5edo: Difference between revisions
Wikispaces>PiotrGrochowski **Imported revision 592319366 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597456972 - 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>2016-10-29 16:37:21 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597456972</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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**in fifths of** | **in fifths of** | ||
**an octave** || **Interval** | **an octave** || **Interval** | ||
**in ¢, DMS** || **Closest** | **in ¢ (coarse, fine), DMS** || **Closest** | ||
**diatonic** | **diatonic** | ||
**interval name** || **The "neighborhood" of just intervals** || | **interval name** || **The "neighborhood" of just intervals** || | ||
|| 0 || 0.0, 0° || unison / prime || exactly 1/1 || | || 0 || 0.0, 0° || unison / prime || exactly 1/1 || | ||
|| 1 || 240.0. | || 1 || 240.0, 288.0, 72° || second / third || +8.826 c (coarse), +10.591 c (fine), +2°38'52" from septimal second 8/7 | ||
72° || second / third || +8.826 c, +2°38'52" from septimal second 8/7 | -4.969 c (coarse), -5.963 c (fine), -1°29'26" from diminished third 144/125 | ||
-4.969 c, -1°29'26" from diminished third 144/125 | -13.076 c (coarse), -15.961 c (fine), -3<span style="line-height: 1.5;">°55'22"</span> from augmented second 125/108 | ||
-13.076 c, -3<span style="line-height: 1.5;">°55'22"</span> from augmented second 125/108 | -26.871 c (coarse), -32.245 c (fine), -8<span style="line-height: 1.5;">°3'41"</span> from septimal minor third 7/6 || | ||
-26.871 c, -8<span style="line-height: 1.5;">°3'41"</span> from septimal minor third 7/6 || | || 2 || 480.0, 576.0, 144° || fourth || +9.219 c (coarse), +11.063 c (fine), +2°45'57" from narrow fourth 21/16 | ||
|| 2 || 480.0, | -0.686 c (coarse), -0.775 c (fine), -11'37" from smaller fourth 33/25 | ||
144° || fourth || +9.219 c, +2°45'57" from narrow fourth 21/16 | -18.045 c (coarse), -21.654 c (fine), -5°24'49" from just fourth 4/3 || | ||
-0.686 c, -11'37" from smaller fourth 33/25 | || 3 || 720.0, 864.0, 216° || fifth || +18.045 c (coarse), +21.654 c (fine), +5°24'49" from just fifth 3/2 | ||
-18.045 c, -5°24'49" from just fourth 4/3 || | +0.686 c (coarse), +0.775 c (fine), +11'37" from bigger fifth 50/33 | ||
|| 3 || 720.0, | -9.219 c (coarse), -11.063 c (fine), -2°45'57" from wide fifth 21/16 || | ||
216° || fifth || +18.045 c, +5°24'49" from just fifth 3/2 | || 4 || 960.0, 1152.0, 288° || sixth, seventh || 26.871 c (coarse), 32.245 c (fine), 8°3'41" from septimal major sixth 12/7 | ||
+0.686 c | 13.076 c (coarse), 15.961 c (fine), 3°55'22" from diminished seventh 216/125 | ||
-9.219 c | 4.969 c (coarse)<span style="line-height: 1.5;">, 5.963 c (fine), 1°29'26" </span>from augmented sixth 125/72 | ||
|| 4 || 960.0, | -8.826 c (coarse), -10.591 c (fine), -2°38'52" from septimal seventh 7/4 || | ||
288° || sixth, seventh || 26.871 c, 8°3'41" from septimal major sixth 12/7 | || 5 || 1200.0, 1440.0, 360° || eighth || exactly 2/1 || | ||
13.076 c, 3°55'22" from diminished seventh 216/125 | |||
4.969 c<span style="line-height: 1.5;">, 1°29'26" </span>from augmented sixth 125/72 | |||
-8.826 c, -2°38'52" from septimal seventh 7/4 || | |||
|| 5 || 1200.0, | |||
360° || eighth || exactly 2/1 || | |||
[[media type="custom" key="24802268"]] | [[media type="custom" key="24802268"]] | ||
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==Commas Tempered== | ==Commas Tempered== | ||
5-EDO tempers out the following commas. (Note: This assumes the val < 5 8 12 14 17 19 |.) | 5-EDO tempers out the following commas. (Note: This assumes the val < 5 [[tel:8 12 14 17 19|8 12 14 17 19]] |.) | ||
||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val || | ||~ Comma ||~ Value (cents) ||~ Name ||~ Second Name ||~ Third Name ||~ Val || | ||
||= 256/243 ||> 90.225 || Limma || Pythagorean Minor 2nd || || | 8 -5 > || | ||= 256/243 ||> 90.225 || Limma || Pythagorean Minor 2nd || || | 8 -5 > || | ||
||= 81/80 ||> 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 > || | ||= 81/80 ||> 21.506 || Syntonic Comma || Didymos Comma || Meantone Comma || | -4 4 -1 > || | ||
||= 2889416/2882415 ||> 4.200 || Vulture || || || | 24 -21 4 > || | ||= [[tel:2889416/2882415|2889416/2882415]] ||> 4.200 || Vulture || || || | 24 -21 4 > || | ||
||= 36/35 ||> 48.770 || Septimal Quarter Tone || || || | 2 2 -1 -1 > || | ||= 36/35 ||> 48.770 || Septimal Quarter Tone || || || | 2 2 -1 -1 > || | ||
||= 49/48 ||> 35.697 || Slendro Diesis || || || | -4 -1 0 2 > || | ||= 49/48 ||> 35.697 || Slendro Diesis || || || | -4 -1 0 2 > || | ||
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||= 19683/19600 ||> 7.316 || Cataharry || || || | -4 9 -2 -2 > || | ||= 19683/19600 ||> 7.316 || Cataharry || || || | -4 9 -2 -2 > || | ||
||= 5120/5103 ||> 5.758 || Hemifamity || || || | 10 -6 1 -1 > || | ||= 5120/5103 ||> 5.758 || Hemifamity || || || | 10 -6 1 -1 > || | ||
||= 1065875/1063543 ||> 3.792 || Wadisma || || || | -26 -1 1 9 > || | ||= [[tel:1065875/1063543|1065875/1063543]] ||> 3.792 || Wadisma || || || | -26 -1 1 9 > || | ||
||= 420175/419904 ||> 1.117 || Wizma || || || | -6 -8 2 5 > || | ||= [[tel:420175/419904|420175/419904]] ||> 1.117 || Wizma || || || | -6 -8 2 5 > || | ||
||= 99/98 ||> 17.576 || Mothwellsma || || || | -1 2 0 -2 1 > || | ||= 99/98 ||> 17.576 || Mothwellsma || || || | -1 2 0 -2 1 > || | ||
||= 896/891 ||> 9.688 || Pentacircle || || || | 7 -4 0 1 -1 > || | ||= 896/891 ||> 9.688 || Pentacircle || || || | 7 -4 0 1 -1 > || | ||
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</td> | </td> | ||
<td><strong>Interval</strong><br /> | <td><strong>Interval</strong><br /> | ||
<strong>in ¢, DMS</strong><br /> | <strong>in ¢ (coarse, fine), DMS</strong><br /> | ||
</td> | </td> | ||
<td><strong>Closest</strong><br /> | <td><strong>Closest</strong><br /> | ||
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<td>1<br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>240.0. | <td>240.0, 288.0, 72°<br /> | ||
72°<br /> | |||
</td> | </td> | ||
<td>second / third<br /> | <td>second / third<br /> | ||
</td> | </td> | ||
<td>+8.826 c, +2°38'52&quot; from septimal second 8/7<br /> | <td>+8.826 c (coarse), +10.591 c (fine), +2°38'52&quot; from septimal second 8/7<br /> | ||
-4.969 c, -1°29'26&quot; from diminished third 144/125<br /> | -4.969 c (coarse), -5.963 c (fine), -1°29'26&quot; from diminished third 144/125<br /> | ||
-13.076 c, -3<span style="line-height: 1.5;">°55'22&quot;</span> from augmented second 125/108<br /> | -13.076 c (coarse), -15.961 c (fine), -3<span style="line-height: 1.5;">°55'22&quot;</span> from augmented second 125/108<br /> | ||
-26.871 c, -8<span style="line-height: 1.5;">°3'41&quot;</span> from septimal minor third 7/6<br /> | -26.871 c (coarse), -32.245 c (fine), -8<span style="line-height: 1.5;">°3'41&quot;</span> from septimal minor third 7/6<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>2<br /> | <td>2<br /> | ||
</td> | </td> | ||
<td>480.0, | <td>480.0, 576.0, 144°<br /> | ||
144°<br /> | |||
</td> | </td> | ||
<td>fourth<br /> | <td>fourth<br /> | ||
</td> | </td> | ||
<td>+9.219 c, +2°45'57&quot; from narrow fourth 21/16<br /> | <td>+9.219 c (coarse), +11.063 c (fine), +2°45'57&quot; from narrow fourth 21/16<br /> | ||
-0.686 c, -11'37&quot; from smaller fourth 33/25<br /> | -0.686 c (coarse), -0.775 c (fine), -11'37&quot; from smaller fourth 33/25<br /> | ||
-18.045 c, -5°24'49&quot; from just fourth 4/3<br /> | -18.045 c (coarse), -21.654 c (fine), -5°24'49&quot; from just fourth 4/3<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>3<br /> | <td>3<br /> | ||
</td> | </td> | ||
<td>720.0, | <td>720.0, 864.0, 216°<br /> | ||
216°<br /> | |||
</td> | </td> | ||
<td>fifth<br /> | <td>fifth<br /> | ||
</td> | </td> | ||
<td>+18.045 c, +5°24'49&quot; from just fifth 3/2<br /> | <td>+18.045 c (coarse), +21.654 c (fine), +5°24'49&quot; from just fifth 3/2<br /> | ||
+0.686 c | +0.686 c (coarse), +0.775 c (fine), +11'37&quot; from bigger fifth 50/33<br /> | ||
-9.219 c | -9.219 c (coarse), -11.063 c (fine), -2°45'57&quot; from wide fifth 21/16<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>4<br /> | <td>4<br /> | ||
</td> | </td> | ||
<td>960.0, | <td>960.0, 1152.0, 288°<br /> | ||
288°<br /> | |||
</td> | </td> | ||
<td>sixth, seventh<br /> | <td>sixth, seventh<br /> | ||
</td> | </td> | ||
<td>26.871 c, 8°3'41&quot; from septimal major sixth 12/7<br /> | <td>26.871 c (coarse), 32.245 c (fine), 8°3'41&quot; from septimal major sixth 12/7<br /> | ||
13.076 c, 3°55'22&quot; from diminished seventh 216/125<br /> | 13.076 c (coarse), 15.961 c (fine), 3°55'22&quot; from diminished seventh 216/125<br /> | ||
4.969 c<span style="line-height: 1.5;">, 1°29'26&quot; </span>from augmented sixth 125/72<br /> | 4.969 c (coarse)<span style="line-height: 1.5;">, 5.963 c (fine), 1°29'26&quot; </span>from augmented sixth 125/72<br /> | ||
-8.826 c, -2°38'52&quot; from septimal seventh 7/4<br /> | -8.826 c (coarse), -10.591 c (fine), -2°38'52&quot; from septimal seventh 7/4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>5<br /> | <td>5<br /> | ||
</td> | </td> | ||
<td>1200.0, | <td>1200.0, 1440.0, 360°<br /> | ||
360°<br /> | |||
</td> | </td> | ||
<td>eighth<br /> | <td>eighth<br /> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:29:&lt;h2&gt; --><h2 id="toc14"><a name="x5-edo in Musicmaking-Commas Tempered"></a><!-- ws:end:WikiTextHeadingRule:29 -->Commas Tempered</h2> | <!-- ws:start:WikiTextHeadingRule:29:&lt;h2&gt; --><h2 id="toc14"><a name="x5-edo in Musicmaking-Commas Tempered"></a><!-- ws:end:WikiTextHeadingRule:29 -->Commas Tempered</h2> | ||
5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 8 12 14 17 19 |.)<br /> | 5-EDO tempers out the following commas. (Note: This assumes the val &lt; 5 <a class="wiki_link" href="http://tel.wikispaces.com/8%2012%2014%2017%2019">8 12 14 17 19</a> |.)<br /> | ||
<br /> | <br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">2889416/2882415<br /> | <td style="text-align: center;">[[tel:2889416/2882415|2889416/2882415]]<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">4.200<br /> | <td style="text-align: right;">4.200<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">1065875/1063543<br /> | <td style="text-align: center;">[[tel:1065875/1063543|1065875/1063543]]<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">3.792<br /> | <td style="text-align: right;">3.792<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">420175/419904<br /> | <td style="text-align: center;">[[tel:420175/419904|420175/419904]]<br /> | ||
</td> | </td> | ||
<td style="text-align: right;">1.117<br /> | <td style="text-align: right;">1.117<br /> | ||