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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | A cluster temperament (named by [[Keenan_Pepper|Keenan Pepper]]) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby JI intervals that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close. |
| 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:keenanpepper|keenanpepper]] and made on <tt>2013-02-24 14:40:34 UTC</tt>.<br>
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| : The original revision id was <tt>409539020</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">A cluster temperament (named by [[Keenan Pepper]]) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma ("diminished", "minor", "major", "augmented"...) include many nearby JI intervals that are individually recognizable, yet conceptually grouped into the same category (or "cluster") because they're so close.
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| An example of something that is **not** a cluster temperament is [[amity]], because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity "thirds" includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get). | | An example of something that is '''not''' a cluster temperament is [[Amity|amity]], because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity "thirds" includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get). |
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| |
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| Another way to describe this property is that the chroma of the near-equal MOS is a kind of "super-comma", a set of many useful commas that are tempered to become the same, non-vanishing, interval. It should be obvious that "cluster temperament" is a vague, qualitative phrase and not mathematically well-defined. | | Another way to describe this property is that the chroma of the near-equal MOS is a kind of "super-comma", a set of many useful commas that are tempered to become the same, non-vanishing, interval. It should be obvious that "cluster temperament" is a vague, qualitative phrase and not mathematically well-defined. |
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| Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved. | | Rather than simply denoting one of a list of rank-2 temperaments, the phrase "cluster scale" is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically "bad" or have "bad MOS structure", because some MOS (in this case slendric[5]) is "too equal" and the next higher MOSes are "too unequal". But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the "step" (a step of the quasi-equal MOS), and the "chroma", and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved. |
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| =Examples= | | =Examples= |
| ==Slendric==
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| Main article: [[Slendric]]
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| Chroma: 49/48~64/63
| |
| || Steps || "Diminished" || "Minor" || "Major" || "Augmented" ||
| |
| || 1 || 9/8 || 8/7 || 7/6 || 32/27 ||
| |
| || 2 || 9/7 || 21/16 || 4/3 || ||
| |
| || 3 || || 3/2 || 32/21 || 14/9 ||
| |
| || 4 || 27/16 || 12/7 || 7/4 || 16/9 ||
| |
| Slendric has two quite different extensions that are both also cluster scales:
| |
| ===Mothra===
| |
| Main article: [[Mothra]]
| |
| Chroma: 33/32~36/35~49/48~55/54~56/55~64/63
| |
| || Steps || || "Diminished" || "Minor" || "Major" || "Augmented" || ||
| |
| || 1 || 12/11 || 10/9~9/8 || 8/7 || 7/6 || 6/5 || 11/9 ||
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| || 2 || 5/4 || 14/11~9/7 || 21/16 || 4/3 || 11/8 || 7/5 ||
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| || 3 || 10/7 || 16/11 || 3/2 || 32/21 || 14/9~11/7 || 8/5 ||
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| || 4 || 18/11 || 5/3 || 12/7 || 7/4 || 16/9~9/5 || 11/6 ||
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| ===Rodan===
| |
| Main article: [[Rodan]]
| |
| Chroma: 49/48~55/54~56/55~64/63~81/80~99/98
| |
| || Steps || || || "Diminished" || "Minor" || "Major" || "Augmented" || || ||
| |
| || 1 || 12/11 || 10/9 || 9/8 || 8/7 || 7/6 || 32/27 || 6/5 || 11/9 ||
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| || 2 || 5/4 || 14/11 || 9/7 || 21/16 || 4/3 || 27/20 || 11/8 || 7/5 ||
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| || 3 || 10/7 || 16/11 || 40/27 || 3/2 || 32/21 || 14/9 || 11/7 || 8/5 ||
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| || 4 || 18/11 || 5/3 || 27/16 || 12/7 || 7/4 || 16/9 || 9/5 || 11/6 ||
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| ==Modus (of the tetracot family)== | | ==Slendric== |
| Main article: [[Modus]] | | Main article: [[Slendric|Slendric]] |
| Chroma: 40/39~45/44~55/54~66/65~81/80~121/120
| |
| || Steps || "Diminished" || "Minor" || "Major" || "Augmented" ||
| |
| || 1 || 16/15 || 13/12~12/11 || 11/10~10/9 || 9/8 ||
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| || 2 || 13/11 || 6/5 || 11/9 || 5/4 ||
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| || 3 || 13/10 || 4/3 || 27/20 || 11/8 ||
| |
| || 4 || 16/11 || 40/27 || 3/2 || 20/13 ||
| |
| || 5 || 8/5 || 18/11 || 5/3 || 22/13~27/16 ||
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| || 6 || 16/9 || 9/5 || 11/6 || 15/8 ||
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| ==Miracle==
| | Chroma: 49/48~64/63 |
| Main article: [[Miracle]]
| |
| Chroma: 45/44~49/48~50/49~55/54~56/55~64/63 | |
| || Steps || || "Diminished" || "Minor" || "Major" || "Augmented" || ||
| |
| || 1 || || 22/21~21/20 || 16/15~15/14 || 12/11 || 10/9 || ||
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| || 2 || 11/10 || 9/8 || 8/7 || 7/6 || 32/27 || ||
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| || 3 || || 6/5 || 11/9 || 5/4 || 14/11 || ||
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| || 4 || || 9/7 || 21/16 || 4/3 || || ||
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| || 5 || || 11/8 || 7/5 || 10/7 || 16/11 || ||
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| || 6 || || || 3/2 || 32/21 || 14/9 || ||
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| || 7 || || 11/7 || 8/5 || 18/11 || 5/3 || ||
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| || 8 || || 27/16 || 12/7 || 7/4 || 16/9 || 20/11 ||
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| || 9 || || 9/5 || 11/6 || 15/8 || 21/11 || ||
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|
| ==Porcupine(fish)== | | {| class="wikitable" |
| Main article: [[Porcupine]]
| | |- |
| Chroma: 22/21~25/24~(26/25)~33/32~36/35~45/44~81/80
| | | | Steps |
| || Steps || "Diminished" || "Minor" || "Major" || "Augmented" || | | | | "Diminished" |
| || 1 || 21/20~16/15 || 12/11~11/10~10/9 || 9/8~8/7 || (13/11) || | | | | "Minor" |
| || 2 || 7/6 || 6/5~11/9 || 5/4 || 9/7~(13/10) ||
| | | | "Major" |
| || 3 || 14/11 || 4/3 || 11/8 || 10/7~(13/9) || | | | | "Augmented" |
| || 4 || 7/5~(18/13) || 16/11 || 3/2 || 11/7 || | | |- |
| || 5 || 14/9~(20/13) || 8/5 || 5/3~18/11 || 12/7 ||
| | | | 1 |
| || 6 || (22/13) || 7/4~16/9 || 9/5~11/6 || 40/21~15/8 || | | | | 9/8 |
| | | | 8/7 |
| | | | 7/6 |
| | | | 32/27 |
| | |- |
| | | | 2 |
| | | | 9/7 |
| | | | 21/16 |
| | | | 4/3 |
| | | | |
| | |- |
| | | | 3 |
| | | | |
| | | | 3/2 |
| | | | 32/21 |
| | | | 14/9 |
| | |- |
| | | | 4 |
| | | | 27/16 |
| | | | 12/7 |
| | | | 7/4 |
| | | | 16/9 |
| | |} |
| | Slendric has two quite different extensions that are both also cluster scales: |
|
| |
|
| ==17-limit valentino== | | ===Mothra=== |
| Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150
| | Main article: [[Mothra|Mothra]] |
| || Steps || || "Diminished" || "Minor" || "Major" || "Augmented" || ||
| |
| || 1 || || 36/35 || 21/20~25/24 || 17/16~16/15 || 13/12 || ||
| |
| || 2 || || 14/13 || 12/11~11/10 || 10/9 || 17/15 || 20/17 ||
| |
| || 3 || || 9/8 || 8/7 || 7/6 || 32/27 || ||
| |
| || 4 || || 13/11 || 6/5 || 11/9~17/14 || || ||
| |
| || 5 || || 16/13~21/17 || 5/4 || 14/11 || 13/10 || 27/20 ||
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| || 6 || || 9/7 || 21/16~17/13 || 4/3 || 34/25 || ||
| |
| || 7 || || 27/20 || 11/8~15/11 || 7/5 || 17/12 || ||
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| || 8 || || 24/17 || 10/7 || 16/11~22/15 || 40/27 || ||
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| || 9 || || 25/17 || 3/2 || 26/17~32/21 || 14/9 || ||
| |
| || 10 || 40/27 || 20/13 || 11/7 || 8/5 || 13/8~34/21 || ||
| |
| || 11 || || || 18/11~28/17 || 5/3 || 22/13 || ||
| |
| || 12 || || 27/16 || 12/7 || 7/4 || 16/9 || ||
| |
| || 13 || 17/10 || 30/14 || 9/5 || 11/6~20/11 || 13/7 || ||
| |
| || 14 || || 24/13 || 15/8 || 40/21~48/25 || 35/18 || ||
| |
|
| |
|
| ==2.3.5.11.13 hitchcock==
| | Chroma: 33/32~36/35~49/48~55/54~56/55~64/63 |
| Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.
| |
| || Steps || || "Diminished" || "Minor" || "Major" || "Augmented" || ||
| |
| || 1 || || 13/12 || 12/11~11/10 || 10/9 || 9/8 || ||
| |
| || 2 || 13/11 || 6/5 || 11/9 || 16/13 || 5/4 || ||
| |
| || 3 || 13/10 || || 4/3 || 27/20 || 11/8 || 18/13 ||
| |
| || 4 || 13/9 || 16/11 || 40/27 || 3/2 || || 20/13 ||
| |
| || 5 || || 8/5 || 13/8 || 18/11 || 5/3 || 22/13 ||
| |
| || 6 || || 16/9 || 9/5 || 11/6 || 24/13 || ||</pre></div>
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| <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>Cluster temperament</title></head><body>A cluster temperament (named by <a class="wiki_link" href="/Keenan%20Pepper">Keenan Pepper</a>) is a very particular kind of rank-2 temperament whose generator is quite near a rational fraction of an octave. Therefore some MOS of the temperament is quasi-equal (which should be reasonably sized for it to be a good cluster temperament, usually between 5 and 10 notes per octave). But not only that; in a cluster temperament, the different versions of each interval, differing by a chroma (&quot;diminished&quot;, &quot;minor&quot;, &quot;major&quot;, &quot;augmented&quot;...) include many nearby JI intervals that are individually recognizable, yet conceptually grouped into the same category (or &quot;cluster&quot;) because they're so close.<br />
| |
| <br />
| |
| An example of something that is <strong>not</strong> a cluster temperament is <a class="wiki_link" href="/amity">amity</a>, because although the amity generator is within 4 cents of 2\7, making amity[7] near equal, amity is too complex of a temperament and most of the intervals differing by a chroma do not represent simple JI intervals at all. For example, the list of amity &quot;thirds&quot; includes ...6/5 (339.5) (363.2) 5/4... where the intervals given in cents are not representable as simple JI intervals (243/200 and 100/81 are about as simple as you can get).<br />
| |
| <br />
| |
| Another way to describe this property is that the chroma of the near-equal MOS is a kind of &quot;super-comma&quot;, a set of many useful commas that are tempered to become the same, non-vanishing, interval. It should be obvious that &quot;cluster temperament&quot; is a vague, qualitative phrase and not mathematically well-defined.<br />
| |
| <br />
| |
| Rather than simply denoting one of a list of rank-2 temperaments, the phrase &quot;cluster scale&quot; is also associated with a compositional philosophy. It is often said that temperaments such as slendric are melodically &quot;bad&quot; or have &quot;bad MOS structure&quot;, because some MOS (in this case slendric[5]) is &quot;too equal&quot; and the next higher MOSes are &quot;too unequal&quot;. But this can be thought of as a feature rather than a bug. Rather than forcing them into the MOS framework, one can think of cluster scales as having two hierarchical levels of melodic structure: the &quot;step&quot; (a step of the quasi-equal MOS), and the &quot;chroma&quot;, and a chroma is so much smaller than a step that the steps seldom go out of order no matter how many chromas are involved.<br />
| |
| <br />
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| <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Examples"></a><!-- ws:end:WikiTextHeadingRule:0 -->Examples</h1>
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| <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Examples-Slendric"></a><!-- ws:end:WikiTextHeadingRule:2 -->Slendric</h2>
| |
| Main article: <a class="wiki_link" href="/Slendric">Slendric</a><br />
| |
| Chroma: 49/48~64/63<br />
| |
|
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|
| | {| class="wikitable" |
| | |- |
| | | | Steps |
| | | | |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | | | |
| | |- |
| | | | 1 |
| | | | 12/11 |
| | | | 10/9~9/8 |
| | | | 8/7 |
| | | | 7/6 |
| | | | 6/5 |
| | | | 11/9 |
| | |- |
| | | | 2 |
| | | | 5/4 |
| | | | 14/11~9/7 |
| | | | 21/16 |
| | | | 4/3 |
| | | | 11/8 |
| | | | 7/5 |
| | |- |
| | | | 3 |
| | | | 10/7 |
| | | | 16/11 |
| | | | 3/2 |
| | | | 32/21 |
| | | | 14/9~11/7 |
| | | | 8/5 |
| | |- |
| | | | 4 |
| | | | 18/11 |
| | | | 5/3 |
| | | | 12/7 |
| | | | 7/4 |
| | | | 16/9~9/5 |
| | | | 11/6 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ===Rodan=== |
| <tr>
| | Main article: [[Rodan|Rodan]] |
| <td>Steps<br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>32/27<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
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| <td>2<br />
| |
| </td>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>32/21<br />
| |
| </td>
| |
| <td>14/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>27/16<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| Slendric has two quite different extensions that are both also cluster scales:<br />
| | Chroma: 49/48~55/54~56/55~64/63~81/80~99/98 |
| <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc2"><a name="Examples-Slendric-Mothra"></a><!-- ws:end:WikiTextHeadingRule:4 -->Mothra</h3>
| |
| Main article: <a class="wiki_link" href="/Mothra">Mothra</a><br />
| |
| Chroma: 33/32~36/35~49/48~55/54~56/55~64/63<br /> | |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | | | Steps |
| | | | |
| | | | |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | | | |
| | | | |
| | |- |
| | | | 1 |
| | | | 12/11 |
| | | | 10/9 |
| | | | 9/8 |
| | | | 8/7 |
| | | | 7/6 |
| | | | 32/27 |
| | | | 6/5 |
| | | | 11/9 |
| | |- |
| | | | 2 |
| | | | 5/4 |
| | | | 14/11 |
| | | | 9/7 |
| | | | 21/16 |
| | | | 4/3 |
| | | | 27/20 |
| | | | 11/8 |
| | | | 7/5 |
| | |- |
| | | | 3 |
| | | | 10/7 |
| | | | 16/11 |
| | | | 40/27 |
| | | | 3/2 |
| | | | 32/21 |
| | | | 14/9 |
| | | | 11/7 |
| | | | 8/5 |
| | |- |
| | | | 4 |
| | | | 18/11 |
| | | | 5/3 |
| | | | 27/16 |
| | | | 12/7 |
| | | | 7/4 |
| | | | 16/9 |
| | | | 9/5 |
| | | | 11/6 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Modus (of the tetracot family)== |
| <tr>
| | Main article: [[Modus|Modus]] |
| <td>Steps<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>10/9~9/8<br />
| |
| </td>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>14/11~9/7<br />
| |
| </td>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>7/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>10/7<br />
| |
| </td>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>32/21<br />
| |
| </td>
| |
| <td>14/9~11/7<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>16/9~9/5<br />
| |
| </td>
| |
| <td>11/6<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Examples-Slendric-Rodan"></a><!-- ws:end:WikiTextHeadingRule:6 -->Rodan</h3>
| | Chroma: 40/39~45/44~55/54~66/65~81/80~121/120 |
| Main article: <a class="wiki_link" href="/Rodan">Rodan</a><br />
| |
| Chroma: 49/48~55/54~56/55~64/63~81/80~99/98<br />
| |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | | | Steps |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | |- |
| | | | 1 |
| | | | 16/15 |
| | | | 13/12~12/11 |
| | | | 11/10~10/9 |
| | | | 9/8 |
| | |- |
| | | | 2 |
| | | | 13/11 |
| | | | 6/5 |
| | | | 11/9 |
| | | | 5/4 |
| | |- |
| | | | 3 |
| | | | 13/10 |
| | | | 4/3 |
| | | | 27/20 |
| | | | 11/8 |
| | |- |
| | | | 4 |
| | | | 16/11 |
| | | | 40/27 |
| | | | 3/2 |
| | | | 20/13 |
| | |- |
| | | | 5 |
| | | | 8/5 |
| | | | 18/11 |
| | | | 5/3 |
| | | | 22/13~27/16 |
| | |- |
| | | | 6 |
| | | | 16/9 |
| | | | 9/5 |
| | | | 11/6 |
| | | | 15/8 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Miracle== |
| <tr>
| | Main article: [[Miracle|Miracle]] |
| <td>Steps<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>32/27<br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>7/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>10/7<br />
| |
| </td>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>32/21<br />
| |
| </td>
| |
| <td>14/9<br />
| |
| </td>
| |
| <td>11/7<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>27/16<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>11/6<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | Chroma: 45/44~49/48~50/49~55/54~56/55~64/63 |
| <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Examples-Modus (of the tetracot family)"></a><!-- ws:end:WikiTextHeadingRule:8 -->Modus (of the tetracot family)</h2>
| |
| Main article: <a class="wiki_link" href="/Modus">Modus</a><br />
| |
| Chroma: 40/39~45/44~55/54~66/65~81/80~121/120<br /> | |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | | | Steps |
| | | | |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | | | |
| | |- |
| | | | 1 |
| | | | |
| | | | 22/21~21/20 |
| | | | 16/15~15/14 |
| | | | 12/11 |
| | | | 10/9 |
| | | | |
| | |- |
| | | | 2 |
| | | | 11/10 |
| | | | 9/8 |
| | | | 8/7 |
| | | | 7/6 |
| | | | 32/27 |
| | | | |
| | |- |
| | | | 3 |
| | | | |
| | | | 6/5 |
| | | | 11/9 |
| | | | 5/4 |
| | | | 14/11 |
| | | | |
| | |- |
| | | | 4 |
| | | | |
| | | | 9/7 |
| | | | 21/16 |
| | | | 4/3 |
| | | | |
| | | | |
| | |- |
| | | | 5 |
| | | | |
| | | | 11/8 |
| | | | 7/5 |
| | | | 10/7 |
| | | | 16/11 |
| | | | |
| | |- |
| | | | 6 |
| | | | |
| | | | |
| | | | 3/2 |
| | | | 32/21 |
| | | | 14/9 |
| | | | |
| | |- |
| | | | 7 |
| | | | |
| | | | 11/7 |
| | | | 8/5 |
| | | | 18/11 |
| | | | 5/3 |
| | | | |
| | |- |
| | | | 8 |
| | | | |
| | | | 27/16 |
| | | | 12/7 |
| | | | 7/4 |
| | | | 16/9 |
| | | | 20/11 |
| | |- |
| | | | 9 |
| | | | |
| | | | 9/5 |
| | | | 11/6 |
| | | | 15/8 |
| | | | 21/11 |
| | | | |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==Porcupine(fish)== |
| <tr>
| | Main article: [[Porcupine|Porcupine]] |
| <td>Steps<br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td>16/15<br />
| |
| </td>
| |
| <td>13/12~12/11<br />
| |
| </td>
| |
| <td>11/10~10/9<br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>11/8<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>20/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>22/13~27/16<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>11/6<br />
| |
| </td>
| |
| <td>15/8<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | Chroma: 22/21~25/24~(26/25)~33/32~36/35~45/44~81/80 |
| <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Examples-Miracle"></a><!-- ws:end:WikiTextHeadingRule:10 -->Miracle</h2>
| |
| Main article: <a class="wiki_link" href="/Miracle">Miracle</a><br />
| |
| Chroma: 45/44~49/48~50/49~55/54~56/55~64/63<br /> | |
|
| |
|
| | {| class="wikitable" |
| | |- |
| | | | Steps |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | |- |
| | | | 1 |
| | | | 21/20~16/15 |
| | | | 12/11~11/10~10/9 |
| | | | 9/8~8/7 |
| | | | (13/11) |
| | |- |
| | | | 2 |
| | | | 7/6 |
| | | | 6/5~11/9 |
| | | | 5/4 |
| | | | 9/7~(13/10) |
| | |- |
| | | | 3 |
| | | | 14/11 |
| | | | 4/3 |
| | | | 11/8 |
| | | | 10/7~(13/9) |
| | |- |
| | | | 4 |
| | | | 7/5~(18/13) |
| | | | 16/11 |
| | | | 3/2 |
| | | | 11/7 |
| | |- |
| | | | 5 |
| | | | 14/9~(20/13) |
| | | | 8/5 |
| | | | 5/3~18/11 |
| | | | 12/7 |
| | |- |
| | | | 6 |
| | | | (22/13) |
| | | | 7/4~16/9 |
| | | | 9/5~11/6 |
| | | | 40/21~15/8 |
| | |} |
|
| |
|
| <table class="wiki_table">
| | ==17-limit valentino== |
| <tr>
| | Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150 |
| <td>Steps<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>22/21~21/20<br />
| |
| </td>
| |
| <td>16/15~15/14<br />
| |
| </td>
| |
| <td>12/11<br />
| |
| </td>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>11/10<br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>32/27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>21/16<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>10/7<br />
| |
| </td>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>32/21<br />
| |
| </td>
| |
| <td>14/9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>11/7<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>27/16<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td>20/11<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>11/6<br />
| |
| </td>
| |
| <td>15/8<br />
| |
| </td>
| |
| <td>21/11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
|
| |
|
| <br />
| | {| class="wikitable" |
| <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Examples-Porcupine(fish)"></a><!-- ws:end:WikiTextHeadingRule:12 -->Porcupine(fish)</h2>
| | |- |
| Main article: <a class="wiki_link" href="/Porcupine">Porcupine</a><br />
| | | | Steps |
| Chroma: 22/21~25/24~(26/25)~33/32~36/35~45/44~81/80<br />
| | | | |
| | | | "Diminished" |
| | | | "Minor" |
| | | | "Major" |
| | | | "Augmented" |
| | | | |
| | |- |
| | | | 1 |
| | | | |
| | | | 36/35 |
| | | | 21/20~25/24 |
| | | | 17/16~16/15 |
| | | | 13/12 |
| | | | |
| | |- |
| | | | 2 |
| | | | |
| | | | 14/13 |
| | | | 12/11~11/10 |
| | | | 10/9 |
| | | | 17/15 |
| | | | 20/17 |
| | |- |
| | | | 3 |
| | | | |
| | | | 9/8 |
| | | | 8/7 |
| | | | 7/6 |
| | | | 32/27 |
| | | | |
| | |- |
| | | | 4 |
| | | | |
| | | | 13/11 |
| | | | 6/5 |
| | | | 11/9~17/14 |
| | | | |
| | | | |
| | |- |
| | | | 5 |
| | | | |
| | | | 16/13~21/17 |
| | | | 5/4 |
| | | | 14/11 |
| | | | 13/10 |
| | | | 27/20 |
| | |- |
| | | | 6 |
| | | | |
| | | | 9/7 |
| | | | 21/16~17/13 |
| | | | 4/3 |
| | | | 34/25 |
| | | | |
| | |- |
| | | | 7 |
| | | | |
| | | | 27/20 |
| | | | 11/8~15/11 |
| | | | 7/5 |
| | | | 17/12 |
| | | | |
| | |- |
| | | | 8 |
| | | | |
| | | | 24/17 |
| | | | 10/7 |
| | | | 16/11~22/15 |
| | | | 40/27 |
| | | | |
| | |- |
| | | | 9 |
| | | | |
| | | | 25/17 |
| | | | 3/2 |
| | | | 26/17~32/21 |
| | | | 14/9 |
| | | | |
| | |- |
| | | | 10 |
| | | | 40/27 |
| | | | 20/13 |
| | | | 11/7 |
| | | | 8/5 |
| | | | 13/8~34/21 |
| | | | |
| | |- |
| | | | 11 |
| | | | |
| | | | |
| | | | 18/11~28/17 |
| | | | 5/3 |
| | | | 22/13 |
| | | | |
| | |- |
| | | | 12 |
| | | | |
| | | | 27/16 |
| | | | 12/7 |
| | | | 7/4 |
| | | | 16/9 |
| | | | |
| | |- |
| | | | 13 |
| | | | 17/10 |
| | | | 30/14 |
| | | | 9/5 |
| | | | 11/6~20/11 |
| | | | 13/7 |
| | | | |
| | |- |
| | | | 14 |
| | | | |
| | | | 24/13 |
| | | | 15/8 |
| | | | 40/21~48/25 |
| | | | 35/18 |
| | | | |
| | |} |
|
| |
|
| | ==2.3.5.11.13 hitchcock== |
| | Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13. |
|
| |
|
| <table class="wiki_table">
| | {| class="wikitable" |
| <tr>
| | |- |
| <td>Steps<br />
| | | | Steps |
| </td>
| | | | |
| <td>&quot;Diminished&quot;<br />
| | | | "Diminished" |
| </td>
| | | | "Minor" |
| <td>&quot;Minor&quot;<br />
| | | | "Major" |
| </td>
| | | | "Augmented" |
| <td>&quot;Major&quot;<br />
| | | | |
| </td>
| | |- |
| <td>&quot;Augmented&quot;<br />
| | | | 1 |
| </td>
| | | | |
| </tr>
| | | | 13/12 |
| <tr>
| | | | 12/11~11/10 |
| <td>1<br />
| | | | 10/9 |
| </td>
| | | | 9/8 |
| <td>21/20~16/15<br />
| | | | |
| </td>
| | |- |
| <td>12/11~11/10~10/9<br />
| | | | 2 |
| </td>
| | | | 13/11 |
| <td>9/8~8/7<br />
| | | | 6/5 |
| </td>
| | | | 11/9 |
| <td>(13/11)<br />
| | | | 16/13 |
| </td>
| | | | 5/4 |
| </tr>
| | | | |
| <tr>
| | |- |
| <td>2<br />
| | | | 3 |
| </td>
| | | | 13/10 |
| <td>7/6<br />
| | | | |
| </td>
| | | | 4/3 |
| <td>6/5~11/9<br />
| | | | 27/20 |
| </td>
| | | | 11/8 |
| <td>5/4<br />
| | | | 18/13 |
| </td>
| | |- |
| <td>9/7~(13/10)<br />
| | | | 4 |
| </td>
| | | | 13/9 |
| </tr>
| | | | 16/11 |
| <tr>
| | | | 40/27 |
| <td>3<br />
| | | | 3/2 |
| </td>
| | | | |
| <td>14/11<br />
| | | | 20/13 |
| </td>
| | |- |
| <td>4/3<br />
| | | | 5 |
| </td>
| | | | |
| <td>11/8<br />
| | | | 8/5 |
| </td>
| | | | 13/8 |
| <td>10/7~(13/9)<br />
| | | | 18/11 |
| </td>
| | | | 5/3 |
| </tr>
| | | | 22/13 |
| <tr>
| | |- |
| <td>4<br />
| | | | 6 |
| </td>
| | | | |
| <td>7/5~(18/13)<br />
| | | | 16/9 |
| </td>
| | | | 9/5 |
| <td>16/11<br />
| | | | 11/6 |
| </td>
| | | | 24/13 |
| <td>3/2<br />
| | | | |
| </td>
| | |} |
| <td>11/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td>14/9~(20/13)<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>5/3~18/11<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td>(22/13)<br />
| |
| </td>
| |
| <td>7/4~16/9<br />
| |
| </td>
| |
| <td>9/5~11/6<br />
| |
| </td>
| |
| <td>40/21~15/8<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Examples-17-limit valentino"></a><!-- ws:end:WikiTextHeadingRule:14 -->17-limit valentino</h2>
| |
| Chroma: 49/48~55/54~56/55~64/63~65/64~85/84~119/117~128/125~143/140~153/150<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td>Steps<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>36/35<br />
| |
| </td>
| |
| <td>21/20~25/24<br />
| |
| </td>
| |
| <td>17/16~16/15<br />
| |
| </td>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>14/13<br />
| |
| </td>
| |
| <td>12/11~11/10<br />
| |
| </td>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>17/15<br />
| |
| </td>
| |
| <td>20/17<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td>8/7<br />
| |
| </td>
| |
| <td>7/6<br />
| |
| </td>
| |
| <td>32/27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9~17/14<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>16/13~21/17<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td>14/11<br />
| |
| </td>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td>27/20<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>9/7<br />
| |
| </td>
| |
| <td>21/16~17/13<br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>34/25<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>11/8~15/11<br />
| |
| </td>
| |
| <td>7/5<br />
| |
| </td>
| |
| <td>17/12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>24/17<br />
| |
| </td>
| |
| <td>10/7<br />
| |
| </td>
| |
| <td>16/11~22/15<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>25/17<br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td>26/17~32/21<br />
| |
| </td>
| |
| <td>14/9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>10<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td>20/13<br />
| |
| </td>
| |
| <td>11/7<br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>13/8~34/21<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>18/11~28/17<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>22/13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>12<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>27/16<br />
| |
| </td>
| |
| <td>12/7<br />
| |
| </td>
| |
| <td>7/4<br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>13<br />
| |
| </td>
| |
| <td>17/10<br />
| |
| </td>
| |
| <td>30/14<br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>11/6~20/11<br />
| |
| </td>
| |
| <td>13/7<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>14<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>24/13<br />
| |
| </td>
| |
| <td>15/8<br />
| |
| </td>
| |
| <td>40/21~48/25<br />
| |
| </td>
| |
| <td>35/18<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| <br />
| |
| <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Examples-2.3.5.11.13 hitchcock"></a><!-- ws:end:WikiTextHeadingRule:16 -->2.3.5.11.13 hitchcock</h2>
| |
| Unlike amity itself, this 2.3.5.11.13 amity extension is a cluster temperament because the intervals between 6/5 and 5/4 are mapped to 11/9 and 16/13.<br />
| |
| | |
| | |
| <table class="wiki_table">
| |
| <tr>
| |
| <td>Steps<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>&quot;Diminished&quot;<br />
| |
| </td>
| |
| <td>&quot;Minor&quot;<br />
| |
| </td>
| |
| <td>&quot;Major&quot;<br />
| |
| </td>
| |
| <td>&quot;Augmented&quot;<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>13/12<br />
| |
| </td>
| |
| <td>12/11~11/10<br />
| |
| </td>
| |
| <td>10/9<br />
| |
| </td>
| |
| <td>9/8<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2<br />
| |
| </td>
| |
| <td>13/11<br />
| |
| </td>
| |
| <td>6/5<br />
| |
| </td>
| |
| <td>11/9<br />
| |
| </td>
| |
| <td>16/13<br />
| |
| </td>
| |
| <td>5/4<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3<br />
| |
| </td>
| |
| <td>13/10<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/3<br />
| |
| </td>
| |
| <td>27/20<br />
| |
| </td>
| |
| <td>11/8<br />
| |
| </td>
| |
| <td>18/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4<br />
| |
| </td>
| |
| <td>13/9<br />
| |
| </td>
| |
| <td>16/11<br />
| |
| </td>
| |
| <td>40/27<br />
| |
| </td>
| |
| <td>3/2<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>20/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>5<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>8/5<br />
| |
| </td>
| |
| <td>13/8<br />
| |
| </td>
| |
| <td>18/11<br />
| |
| </td>
| |
| <td>5/3<br />
| |
| </td>
| |
| <td>22/13<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>6<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>16/9<br />
| |
| </td>
| |
| <td>9/5<br />
| |
| </td>
| |
| <td>11/6<br />
| |
| </td>
| |
| <td>24/13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |