15edo: Difference between revisions
Wikispaces>k9assassin **Imported revision 561701355 - Original comment: ** |
Wikispaces>k9assassin **Imported revision 562309351 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:k9assassin|k9assassin]] and made on <tt>2015-10- | : This revision was by author [[User:k9assassin|k9assassin]] and made on <tt>2015-10-13 10:59:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>562309351</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> | ||
| Line 15: | Line 15: | ||
15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, and 6/5) that has a positive [[81_80|syntonic comma]]. | 15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, and 6/5) that has a positive [[81_80|syntonic comma]]. | ||
In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. | In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. | ||
A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160c) of 15-edo while the "small quill" (80c) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework. | |||
=Images= | =Images= | ||
| Line 24: | Line 26: | ||
|| Degree || Cents | || Degree || Cents | ||
DMS || Solfege | DMS || Solfege | ||
(porcupine-based) || Blackwood | (porcupine-based) || Porcupine[8] | ||
"guitar notation" || Porcupine[7] || Blackwood | based notation || Blackwood | ||
"guitar notation" || Porcupine[7] | |||
(traditional) || Blackwood | |||
Decimal ||= Approximate Ratios* || | Decimal ||= Approximate Ratios* || | ||
|| 0 || 0 || do || E || G || 1 ||= 1/1 || | || 0 || 0 || do || b || E || G || 1 ||= 1/1 || | ||
|| 1 || 80 | || 1 || 80 | ||
24° || di || E# || G# / Abb || 1# / 2b ||= 25/24, 21/20, 16/15 || | 24° || di || cb || E# || G# / Abb || 1# / 2b ||= 25/24, 21/20, 16/15 || | ||
|| 2 || 160 | || 2 || 160 | ||
48° || ru || Gb || Gx / Ab || 2 ||= 11/10, 12/11, 10/9 || | 48° || ru || c || Gb || Gx / Ab || 2 ||= 11/10, 12/11, 10/9 || | ||
|| 3 || 240 | || 3 || 240 | ||
72° || re || G || A || 3 ||= 8/7, 7/6, 9/8 || | 72° || re || d || G || A || 3 ||= 8/7, 7/6, 9/8 || | ||
|| 4 || 320 | || 4 || 320 | ||
96° || me || G# || A# / Bb || 3# / 4b ||= 6/5, 11/9 || | 96° || me || db || G# || A# / Bb || 3# / 4b ||= 6/5, 11/9 || | ||
|| 5 || 400 | || 5 || 400 | ||
120° || mi || Ab || B || 4 ||= 5/4, 14/11 || | 120° || mi || ð (eth) || Ab || B || 4 ||= 5/4, 14/11 || | ||
|| 6 || 480 | || 6 || 480 | ||
144° || fa || A || B# / Cb || 5 ||= 4/3, 9/7, 21/16 || | 144° || fa || ð# || A || B# / Cb || 5 ||= 4/3, 9/7, 21/16 || | ||
|| 7 || 560 | || 7 || 560 | ||
168° || fu || A# || C || 5# / 6b ||= 11/8, 7/5 || | 168° || fu || e || A# || C || 5# / 6b ||= 11/8, 7/5 || | ||
|| 8 || 640 | || 8 || 640 | ||
192° || su || Bb || C# / Db || 6 ||= 16/11, 10/7 || | 192° || su || e# || Bb || C# / Db || 6 ||= 16/11, 10/7 || | ||
|| 9 || 720 | || 9 || 720 | ||
216° || sol || B || D || 7 ||= 3/2, 14/9, 32/21 || | 216° || sol || f || B || D || 7 ||= 3/2, 14/9, 32/21 || | ||
|| 10 || 800 | || 10 || 800 | ||
240° || le || B# || D# / Eb || 7# / 8b ||= 8/5, 11/7 || | 240° || le || f# || B# || D# / Eb || 7# / 8b ||= 8/5, 11/7 || | ||
|| 11 || 880 | || 11 || 880 | ||
264° || la || Db || E || 8 ||= 5/3, 18/11 || | 264° || la || þ (thorn) || Db || E || 8 ||= 5/3, 18/11 || | ||
|| 12 || 960 | || 12 || 960 | ||
288° || ta || D || E# / Fb || 9 ||= 7/4, 12/7, 16/9 || | 288° || ta || þ# || D || E# / Fb || 9 ||= 7/4, 12/7, 16/9 || | ||
|| 13 || 1040 | || 13 || 1040 | ||
312° || tu || D# || F || 9# / 0b ||= 20/11, 11/6, 9/5 || | 312° || tu || æ (ash) || D# || F || 9# / 0b ||= 20/11, 11/6, 9/5 || | ||
|| 14 || 1120 | || 14 || 1120 | ||
336° || ti || Eb || F# /Gb || 0 ||= 48/25, 40/21, 15/8 || | 336° || ti || æ# || Eb || F# /Gb || 0 ||= 48/25, 40/21, 15/8 || | ||
|| 15 || 1200 | || 15 || 1200 | ||
360° || do || E || G || 1 ||= 2/1 || | 360° || do || b || E || G || 1 ||= 2/1 || | ||
*based on treating 15-EDO as an 11-limit temperament; other approaches are possible | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible | ||
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | 15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | ||
| Line 105: | Line 109: | ||
==Porcupine[8] Based Notation== | ==Porcupine[8] Based Notation== | ||
[[image:porcupine alphabet.png width="400" height="81"]] | [[image:porcupine alphabet.png width="400" height="81"]] | ||
William Lynch proposes notating 15 EDO based on an eight nominal system using the old english letters: b c d ð e f þ æ as the alphabet. | William Lynch proposes notating 15 EDO based on an eight nominal system using the old english letters: b c d ð e f þ æ as the alphabet. | ||
Porcupine[7] can also be notated by omitting "ð" | Porcupine[7] can also be notated by omitting "ð" | ||
The full alphabet with normal sharps and flats: b b# c c# d ð ð# e e# f f# þ þ# æ æ# | The full alphabet with normal sharps and flats: b b# c c# d ð ð# e e# f f# þ þ# æ æ# | ||
alphabet with ups and downs: b b^ c c^ d ð ð^ e e^ f f^ þ þ^ æ æ^ | alphabet with ups and downs: b b^ c c^ d ð ð^ e e^ f f^ þ þ^ æ æ^ | ||
| Line 222: | Line 226: | ||
15-edo can be seen as a <a class="wiki_link" href="/7-limit">7-limit</a> temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to <a class="wiki_link" href="/11-limit">11-limit</a> intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, and 6/5) that has a positive <a class="wiki_link" href="/81_80">syntonic comma</a>.<br /> | 15-edo can be seen as a <a class="wiki_link" href="/7-limit">7-limit</a> temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to <a class="wiki_link" href="/11-limit">11-limit</a> intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, and 6/5) that has a positive <a class="wiki_link" href="/81_80">syntonic comma</a>.<br /> | ||
<br /> | <br /> | ||
In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo.<br /> | In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. <br /> | ||
<br /> | |||
A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the &quot;quill&quot; is the name given to the two step interval (160c) of 15-edo while the &quot;small quill&quot; (80c) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework. <br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:4 -->Images</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc1"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:4 -->Images</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:931:&lt;img src=&quot;/file/view/15edo%20wheel.png/516943384/225x225/15edo%20wheel.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 225px; width: 225px;&quot; /&gt; --><img src="/file/view/15edo%20wheel.png/516943384/225x225/15edo%20wheel.png" alt="15edo wheel.png" title="15edo wheel.png" style="height: 225px; width: 225px;" /><!-- ws:end:WikiTextLocalImageRule:931 --><!-- ws:start:WikiTextLocalImageRule:932:&lt;img src=&quot;/file/view/15edo%20wheel%2002.png/516943402/250x250/15edo%20wheel%2002.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 250px; width: 250px;&quot; /&gt; --><img src="/file/view/15edo%20wheel%2002.png/516943402/250x250/15edo%20wheel%2002.png" alt="15edo wheel 02.png" title="15edo wheel 02.png" style="height: 250px; width: 250px;" /><!-- ws:end:WikiTextLocalImageRule:932 --><!-- ws:start:WikiTextLocalImageRule:933:&lt;img src=&quot;/file/view/15edo%20wheel%2003.png/516943418/220x220/15edo%20wheel%2003.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 220px; width: 220px;&quot; /&gt; --><img src="/file/view/15edo%20wheel%2003.png/516943418/220x220/15edo%20wheel%2003.png" alt="15edo wheel 03.png" title="15edo wheel 03.png" style="height: 220px; width: 220px;" /><!-- ws:end:WikiTextLocalImageRule:933 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:6 -->Intervals</h1> | ||
| Line 240: | Line 246: | ||
<td>Solfege<br /> | <td>Solfege<br /> | ||
(porcupine-based)<br /> | (porcupine-based)<br /> | ||
</td> | |||
<td>Porcupine[8]<br /> | |||
based notation<br /> | |||
</td> | </td> | ||
<td>Blackwood<br /> | <td>Blackwood<br /> | ||
| Line 245: | Line 254: | ||
</td> | </td> | ||
<td>Porcupine[7]<br /> | <td>Porcupine[7]<br /> | ||
(traditional)<br /> | |||
</td> | </td> | ||
<td>Blackwood<br /> | <td>Blackwood<br /> | ||
| Line 258: | Line 268: | ||
</td> | </td> | ||
<td>do<br /> | <td>do<br /> | ||
</td> | |||
<td>b<br /> | |||
</td> | </td> | ||
<td>E<br /> | <td>E<br /> | ||
| Line 275: | Line 287: | ||
</td> | </td> | ||
<td>di<br /> | <td>di<br /> | ||
</td> | |||
<td>cb<br /> | |||
</td> | </td> | ||
<td>E#<br /> | <td>E#<br /> | ||
| Line 292: | Line 306: | ||
</td> | </td> | ||
<td>ru<br /> | <td>ru<br /> | ||
</td> | |||
<td>c<br /> | |||
</td> | </td> | ||
<td>Gb<br /> | <td>Gb<br /> | ||
| Line 309: | Line 325: | ||
</td> | </td> | ||
<td>re<br /> | <td>re<br /> | ||
</td> | |||
<td>d<br /> | |||
</td> | </td> | ||
<td>G<br /> | <td>G<br /> | ||
| Line 326: | Line 344: | ||
</td> | </td> | ||
<td>me<br /> | <td>me<br /> | ||
</td> | |||
<td>db<br /> | |||
</td> | </td> | ||
<td>G#<br /> | <td>G#<br /> | ||
| Line 343: | Line 363: | ||
</td> | </td> | ||
<td>mi<br /> | <td>mi<br /> | ||
</td> | |||
<td>ð (eth)<br /> | |||
</td> | </td> | ||
<td>Ab<br /> | <td>Ab<br /> | ||
| Line 360: | Line 382: | ||
</td> | </td> | ||
<td>fa<br /> | <td>fa<br /> | ||
</td> | |||
<td>ð#<br /> | |||
</td> | </td> | ||
<td>A<br /> | <td>A<br /> | ||
| Line 377: | Line 401: | ||
</td> | </td> | ||
<td>fu<br /> | <td>fu<br /> | ||
</td> | |||
<td>e<br /> | |||
</td> | </td> | ||
<td>A#<br /> | <td>A#<br /> | ||
| Line 394: | Line 420: | ||
</td> | </td> | ||
<td>su<br /> | <td>su<br /> | ||
</td> | |||
<td>e#<br /> | |||
</td> | </td> | ||
<td>Bb<br /> | <td>Bb<br /> | ||
| Line 411: | Line 439: | ||
</td> | </td> | ||
<td>sol<br /> | <td>sol<br /> | ||
</td> | |||
<td>f<br /> | |||
</td> | </td> | ||
<td>B<br /> | <td>B<br /> | ||
| Line 428: | Line 458: | ||
</td> | </td> | ||
<td>le<br /> | <td>le<br /> | ||
</td> | |||
<td>f#<br /> | |||
</td> | </td> | ||
<td>B#<br /> | <td>B#<br /> | ||
| Line 445: | Line 477: | ||
</td> | </td> | ||
<td>la<br /> | <td>la<br /> | ||
</td> | |||
<td>þ (thorn)<br /> | |||
</td> | </td> | ||
<td>Db<br /> | <td>Db<br /> | ||
| Line 462: | Line 496: | ||
</td> | </td> | ||
<td>ta<br /> | <td>ta<br /> | ||
</td> | |||
<td>þ#<br /> | |||
</td> | </td> | ||
<td>D<br /> | <td>D<br /> | ||
| Line 479: | Line 515: | ||
</td> | </td> | ||
<td>tu<br /> | <td>tu<br /> | ||
</td> | |||
<td>æ (ash)<br /> | |||
</td> | </td> | ||
<td>D#<br /> | <td>D#<br /> | ||
| Line 496: | Line 534: | ||
</td> | </td> | ||
<td>ti<br /> | <td>ti<br /> | ||
</td> | |||
<td>æ#<br /> | |||
</td> | </td> | ||
<td>Eb<br /> | <td>Eb<br /> | ||
| Line 513: | Line 553: | ||
</td> | </td> | ||
<td>do<br /> | <td>do<br /> | ||
</td> | |||
<td>b<br /> | |||
</td> | </td> | ||
<td>E<br /> | <td>E<br /> | ||
| Line 525: | Line 567: | ||
</table> | </table> | ||
*based on treating 15-EDO as an 11-limit temperament; other approaches are possible<br /> | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible <br /> | ||
<br /> | <br /> | ||
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> in the paper &quot;<a class="wiki_link_ext" href="http://www.cityoftheasleep.com/etc/5nEDOs.pdf" rel="nofollow">Five is Not an Odd Number</a>&quot;. For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see <a class="wiki_link" href="/Harmony%20in%2015edo%20Blacksmith" target="_blank">Harmony in 15edo Blacksmith[10</a>].<br /> | 15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> in the paper &quot;<a class="wiki_link_ext" href="http://www.cityoftheasleep.com/etc/5nEDOs.pdf" rel="nofollow">Five is Not an Odd Number</a>&quot;. For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see <a class="wiki_link" href="/Harmony%20in%2015edo%20Blacksmith" target="_blank">Harmony in 15edo Blacksmith[10</a>].<br /> | ||
| Line 531: | Line 573: | ||
<!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802896?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802896&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/15ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:0 --><br /> | <!-- ws:start:WikiTextMediaRule:0:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/custom/24802896?h=0&amp;w=0&quot; class=&quot;WikiMedia WikiMediaCustom&quot; id=&quot;wikitext@@media@@type=&amp;quot;custom&amp;quot; key=&amp;quot;24802896&amp;quot;&quot; title=&quot;Custom Media&quot;/&gt; --><object id="example" type="image/svg+xml" data="http://xenharmonic.wikispaces.com/file/view/15ed2-001.svg">alt : Your browser has no SVG support.</object><!-- ws:end:WikiTextMediaRule:0 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:935:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/15ed2-001.svg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@15ed2-001.svg&quot; title=&quot;File: 15ed2-001.svg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/15ed2-001.svg/480716490/15ed2-001.svg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="15ed2-001.svg" /></a><div><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg" onclick="ws.common.trackFileLink('/file/view/15ed2-001.svg/480716490/15ed2-001.svg');" class="filename" title="15ed2-001.svg">15ed2-001.svg</a><br /><ul><li><a href="/file/detail/15ed2-001.svg">Details</a></li><li><a href="/file/view/15ed2-001.svg/480716490/15ed2-001.svg">Download</a></li><li style="color: #666">16 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:935 --><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Intervals-Intervals by patent val error"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals by patent val error</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc3"><a name="Intervals-Intervals by patent val error"></a><!-- ws:end:WikiTextHeadingRule:8 -->Intervals by patent val error</h2> | ||
| Line 698: | Line 740: | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Porcupine Notation"></a><!-- ws:end:WikiTextHeadingRule:14 -->Porcupine Notation</h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc6"><a name="Notation-Porcupine Notation"></a><!-- ws:end:WikiTextHeadingRule:14 -->Porcupine Notation</h2> | ||
<ul><li>See the main <a class="wiki_link" href="/Porcupine%20Notation">porcupine notation</a> page.</li></ul><!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-Porcupine[8] Based Notation"></a><!-- ws:end:WikiTextHeadingRule:16 -->Porcupine[8] Based Notation</h2> | <ul><li>See the main <a class="wiki_link" href="/Porcupine%20Notation">porcupine notation</a> page.</li></ul><!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc7"><a name="Notation-Porcupine[8] Based Notation"></a><!-- ws:end:WikiTextHeadingRule:16 -->Porcupine[8] Based Notation</h2> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:934:&lt;img src=&quot;/file/view/porcupine%20alphabet.png/561701315/400x81/porcupine%20alphabet.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 81px; width: 400px;&quot; /&gt; --><img src="/file/view/porcupine%20alphabet.png/561701315/400x81/porcupine%20alphabet.png" alt="porcupine alphabet.png" title="porcupine alphabet.png" style="height: 81px; width: 400px;" /><!-- ws:end:WikiTextLocalImageRule:934 --><br /> | ||
William Lynch proposes notating 15 EDO based on an eight nominal system using the old english letters: b c d ð e f þ æ as the alphabet. <br /> | William Lynch proposes notating 15 EDO based on an eight nominal system using the old english letters: b c d ð e f þ æ as the alphabet.<br /> | ||
Porcupine[7] can also be notated by omitting &quot;ð&quot;<br /> | Porcupine[7] can also be notated by omitting &quot;ð&quot;<br /> | ||
<br /> | <br /> | ||
The full alphabet with normal sharps and flats: b b# c c# d ð ð# e e# f f# þ þ# æ æ# <br /> | The full alphabet with normal sharps and flats: b b# c c# d ð ð# e e# f f# þ þ# æ æ#<br /> | ||
alphabet with ups and downs: b b^ c c^ d ð ð^ e e^ f f^ þ þ^ æ æ^ <br /> | alphabet with ups and downs: b b^ c c^ d ð ð^ e e^ f f^ þ þ^ æ æ^<br /> | ||
<br /> | <br /> | ||
<br /> | <br /> | ||
| Line 1,175: | Line 1,217: | ||
<a class="wiki_link_ext" href="http://youtu.be/6TyQ9kDm2fk" rel="nofollow">Ode For Ada</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html" rel="nofollow">blog entry</a>)<br /> | <a class="wiki_link_ext" href="http://youtu.be/6TyQ9kDm2fk" rel="nofollow">Ode For Ada</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html" rel="nofollow">blog entry</a>)<br /> | ||
Suite in 15-Note Equal Tuning, opus 33 by Easley Blackwood (as well as one of the Twelve Microtonal Etudes, opus 28)<br /> | Suite in 15-Note Equal Tuning, opus 33 by Easley Blackwood (as well as one of the Twelve Microtonal Etudes, opus 28)<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:936:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/15edo-Chords.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@15edo-Chords.ogg&quot; title=&quot;File: 15edo-Chords.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg" onclick="ws.common.trackFileLink('/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="15edo-Chords.ogg" /></a><div><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg" onclick="ws.common.trackFileLink('/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg');" class="filename" title="15edo-Chords.ogg">15edo-Chords.ogg</a><br /><ul><li><a href="/file/detail/15edo-Chords.ogg">Details</a></li><li><a href="/file/view/15edo-Chords.ogg/252472844/15edo-Chords.ogg">Download</a></li><li style="color: #666">2 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:936 --> Some nice sounds I found in 15 EDO<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:937:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/happenstance15.ogg?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@happenstance15.ogg&quot; title=&quot;File: happenstance15.ogg&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg" onclick="ws.common.trackFileLink('/file/view/happenstance15.ogg/257380320/happenstance15.ogg');"><img src="http://www.wikispaces.com/i/mime/32/empty.png" height="32" width="32" alt="happenstance15.ogg" /></a><div><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg" onclick="ws.common.trackFileLink('/file/view/happenstance15.ogg/257380320/happenstance15.ogg');" class="filename" title="happenstance15.ogg">happenstance15.ogg</a><br /><ul><li><a href="/file/detail/happenstance15.ogg">Details</a></li><li><a href="/file/view/happenstance15.ogg/257380320/happenstance15.ogg">Download</a></li><li style="color: #666">6 MB</li></ul></div></div><!-- ws:end:WikiTextFileRule:937 -->Sonic experiment in 15. Somewhat familiar tonality.<br /> | ||
<span class="long-title"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=kQECU5ecCd4" rel="nofollow" target="_blank">Portrait of insects with 15-tone equal tempered guitar music </a></span><br /> | <span class="long-title"><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=kQECU5ecCd4" rel="nofollow" target="_blank">Portrait of insects with 15-tone equal tempered guitar music </a></span><br /> | ||
<a class="wiki_link_ext" href="http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et" rel="nofollow">PentadecafoniCoda (15et)</a> by <span class="wiki_link_ext">F.F.F. Fiale</span><br /> | <a class="wiki_link_ext" href="http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et" rel="nofollow">PentadecafoniCoda (15et)</a> by <span class="wiki_link_ext">F.F.F. Fiale</span><br /> | ||