13edo: Difference between revisions
Wikispaces>cookiemeows **Imported revision 505638932 - Original comment: ** |
Wikispaces>cookiemeows **Imported revision 505638954 - 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:cookiemeows|cookiemeows]] and made on <tt>2014-04-30 16:04: | : This revision was by author [[User:cookiemeows|cookiemeows]] and made on <tt>2014-04-30 16:04:11 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>505638954</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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Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a "stack of 3rds" the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (__[[13edo#top|degree]]s__ 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the [[k*N subgroups|2*13 subgroup]] 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et. | Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a "stack of 3rds" the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (__[[13edo#top|degree]]s__ 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the [[k*N subgroups|2*13 subgroup]] 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et. | ||
The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite __[[13edo#top|close]]__ to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). | The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite __[[13edo#top|close]]__ to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). | ||
=Scales in 13edo= | =Scales in 13edo= | ||
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From a temperament perspective, we can probably make the "best" use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping <1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to "Sephiroth" modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping <2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament). | From a temperament perspective, we can probably make the "best" use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping <1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to "Sephiroth" modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping <2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament). | ||
2.5.9 and 2.5.11 are both best-served by the 2\13 generator, corresponding to the 1st horagram above, having the (octave-equivalent) mappings of <2 1| (for 5 and 9) and <2 3| (for 5 and 11). This generator incidentally is also the most efficient at generating a full 2.5.9.11.13 pentad, which it achieves in the space of 5 generators via the octave-equivalent mapping <2 1 3 -2|. Being that this scale is the most well-supplied with the greatest number of target triads, we might want to consider it as a tonal basis for 13-EDO, analogous to the diatonic scale in 12-TET. We could, conveniently enough, use the 7-note MOS scale as a basis for 13-EDO notation, leading to a notation very much like 12-TET except for the insertion of an additional accidental between E and F, as in the above interval chart (in the 6L1s column). It can be thought of as a "circle of major 2nds" rather than a circle of 5ths. This allows us to create chord progressions that have a sort of lydian/wholetone flavor but in a way that sounds completely different from 12 edo. | 2.5.9 and 2.5.11 are both best-served by the 2\13 generator, corresponding to the 1st horagram above, having the (octave-equivalent) mappings of <2 1| (for 5 and 9) and <2 3| (for 5 and 11). This generator incidentally is also the most efficient at generating a full 2.5.9.11.13 pentad, which it achieves in the space of 5 generators via the octave-equivalent mapping <2 1 3 -2|. Being that this scale is the most well-supplied with the greatest number of target triads, we might want to consider it as a tonal basis for 13-EDO, analogous to the diatonic scale in 12-TET. We could, conveniently enough, use the 7-note MOS scale as a basis for 13-EDO notation, leading to a notation very much like 12-TET except for the insertion of an additional accidental between E and F, as in the above interval chart (in the 6L1s column). It can be thought of as a "circle of major 2nds" rather than a circle of 5ths. This allows us to create chord progressions that have a sort of lydian/wholetone flavor but in a way that sounds completely different from 12 edo. | ||
For the 2.9.21 subgroup, we can use the 5\13 generator, the closest thing 13-EDO has to a "perfect 4th", giving an octave-equivalent mapping of <3 1| and MOS scales corresponding to the 4th horagram above. The 8-note MOS scale of 5L3s, independently discovered by Easley Blackwood Jr, Paul Rapoport, and Erv Wilson (among others), is excellent for melody, being somewhat similar to the 12-TET diatonic scale but with an extra semitone added. It is also a conceivable basis for 13-EDO notation, using a modified "circle of fifths" (8\13, the octave inversion of 5\13) including an H: B#-G#-D#-A#-F#-C#-H-E-B-G-D-A-F-C-Hb-Eb-Bb-Gb-Db-Ab, which when arranged in order of ascending pitch within the octave gives the 5L3s names in the above interval chart. This notation has the advantage of preserving some familiar features: diatonic semitones still occur between B and C and E and F, and the dyads E-B, G-D, D-A, and F-C (and associated accidentals) sound approximately like "fifths". Also, the 5L3s scale on C somewhat approximates a 12-TET C major scale (if H is omitted). | For the 2.9.21 subgroup, we can use the 5\13 generator, the closest thing 13-EDO has to a "perfect 4th", giving an octave-equivalent mapping of <3 1| and MOS scales corresponding to the 4th horagram above. The 8-note MOS scale of 5L3s, independently discovered by Easley Blackwood Jr, Paul Rapoport, and Erv Wilson (among others), is excellent for melody, being somewhat similar to the 12-TET diatonic scale but with an extra semitone added. It is also a conceivable basis for 13-EDO notation, using a modified "circle of fifths" (8\13, the octave inversion of 5\13) including an H: B#-G#-D#-A#-F#-C#-H-E-B-G-D-A-F-C-Hb-Eb-Bb-Gb-Db-Ab, which when arranged in order of ascending pitch within the octave gives the 5L3s names in the above interval chart. This notation has the advantage of preserving some familiar features: diatonic semitones still occur between B and C and E and F, and the dyads E-B, G-D, D-A, and F-C (and associated accidentals) sound approximately like "fifths". Also, the 5L3s scale on C somewhat approximates a 12-TET C major scale (if H is omitted). | ||
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To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's "Dream Cycle" mythos. The 2\13-based heptatonic has been named "archeotonic" after the "Old Ones" that rule the Dreamlands, and the 5\13-based octatonic has been named "oneirotonic" after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper "The Case for Thirteen": | To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's "Dream Cycle" mythos. The 2\13-based heptatonic has been named "archeotonic" after the "Old Ones" that rule the Dreamlands, and the 5\13-based octatonic has been named "oneirotonic" after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper "The Case for Thirteen": | ||
[[image:Archeotonic.png]] | [[image:Archeotonic.png]] | ||
Listen to Ryonian on F#: [[media type="file" key="13 edo Ryo mode.wav"]] | Listen to Ryonian on F#: [[media type="file" key="13 edo Ryo mode.wav" width="300" height="50"]] | ||
[[image:Oneirotonic.png]] | [[image:Oneirotonic.png]] | ||
Listen to Dylathian on F#: [[media type="file" key="13 edo 8 tone mode 1.wav"]] | Listen to Dylathian on F#: [[media type="file" key="13 edo 8 tone mode 1.wav" width="300" height="50"]] | ||
=Mapping to Standard Keyboards= | =Mapping to Standard Keyboards= | ||
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Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | Contrary to popular belief, consonant harmony is possible in 13-EDO, but it requires a radically different approach than that used in 12-EDO (or other Pythagorean or Meantone-based tunings). Trying to approximate the usual major and minor triads of 12-EDO within 13-EDO is usually a disappointment if consonance is the goal; 0-3-7, 0-4-7, 0-3-8, and 0-4-8 are all rather rough in 13-EDO. Typically, the most consonant harmonies do not use a &quot;stack of 3rds&quot; the way they do in 12-TET, since the strongest dissonances in 13-EDO are near the middle of the octave (<u><a class="wiki_link" href="/13edo#top">degree</a>s</u> 6, 7, and 8). Instead, a stack of whole-tones, or a mixture of whole-tones and minor 3rds, often yields good results. For example, one way to view 13-EDO is as a subgroup temperament of harmonics 2.5.9.11.13. It actually performs quite admirably in this regard, and a chord of 0-4-15-19-22 (approximating 4:5:9:11:13) sounds very convincing. An even larger subgroup is the <a class="wiki_link" href="/k%2AN%20subgroups">2*13 subgroup</a> 2.9.5.21.11.13, on which 13 has the same tuning and commas as 26et.<br /> | ||
<br /> | <br /> | ||
The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite <u><a class="wiki_link" href="/13edo#top">close</a></u> to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad). <br /> | The 2.9.5.11.13 subgroup has commas 45/44, 65/64 and 81/80, leading to a linear temperament with POTE generator 185.728 cents, quite <u><a class="wiki_link" href="/13edo#top">close</a></u> to 2\13. Use this as a generator, and at 7 notes (6L1s) two full pentads are available (as well as two more 4:5:9:11 tetrad, and one 4:5:9:13 tetrad).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:8 -->Scales in 13edo</h1> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc2"><a name="Scales in 13edo"></a><!-- ws:end:WikiTextHeadingRule:8 -->Scales in 13edo</h1> | ||
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From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | From a temperament perspective, we can probably make the &quot;best&quot; use of 13-EDO as a 2.5.9.11.13.21 subgroup, but assuming our goal is to make reasonably-tonal, triad-based music, we might prefer to think in terms of subsets of this subgroup. The simplest and most accurately-tuned subsets are 2.5.9, 2.5.11, 2.5.13, 2.11.13, and 2.9.21, and for each of these, there is a corresponding MOS generator that is maximally-efficient at producing the desired triad. For 2.5.13, the simplest generator is 4\13, with an octave-equivalent mapping &lt;1 -1| (for 5 and 13), corresponding to the 3rd horagram above. This gives rise to &quot;Sephiroth&quot; modes, in which the generator is any flatly tempered 13th harmonic. For 2.11.13, the simplest generator is 3\13, with an octave-equivalent mapping &lt;2 3| (for 11 and 13). This corresponds to the 2nd horagram above. This scale bears a superficial resemblance to the 9-note MOS of Orwell temperament, although its approximations to the 3rd, 5th, and 7th harmonics are much more distant than in more optimal tunings of the temperament (on the other hand, its approximations to the 11th and 13th harmonics are much better than in optimal tunings of the temperament).<br /> | ||
<br /> | <br /> | ||
2.5.9 and 2.5.11 are both best-served by the 2\13 generator, corresponding to the 1st horagram above, having the (octave-equivalent) mappings of &lt;2 1| (for 5 and 9) and &lt;2 3| (for 5 and 11). This generator incidentally is also the most efficient at generating a full 2.5.9.11.13 pentad, which it achieves in the space of 5 generators via the octave-equivalent mapping &lt;2 1 3 -2|. Being that this scale is the most well-supplied with the greatest number of target triads, we might want to consider it as a tonal basis for 13-EDO, analogous to the diatonic scale in 12-TET. We could, conveniently enough, use the 7-note MOS scale as a basis for 13-EDO notation, leading to a notation very much like 12-TET except for the insertion of an additional accidental between E and F, as in the above interval chart (in the 6L1s column). It can be thought of as a &quot;circle of major 2nds&quot; rather than a circle of 5ths. This allows us to create chord progressions that have a sort of lydian/wholetone flavor but in a way that sounds completely different from 12 edo. <br /> | 2.5.9 and 2.5.11 are both best-served by the 2\13 generator, corresponding to the 1st horagram above, having the (octave-equivalent) mappings of &lt;2 1| (for 5 and 9) and &lt;2 3| (for 5 and 11). This generator incidentally is also the most efficient at generating a full 2.5.9.11.13 pentad, which it achieves in the space of 5 generators via the octave-equivalent mapping &lt;2 1 3 -2|. Being that this scale is the most well-supplied with the greatest number of target triads, we might want to consider it as a tonal basis for 13-EDO, analogous to the diatonic scale in 12-TET. We could, conveniently enough, use the 7-note MOS scale as a basis for 13-EDO notation, leading to a notation very much like 12-TET except for the insertion of an additional accidental between E and F, as in the above interval chart (in the 6L1s column). It can be thought of as a &quot;circle of major 2nds&quot; rather than a circle of 5ths. This allows us to create chord progressions that have a sort of lydian/wholetone flavor but in a way that sounds completely different from 12 edo.<br /> | ||
<br /> | <br /> | ||
For the 2.9.21 subgroup, we can use the 5\13 generator, the closest thing 13-EDO has to a &quot;perfect 4th&quot;, giving an octave-equivalent mapping of &lt;3 1| and MOS scales corresponding to the 4th horagram above. The 8-note MOS scale of 5L3s, independently discovered by Easley Blackwood Jr, Paul Rapoport, and Erv Wilson (among others), is excellent for melody, being somewhat similar to the 12-TET diatonic scale but with an extra semitone added. It is also a conceivable basis for 13-EDO notation, using a modified &quot;circle of fifths&quot; (8\13, the octave inversion of 5\13) including an H: B#-G#-D#-A#-F#-C#-H-E-B-G-D-A-F-C-Hb-Eb-Bb-Gb-Db-Ab, which when arranged in order of ascending pitch within the octave gives the 5L3s names in the above interval chart. This notation has the advantage of preserving some familiar features: diatonic semitones still occur between B and C and E and F, and the dyads E-B, G-D, D-A, and F-C (and associated accidentals) sound approximately like &quot;fifths&quot;. Also, the 5L3s scale on C somewhat approximates a 12-TET C major scale (if H is omitted).<br /> | For the 2.9.21 subgroup, we can use the 5\13 generator, the closest thing 13-EDO has to a &quot;perfect 4th&quot;, giving an octave-equivalent mapping of &lt;3 1| and MOS scales corresponding to the 4th horagram above. The 8-note MOS scale of 5L3s, independently discovered by Easley Blackwood Jr, Paul Rapoport, and Erv Wilson (among others), is excellent for melody, being somewhat similar to the 12-TET diatonic scale but with an extra semitone added. It is also a conceivable basis for 13-EDO notation, using a modified &quot;circle of fifths&quot; (8\13, the octave inversion of 5\13) including an H: B#-G#-D#-A#-F#-C#-H-E-B-G-D-A-F-C-Hb-Eb-Bb-Gb-Db-Ab, which when arranged in order of ascending pitch within the octave gives the 5L3s names in the above interval chart. This notation has the advantage of preserving some familiar features: diatonic semitones still occur between B and C and E and F, and the dyads E-B, G-D, D-A, and F-C (and associated accidentals) sound approximately like &quot;fifths&quot;. Also, the 5L3s scale on C somewhat approximates a 12-TET C major scale (if H is omitted).<br /> | ||
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To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | To facilitate discussion of these scales, Igliashon has ascribed them names based on H.P. Lovecraft's &quot;Dream Cycle&quot; mythos. The 2\13-based heptatonic has been named &quot;archeotonic&quot; after the &quot;Old Ones&quot; that rule the Dreamlands, and the 5\13-based octatonic has been named &quot;oneirotonic&quot; after the Dreamlands themselves. Modes of the archeotonic are named after the individual Old Ones themselves; modes of the oneirotonic are named after cities in the Dreamlands. See the charts of modes of the two scales below, excerpted from Igliashon's forthcoming paper &quot;The Case for Thirteen&quot;:<br /> | ||
<!-- ws:start:WikiTextLocalImageRule:775:&lt;img src=&quot;/file/view/Archeotonic.png/252639498/Archeotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" /><!-- ws:end:WikiTextLocalImageRule:775 --><br /> | <!-- ws:start:WikiTextLocalImageRule:775:&lt;img src=&quot;/file/view/Archeotonic.png/252639498/Archeotonic.png&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/Archeotonic.png/252639498/Archeotonic.png" alt="Archeotonic.png" title="Archeotonic.png" /><!-- ws:end:WikiTextLocalImageRule:775 --><br /> | ||
Listen to Ryonian on F#: <!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:2 --><br /> | Listen to Ryonian on F#: <!-- ws:start:WikiTextMediaRule:2:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%20Ryo%20mode.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo Ryo mode.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+Ryo+mode.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:2 --><br /> | ||
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Listen to Dylathian on F#: <!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | Listen to Dylathian on F#: <!-- ws:start:WikiTextMediaRule:3:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/13%20edo%208%20tone%20mode%201.wav?h=50&amp;w=300&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;13 edo 8 tone mode 1.wav&amp;quot; width=&amp;quot;300&amp;quot; height=&amp;quot;50&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;50&quot; width=&quot;300&quot;/&gt; --><embed type="audio/wav" style="cursor:hand; cursor:pointer;" src="http://xenharmonic.wikispaces.com/file/view/13+edo+8+tone+mode+1.wav" width="300" height="50" autoplay="false" target="myself" controller="true" loop="false" scale="aspect" bgcolor="#FFFFFF" pluginspage="http://www.apple.com/quicktime/download/"></embed><!-- ws:end:WikiTextMediaRule:3 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc6"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mapping to Standard Keyboards</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc6"><a name="Mapping to Standard Keyboards"></a><!-- ws:end:WikiTextHeadingRule:16 -->Mapping to Standard Keyboards</h1> | ||