16edo: Difference between revisions
Wikispaces>TallKite **Imported revision 599359330 - Original comment: ** |
Wikispaces>TallKite **Imported revision 599359354 - 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:TallKite|TallKite]] and made on <tt>2016-11-14 02: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-14 02:54:17 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>599359354</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 second approach is to preserve the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter: | The second approach is to preserve the __harmonic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always further fifthwards on the chain of fifths than the latter: | ||
||= D ||= | ||= ---D--- ||= -------- ||= ---E--- ||= --------- ||= --------- ||= ---F--- ||= --------- ||= ---G--- ||= --------- ||= ---A--- ||= --------- ||= ---B--- ||= --------- ||= --------- ||= ---C--- ||= --------- ||= ---D--- || | ||
|| D || Db/E# || E || Eb || F# || F || Fb/G# || G || Gb/A# || A || Ab/B# || B || Bb || C# || C || Cb/D# || D || | || D || Db/E# || E || Eb || F# || F || Fb/G# || G || Gb/A# || A || Ab/B# || B || Bb || C# || C || Cb/D# || D || | ||
||= P1 ||= d1/A2 ||= M2 ||= m2 ||= M3 ||= m3 ||= d3/A4 ||= P4 ||= d4/A5 ||= P5 ||= d5/A6 ||= M6 ||= m6 ||= M7 ||= m7 ||= d7/A8 ||= P8 || | ||= P1 ||= d1/A2 ||= M2 ||= m2 ||= M3 ||= m3 ||= d3/A4 ||= P4 ||= d4/A5 ||= P5 ||= d5/A6 ||= M6 ||= m6 ||= M7 ||= m7 ||= d7/A8 ||= P8 || | ||
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<!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc0"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:3 -->Images</h1> | <!-- ws:start:WikiTextHeadingRule:3:&lt;h1&gt; --><h1 id="toc0"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:3 -->Images</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:5:&lt;h1&gt; --><h1 id="toc1"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:5 -->Intervals</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:9 -->Hexadecaphonic Octave Theory</h1> | <!-- ws:start:WikiTextHeadingRule:9:&lt;h1&gt; --><h1 id="toc3"><a name="Hexadecaphonic Octave Theory"></a><!-- ws:end:WikiTextHeadingRule:9 -->Hexadecaphonic Octave Theory</h1> | ||
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Another interesting approach can include two interwoven <a class="wiki_link" href="/8edo">8-EDO</a> scales (narrow 12/11 neutral seconds). There are two major seventh intervals, a harmonic seventh at step 13\16, a 7/4 ratio approximation, sharp by 6.174 cents, followed by an undecimal 11/6 ratio or neutral seventh (which is mapped in 16's <strong>Mavila</strong> as a major seventh). If we take the 300-cent minor third as an approximation of the harmonic 19th (<a class="wiki_link" href="/19_16">19/16</a>, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad (pictured below).<br /> | Another interesting approach can include two interwoven <a class="wiki_link" href="/8edo">8-EDO</a> scales (narrow 12/11 neutral seconds). There are two major seventh intervals, a harmonic seventh at step 13\16, a 7/4 ratio approximation, sharp by 6.174 cents, followed by an undecimal 11/6 ratio or neutral seventh (which is mapped in 16's <strong>Mavila</strong> as a major seventh). If we take the 300-cent minor third as an approximation of the harmonic 19th (<a class="wiki_link" href="/19_16">19/16</a>, approximately 297.5 cents), that adds another overtone which can combine with the approximation of the harmonic seventh to form a 16:19:28 triad (pictured below).<br /> | ||
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The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &quot;narrow fifth&quot;. Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19.<br /> | The interval between the 28th &amp; 19th overtones, 28:19, measures approximately 671.3 cents, which is 3.7 cents away from 16edo's &quot;narrow fifth&quot;. Another voicing for this chord is 14:16:19, which features 19:14 as the outer interval (528.7 cents just, 525.0 cents in 16edo). A perhaps more consonant open voicing is 7:16:19.<br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">---D---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">---E---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">---F---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">---G---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">---A---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">---B---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">---C---<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">< | <td style="text-align: center;"><hr /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">---D---<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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16-EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.<br /> | 16-EDO notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. Armodue of Italy uses a 4-line staff for 16-EDO.<br /> | ||
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In 16-EDO diatonic scales are dissonant and &quot;shimmery&quot; because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. Scales like the Harmonic Minor scale in 16-EDO require 4 step sizes.<br /> | In 16-EDO diatonic scales are dissonant and &quot;shimmery&quot; because of the 25 cent raised superfourth in conjunction with the 25 cent subtracted fifth / poor 3/2 approximation. Scales like the Harmonic Minor scale in 16-EDO require 4 step sizes.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc5"><a name="Hexadecaphonic Notation-16 Tone Piano Layout Based on the Anti-diatonic Scale"></a><!-- ws:end:WikiTextHeadingRule:13 -->16 Tone Piano Layout Based on the Anti-diatonic Scale</h2> | <!-- ws:start:WikiTextHeadingRule:13:&lt;h2&gt; --><h2 id="toc5"><a name="Hexadecaphonic Notation-16 Tone Piano Layout Based on the Anti-diatonic Scale"></a><!-- ws:end:WikiTextHeadingRule:13 -->16 Tone Piano Layout Based on the Anti-diatonic Scale</h2> | ||
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This Layout places Mavila[7] on the white keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.<br /> | This Layout places Mavila[7] on the white keys and Mavila[9] on the white keys. As you can see, flats are higher than naturals and sharps are lower.<br /> | ||
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