9edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599951430 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 601329588 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-04 10:06:52 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>601329588</tt>.<br> | ||
: The revision comment was: <tt></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> | 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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The 9EDO scale, which divides the octave into nine equal parts each of 133+1/3 cents precisely, has the peculiar property of representing certain [[Harmonic Limit|7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes | The 9EDO scale, which divides the octave into nine equal parts each of 133+1/3 cents precisely, has the peculiar property of representing certain [[Harmonic Limit|7-limit]] intervals almost exactly. A 7-limit version of 9EDO goes | ||
1: 27/25 133.238 large limma, BP small semitone | 1: 27/25 133.238/1 large limma, BP small semitone | ||
2: 7/6 266.871 septimal minor third | 2: 7/6 266.871 septimal minor third | ||
3: 63/50 400.108 quasi-equal major third | 3: 63/50 400.108/1 quasi-equal major third | ||
4: 49/36 533.742 Arabic lute acute fourth | 4: 49/36 533.742/1 Arabic lute acute fourth | ||
5: 72/49 666.258 Arabic lute grave fifth | 5: 72/49 666.258/1 Arabic lute grave fifth | ||
6: 100/63 799.892 quasi-equal minor sixth | 6: 100/63 799.892/1 quasi-equal minor sixth | ||
7: 12/7 933.129 septimal major sixth | 7: 12/7 933.129 septimal major sixth | ||
8: 50/27 1066.762 grave major seventh | 8: 50/27 1066.762/1 grave major seventh | ||
9: 2/1 1200.000 octave | 9: 2/1 1200.000 octave | ||
Here the characterizations are taken from [[http://en.wikipedia.org/wiki/Scala_%28program%29|Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9EDO. The above scale generates the [[Just intonation subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO. | Here the characterizations are taken from [[http://en.wikipedia.org/wiki/Scala_%28program%29|Scala]], which also describes the scale itself as "Pelog Nawanada: Sunda". Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the [[Just intonation subgroups|just intonation subgroup]] 2.27/25.7/3, which is closely related to 9EDO. | ||
Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour: | Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour: | ||
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==Commas== | ==Commas== | ||
9 EDO tempers out the following commas. (Note: This assumes val < 9 14 21 25 31 33 |.) | 9 EDO tempers out the following commas. (Note: This assumes val < 9 14 21 25 31 33/1 |.) | ||
||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||~ Comma ||~ Monzo ||~ Value (Cents) ||~ Name 1 ||~ Name 2 ||~ Name 3 || | ||
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||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || | ||= 16875/16384 || | -14 3 4 > ||> 51.12 ||= Negri Comma ||= Double Augmentation Diesis || || | ||
||= 128/125 || | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma || || | ||= 128/125 || | 7 0 -3 > ||> 41.06 ||= Diesis ||= Augmented Comma || || | ||
||= | ||= || | -21 3 7 > ||> 10.06 ||= Semicomma ||= Fokker Comma || || | ||
||= 36/35 || | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= || || | ||= 36/35 || | 2 2 -1 -1 > ||> 48.77 ||= Septimal Quarter Tone ||= || || | ||
||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicenna ||= Avicenna's Enharmonic Diesis || || | ||= 525/512 || | -9 1 2 1 > ||> 43.41 ||= Avicenna ||= Avicenna's Enharmonic Diesis || || | ||
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The 9EDO scale, which divides the octave into nine equal parts each of 133+1/3 cents precisely, has the peculiar property of representing certain <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> intervals almost exactly. A 7-limit version of 9EDO goes<br /> | The 9EDO scale, which divides the octave into nine equal parts each of 133+1/3 cents precisely, has the peculiar property of representing certain <a class="wiki_link" href="/Harmonic%20Limit">7-limit</a> intervals almost exactly. A 7-limit version of 9EDO goes<br /> | ||
<br /> | <br /> | ||
1: 27/25 133.238 large limma, BP small semitone<br /> | 1: 27/25 133.238/1 large limma, BP small semitone<br /> | ||
2: 7/6 266.871 septimal minor third<br /> | 2: 7/6 266.871 septimal minor third<br /> | ||
3: 63/50 400.108 quasi-equal major third<br /> | 3: 63/50 400.108/1 quasi-equal major third<br /> | ||
4: 49/36 533.742 Arabic lute acute fourth<br /> | 4: 49/36 533.742/1 Arabic lute acute fourth<br /> | ||
5: 72/49 666.258 Arabic lute grave fifth<br /> | 5: 72/49 666.258/1 Arabic lute grave fifth<br /> | ||
6: 100/63 799.892 quasi-equal minor sixth<br /> | 6: 100/63 799.892/1 quasi-equal minor sixth<br /> | ||
7: 12/7 933.129 septimal major sixth<br /> | 7: 12/7 933.129 septimal major sixth<br /> | ||
8: 50/27 1066.762 grave major seventh<br /> | 8: 50/27 1066.762/1 grave major seventh<br /> | ||
9: 2/1 1200.000 octave<br /> | 9: 2/1 1200.000 octave<br /> | ||
<br /> | <br /> | ||
Here the characterizations are taken from <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scala_%28program%29" rel="nofollow">Scala</a>, which also describes the scale itself as &quot;Pelog Nawanada: Sunda&quot;. Chords such as 1/1 - 7/6 - 49/36 - 12/7 are therefore natural ones for 9EDO. The above scale generates the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.27/25.7/3, which is closely related to 9EDO.<br /> | Here the characterizations are taken from <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Scala_%28program%29" rel="nofollow">Scala</a>, which also describes the scale itself as &quot;Pelog Nawanada: Sunda&quot;. Chords such as 1/1 - 7/6 - 49/36 - 12/7/1 are therefore natural ones for 9EDO. The above scale generates the <a class="wiki_link" href="/Just%20intonation%20subgroups">just intonation subgroup</a> 2.27/25.7/3, which is closely related to 9EDO.<br /> | ||
<br /> | <br /> | ||
Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:<br /> | Like 16edo, 9edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="Images-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc1"><a name="Images-Commas"></a><!-- ws:end:WikiTextHeadingRule:4 -->Commas</h2> | ||
9 EDO tempers out the following commas. (Note: This assumes val &lt; 9 14 21 25 31 33 |.)<br /> | 9 EDO tempers out the following commas. (Note: This assumes val &lt; 9 14 21 25 31 33/1 |.)<br /> | ||
<br /> | <br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td>| -21 3 7 &gt;<br /> | <td>| -21 3 7 &gt;<br /> | ||