |
| <td>3\<a class="wiki_link" href="/8edo">8edo</a><br />
| | | | 30/23 |
| </td>
| | | | 459.994 |
| <td>450.000<br />
| | | | 23 |
| </td>
| | |- |
| <td>-<br />
| | | | 5\[[13edo|13edo]] |
| </td>
| | | | 461.538 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>48/37<br />
| | | | 47/36 |
| </td>
| | | | 461.597 |
| <td>450.611<br />
| | | | 47 |
| </td>
| | |- |
| <td>37<br />
| | | | [[64/49|64/49]] |
| </td>
| | | | 462.348 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/13_10">13/10</a><br />
| | | | 98/75 |
| </td>
| | | | 463.069 |
| <td>454.214<br />
| | | | 7 |
| </td>
| | |- |
| <td>13<br />
| | | | [[17/13|17/13]] |
| </td>
| | | | 464.428 |
| </tr>
| | | | 17 |
| <tr>
| | |- |
| <td>11\<a class="wiki_link" href="/29edo">29edo</a><br />
| | | | 12\[[31edo|31edo]] |
| </td>
| | | | 464.516 |
| <td>455.172<br />
| | | | - |
| </td>
| | |- |
| <td>-<br />
| | | | 7\[[18edo|18edo]] |
| </td>
| | | | 466.667 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>125/96<br />
| | | | 38/29 |
| </td>
| | | | 467.936 |
| <td>456.986<br />
| | | | 29 |
| </td>
| | |} |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8\<a class="wiki_link" href="/21edo">21edo</a><br />
| |
| </td>
| |
| <td>457.143<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>56/43<br />
| |
| </td>
| |
| <td>457.308<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>43/33<br />
| |
| </td>
| |
| <td>458.245<br />
| |
| </td>
| |
| <td>43<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>30/23<br />
| |
| </td>
| |
| <td>459.994<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5\<a class="wiki_link" href="/13edo">13edo</a><br />
| |
| </td>
| |
| <td>461.538<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/36<br />
| |
| </td>
| |
| <td>461.597<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/64_49">64/49</a><br />
| |
| </td>
| |
| <td>462.348<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>98/75<br />
| |
| </td>
| |
| <td>463.069<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/17_13">17/13</a><br />
| |
| </td>
| |
| <td>464.428<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12\<a class="wiki_link" href="/31edo">31edo</a><br />
| |
| </td>
| |
| <td>464.516<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7\<a class="wiki_link" href="/18edo">18edo</a><br />
| |
| </td>
| |
| <td>466.667<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>38/29<br />
| |
| </td>
| |
| <td>467.936<br />
| |
| </td>
| |
| <td>29<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ===5-min6 - 732¢-760¢=== |
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x-Examples-5-min6 - 732¢-760¢"></a><!-- ws:end:WikiTextHeadingRule:6 -->5-min6 - 732¢-760¢</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Interval<br />
| | ! | Interval |
| </th>
| | ! | Cents Value |
| <th>Cents Value<br />
| | ! | Prime Limit (if applicable) |
| </th>
| | |- |
| <th>Prime Limit (if applicable)<br />
| | | | 5\[[Bohlen-Pierce|Bohlen-Pierce]] |
| </th>
| | | | 731.521 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>5\<a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a><br />
| | | | 29/19 |
| </td>
| | | | 732.064 |
| <td>731.521<br />
| | | | 29 |
| </td>
| | |- |
| <td>-<br />
| | | | 11\[[18edo|18edo]] |
| </td>
| | | | 733.333 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>29/19<br />
| | | | 19\[[31edo|31edo]] |
| </td>
| | | | 735.484 |
| <td>732.064<br />
| | | | - |
| </td>
| | |- |
| <td>29<br />
| | | | [[26/17|26/17]] |
| </td>
| | | | 735.572 |
| </tr>
| | | | 17 |
| <tr>
| | |- |
| <td>11\<a class="wiki_link" href="/18edo">18edo</a><br />
| | | | 49/75 |
| </td>
| | | | 736.931 |
| <td>733.333<br />
| | | | 7 |
| </td>
| | |- |
| <td>-<br />
| | | | [[49/32|49/32]] |
| </td>
| | | | 737.652 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td>19\<a class="wiki_link" href="/31edo">31edo</a><br />
| | | | 72/47 |
| </td>
| | | | 738.403 |
| <td>735.484<br />
| | | | 47 |
| </td>
| | |- |
| <td>-<br />
| | | | 23/15 |
| </td>
| | | | 740.006 |
| </tr>
| | | | 23 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/26_17">26/17</a><br />
| | | | 66/43 |
| </td>
| | | | 741.755 |
| <td>735.572<br />
| | | | 43 |
| </td>
| | |- |
| <td>17<br />
| | | | 43/28 |
| </td>
| | | | 742.692 |
| </tr>
| | | | 43 |
| <tr>
| | |- |
| <td>49/75<br />
| | | | 13\[[21edo|21edo]] |
| </td>
| | | | 742.857 |
| <td>736.931<br />
| | | | - |
| </td>
| | |- |
| <td>7<br />
| | | | 182/125 |
| </td>
| | | | 743.014 |
| </tr>
| | | | 5 |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/49_32">49/32</a><br />
| | | | 18\[[29edo|29edo]] |
| </td>
| | | | 744.828 |
| <td>737.652<br />
| | | | - |
| </td>
| | |- |
| <td>7<br />
| | | | [[20/13|20/13]] |
| </td>
| | | | 745.786 |
| </tr>
| | | | 13 |
| <tr>
| | |- |
| <td>72/47<br />
| | | | 37/24 |
| </td>
| | | | 749.389 |
| <td>738.403<br />
| | | | 37 |
| </td>
| | |- |
| <td>47<br />
| | | | 5\[[8edo|8edo]] |
| </td>
| | | | 750.000 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>23/15<br />
| | | | 54/35 |
| </td>
| | | | 750.725 |
| <td>740.006<br />
| | | | 7 |
| </td>
| | |- |
| <td>23<br />
| | | | [[17/11|17/11]] |
| </td>
| | | | 753.637 |
| </tr>
| | | | 17 |
| <tr>
| | |- |
| <td>66/43<br />
| | | | 17\[[27edo|27edo]] |
| </td>
| | | | 755.556 |
| <td>741.755<br />
| | | | - |
| </td>
| | |- |
| <td>43<br />
| | | | 48/31 |
| </td>
| | | | 756.919 |
| </tr>
| | | | 31 |
| <tr>
| | |- |
| <td>43/28<br />
| | | | 12\[[19edo|19edo]] |
| </td>
| | | | 757.895 |
| <td>742.692<br />
| | | | - |
| </td>
| | |- |
| <td>43<br />
| | | | 31/20 |
| </td>
| | | | 758.722 |
| </tr>
| | | | 31 |
| <tr>
| | |- |
| <td>13\<a class="wiki_link" href="/21edo">21edo</a><br />
| | | | 19\[[30edo|30edo]] |
| </td>
| | | | 760.000 |
| <td>742.857<br />
| | | | - |
| </td>
| | |} |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>182/125<br />
| |
| </td>
| |
| <td>743.014<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>18\<a class="wiki_link" href="/29edo">29edo</a><br />
| |
| </td>
| |
| <td>744.828<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/20_13">20/13</a><br />
| |
| </td>
| |
| <td>745.786<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>37/24<br />
| |
| </td>
| |
| <td>749.389<br />
| |
| </td>
| |
| <td>37<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5\<a class="wiki_link" href="/8edo">8edo</a><br />
| |
| </td>
| |
| <td>750.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>54/35<br />
| |
| </td>
| |
| <td>750.725<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/17_11">17/11</a><br />
| |
| </td>
| |
| <td>753.637<br />
| |
| </td>
| |
| <td>17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>17\<a class="wiki_link" href="/27edo">27edo</a><br />
| |
| </td>
| |
| <td>755.556<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>48/31<br />
| |
| </td>
| |
| <td>756.919<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12\<a class="wiki_link" href="/19edo">19edo</a><br />
| |
| </td>
| |
| <td>757.895<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>31/20<br />
| |
| </td>
| |
| <td>758.722<br />
| |
| </td>
| |
| <td>31<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\<a class="wiki_link" href="/30edo">30edo</a><br />
| |
| </td>
| |
| <td>760.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | ===Maj6-min7 - 940-960=== |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x-Examples-Maj6-min7 - 940-960"></a><!-- ws:end:WikiTextHeadingRule:8 -->Maj6-min7 - 940-960</h3>
| |
|
| |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <th>Interval<br />
| | ! | Interval |
| </th>
| | ! | Cents Value |
| <th>Cents Value<br />
| | ! | Prime Limit (if applicable) |
| </th>
| | |- |
| <th>Prime Limit (if applicable)<br />
| | | | 18\[[23edo|23edo]] |
| </th>
| | | | 939.130 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>18\<a class="wiki_link" href="/23edo">23edo</a><br />
| | | | 31/18 |
| </td>
| | | | 941.126 |
| <td>939.130<br />
| | | | 31 |
| </td>
| | |- |
| <td>-<br />
| | | | 512/297 |
| </td>
| | | | 942.817 |
| </tr>
| | | | 11 |
| <tr>
| | |- |
| <td>31/18<br />
| | | | 11\[[14edo|14edo]] |
| </td>
| | | | 942.857 |
| <td>941.126<br />
| | | | - |
| </td>
| | |- |
| <td>31<br />
| | | | 50/29 |
| </td>
| | | | 943.050 |
| </tr>
| | | | 29 |
| <tr>
| | |- |
| <td>512/297<br />
| | | | [[19/11|19/11]] |
| </td>
| | | | 946.195 |
| <td>942.817<br />
| | | | 19 |
| </td>
| | |- |
| <td>11<br />
| | | | 140/81 |
| </td>
| | | | 947.320 |
| </tr>
| | | | 7 |
| <tr>
| | |- |
| <td>11\<a class="wiki_link" href="/14edo">14edo</a><br />
| | | | 15\[[19edo|19edo]] |
| </td>
| | | | 947.368 |
| <td>942.857<br />
| | | | - |
| </td>
| | |- |
| <td>-<br />
| | | | 64/37 |
| </td>
| | | | 948.656 |
| </tr>
| | | | 37 |
| <tr>
| | |- |
| <td>50/29<br />
| | | | 45/26 |
| </td>
| | | | 949.696 |
| <td>943.050<br />
| | | | 13 |
| </td>
| | |- |
| <td>29<br />
| | | | 19\[[24edo|24edo]] |
| </td>
| | | | 950.000 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td><a class="wiki_link" href="/19_11">19/11</a><br />
| | | | 23\[[29edo|29edo]] |
| </td>
| | | | 951.724 |
| <td>946.195<br />
| | | | - |
| </td>
| | |- |
| <td>19<br />
| | | | [[26/15|26/15]] |
| </td>
| | | | 952.259 |
| </tr>
| | | | 13 |
| <tr>
| | |- |
| <td>140/81<br />
| | | | 125/72 |
| </td>
| | | | 955.031 |
| <td>947.320<br />
| | | | 5 |
| </td>
| | |- |
| <td>7<br />
| | | | 33/19 |
| </td>
| | | | 955.760 |
| </tr>
| | | | 19 |
| <tr>
| | |- |
| <td>15\<a class="wiki_link" href="/19edo">19edo</a><br />
| | | | 1001/576 |
| </td>
| | | | 956.762 |
| <td>947.368<br />
| | | | 13 |
| </td>
| | |- |
| <td>-<br />
| | | | 40/23 |
| </td>
| | | | 958.039 |
| </tr>
| | | | 23 |
| <tr>
| | |- |
| <td>64/37<br />
| | | | 47/27 |
| </td>
| | | | 959.642 |
| <td>948.656<br />
| | | | 47 |
| </td>
| | |- |
| <td>37<br />
| | | | 4\[[5edo|5edo]] |
| </td>
| | | | 960.000 |
| </tr>
| | | | - |
| <tr>
| | |- |
| <td>45/26<br />
| | | | 256/147 |
| </td>
| | | | 960.393 |
| <td>949.696<br />
| | | | 7 |
| </td>
| | |} |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>19\<a class="wiki_link" href="/24edo">24edo</a><br />
| |
| </td>
| |
| <td>950.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>23\<a class="wiki_link" href="/29edo">29edo</a><br />
| |
| </td>
| |
| <td>951.724<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><a class="wiki_link" href="/26_15">26/15</a><br />
| |
| </td>
| |
| <td>952.259<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>125/72<br />
| |
| </td>
| |
| <td>955.031<br />
| |
| </td>
| |
| <td>5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>33/19<br />
| |
| </td>
| |
| <td>955.760<br />
| |
| </td>
| |
| <td>19<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1001/576<br />
| |
| </td>
| |
| <td>956.762<br />
| |
| </td>
| |
| <td>13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>40/23<br />
| |
| </td>
| |
| <td>958.039<br />
| |
| </td>
| |
| <td>23<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>47/27<br />
| |
| </td>
| |
| <td>959.642<br />
| |
| </td>
| |
| <td>47<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4\<a class="wiki_link" href="/5edo">5edo</a><br />
| |
| </td>
| |
| <td>960.000<br />
| |
| </td>
| |
| <td>-<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>256/147<br />
| |
| </td>
| |
| <td>960.393<br />
| |
| </td>
| |
| <td>7<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | See: [[interval_category|Interval Category]], [[Gallery_of_Just_Intervals|Gallery of Just Intervals]] [[Category:interseptimal]] |
| <br />
| | [[Category:interval_category]] |
| See: <a class="wiki_link" href="/Interval%20Category">Interval Category</a>, <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div> | |