16edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602808596 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602808826 - 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>2016-12-25 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-25 20:08:25 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602808826</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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=Intervals= | =Intervals= | ||
16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5. | |||
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. Sharp is lower in pitch than flat, major is narrower than minor, etc. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 16edo "on the fly". | |||
|| Degree || Cents ||= Approximate | || Degree || Cents ||= Approximate | ||
Ratios* || Interval Names | Ratios* || Interval | ||
Just || Interval Names | Names | ||
Simplified || Interval names | Just ||= Interval | ||
Names | |||
than minor || Interval names, | Simplified ||||= Interval names, | ||
major wider | |||
than minor ||||= Interval names, | |||
major narrower | major narrower | ||
than minor || | than minor || | ||
|| 0 || 0 ||= 1/1 || Unison || | || 0 || 0 ||= 1/1 || Unison ||= unison ||= unison ||= D ||= unison ||= D || | ||
|| 1 || 75 ||= 28/27, 27/26 || Subminor 2nd || | || 1 || 75 ||= 28/27, 27/26 || Subminor 2nd ||= min 2nd ||= aug 1, dim 2nd ||= D#, Eb ||= dim 1, aug 2nd ||= Db, E# || | ||
|| 2 || 150 ||= 12/11, 35/32 || Neutral 2nd || | || 2 || 150 ||= 12/11, 35/32 || Neutral 2nd ||= maj 2nd ||= min 2nd ||= E ||= maj 2nd ||= E || | ||
|| 3 || 225 ||= 8/7 || Supermajor 2nd, | || 3 || 225 ||= 8/7 || Supermajor 2nd, | ||
Septimal Whole-Tone || | Septimal Whole-Tone ||= perf 2nd ||= maj 2nd ||= E# ||= min 2nd ||= Eb || | ||
|| 4 || 300 ||= 19/16, 32/27 || Minor 3rd || | || 4 || 300 ||= 19/16, 32/27 || Minor 3rd ||= min 3rd ||= min 3rd ||= Fb ||= maj 3rd ||= F# || | ||
|| 5 || 375 ||= 5/4, 26/21 || Major 3rd || | || 5 || 375 ||= 5/4, 26/21 || Major 3rd ||= maj 3rd ||= maj 3rd ||= F ||= min 3rd ||= F || | ||
|| 6 || 450 ||= 13/10, 35/27 || Sub-4th, | || 6 || 450 ||= 13/10, 35/27 || Sub-4th, | ||
Supermajor 3rd || | Supermajor 3rd ||= min 4th ||= aug 3rd, dim 4th ||= F#, Gb ||= dim 3rd, aug 4th ||= Fb, G# || | ||
|| 7 || 525 ||= 27/20, 52/35, 256/189 || Wide 4th || | || 7 || 525 ||= 27/20, 52/35, 256/189 || Wide 4th ||= maj 4th ||= perf 4th ||= G ||= perf 4th ||= G || | ||
|| 8 || 600 ||= 7/5, 10/7 || Tritone || | || 8 || 600 ||= 7/5, 10/7 || Tritone ||= aug 4th, | ||
dim 5th ||= aug 4th, dim 5th ||= G#, Ab ||= dim 4th, aug 5th ||= Gb, A# || | |||
|| 9 || 675 ||= 40/27, 35/26, 189/128 || Narrow 5th || | || 9 || 675 ||= 40/27, 35/26, 189/128 || Narrow 5th ||= min 5th ||= perf 5th ||= A ||= perf 5th ||= A || | ||
|| 10 || 750 ||= 20/13, 54/35 || Super-5th, | || 10 || 750 ||= 20/13, 54/35 || Super-5th, | ||
Subminor 6th || | Subminor 6th ||= maj 5th ||= aug 5th, dim 6th ||= A#, Bb ||= dim 5th, aug 6th ||= Ab, B# || | ||
|| 11 || 825 ||= 8/5, 21/13 || Minor 6th || | || 11 || 825 ||= 8/5, 21/13 || Minor 6th ||= min 6th ||= min 6th ||= B ||= maj 6th ||= B || | ||
|| 12 || 900 ||= 27/16, 32/19 || Major 6th || | || 12 || 900 ||= 27/16, 32/19 || Major 6th ||= maj 6th ||= maj 6th ||= B# ||= min 6th ||= Bb || | ||
|| 13 || 975 ||= 7/4 || Subminor 7th, | || 13 || 975 ||= 7/4 || Subminor 7th, | ||
Septimal Minor 7th || | Septimal Minor 7th ||= perf 7th ||= min 7th ||= Cb ||= maj 7th ||= C# || | ||
|| 14 || 1050 ||= 11/6, 64/35 || Neutral 7th || | || 14 || 1050 ||= 11/6, 64/35 || Neutral 7th ||= min 7th ||= maj 7th ||= C ||= min 7th ||= C || | ||
|| 15 || 1125 ||= 27/14, 52/27 || Supermajor 7th || | || 15 || 1125 ||= 27/14, 52/27 || Supermajor 7th ||= maj 7th ||= aug 7th, dim 8ve ||= C# ||= dim 7th, aug 8ve ||= D# || | ||
|| 16 || 1200 ||= 2/1 || | || 16 || 1200 ||= 2/1 || octave ||= octave ||= 8ve ||= D ||= 8ve ||= D || | ||
*based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible. | *based on treating 16-EDO as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible. | ||
| Line 97: | Line 104: | ||
=Hexadecaphonic Notation= | =Hexadecaphonic Notation= | ||
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. | 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. | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextLocalImageRule: | <!-- ws:start:WikiTextLocalImageRule:909:&lt;img src=&quot;/file/view/16edo%20wheel%2001.png/516947132/325x325/16edo%20wheel%2001.png&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 325px; width: 325px;&quot; /&gt; --><img src="/file/view/16edo%20wheel%2001.png/516947132/325x325/16edo%20wheel%2001.png" alt="16edo wheel 01.png" title="16edo wheel 01.png" style="height: 325px; width: 325px;" /><!-- ws:end:WikiTextLocalImageRule:909 --><br /> | ||
<br /> | <br /> | ||
<!-- 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> | ||
<br /> | |||
16edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that the former is always higher pitched than the latter. The disadvantage to this approach is that conventional interval arithmetic no longer works. e.g. M2 + M2 isn't M3, and D + M2 isn't E. Chord names are different because C - E - G isn't P1 - M3 - P5.<br /> | |||
<br /> | |||
The second approach is to preserve the <u>harmonic</u> 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. Sharp is lower in pitch than flat, major is narrower than minor, etc. While this approach may seem bizarre at first, interval arithmetic and chord names work as usual. Furthermore, conventional 12edo music can be directly translated to 16edo &quot;on the fly&quot;.<br /> | |||
<br /> | |||
<table class="wiki_table"> | <table class="wiki_table"> | ||
| Line 276: | Line 258: | ||
Ratios*<br /> | Ratios*<br /> | ||
</td> | </td> | ||
<td>Interval Names<br /> | <td>Interval <br /> | ||
Names<br /> | |||
Just<br /> | Just<br /> | ||
</td> | </td> | ||
<td>Interval Names<br /> | <td style="text-align: center;">Interval<br /> | ||
Names<br /> | |||
Simplified<br /> | Simplified<br /> | ||
</td> | </td> | ||
<td>Interval names<br /> | <td colspan="2" style="text-align: center;">Interval names,<br /> | ||
major wider <br /> | |||
than minor<br /> | than minor<br /> | ||
</td> | </td> | ||
<td>Interval names,<br /> | <td colspan="2" style="text-align: center;">Interval names, <br /> | ||
major narrower<br /> | major narrower<br /> | ||
than minor<br /> | than minor<br /> | ||
| Line 300: | Line 284: | ||
<td>Unison<br /> | <td>Unison<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">unison<br /> | ||
</td> | |||
<td style="text-align: center;">unison<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | </td> | ||
<td>unison<br /> | <td style="text-align: center;">unison<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 316: | Line 304: | ||
<td>Subminor 2nd<br /> | <td>Subminor 2nd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 2nd<br /> | ||
</td> | |||
<td style="text-align: center;">aug 1, dim 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">D#, Eb<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">dim 1, aug 2nd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Db, E#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 332: | Line 324: | ||
<td>Neutral 2nd<br /> | <td>Neutral 2nd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 2nd<br /> | ||
</td> | </td> | ||
<td>min 2nd<br /> | <td style="text-align: center;">min 2nd<br /> | ||
</td> | </td> | ||
<td>maj 2nd<br /> | <td style="text-align: center;">E<br /> | ||
</td> | |||
<td style="text-align: center;">maj 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">E<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 349: | Line 345: | ||
Septimal Whole-Tone<br /> | Septimal Whole-Tone<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">perf 2nd<br /> | ||
</td> | </td> | ||
<td>maj 2nd<br /> | <td style="text-align: center;">maj 2nd<br /> | ||
</td> | </td> | ||
<td>min 2nd<br /> | <td style="text-align: center;">E#<br /> | ||
</td> | |||
<td style="text-align: center;">min 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">Eb<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 365: | Line 365: | ||
<td>Minor 3rd<br /> | <td>Minor 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">min 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">Fb<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">F#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 381: | Line 385: | ||
<td>Major 3rd<br /> | <td>Major 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 3rd<br /> | ||
</td> | |||
<td style="text-align: center;">maj 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">F<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">F<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 398: | Line 406: | ||
Supermajor 3rd<br /> | Supermajor 3rd<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 4th<br /> | ||
</td> | </td> | ||
<td>aug 3rd, dim 4th<br /> | <td style="text-align: center;">aug 3rd, dim 4th<br /> | ||
</td> | </td> | ||
<td>dim 3rd, aug 4th<br /> | <td style="text-align: center;">F#, Gb<br /> | ||
</td> | |||
<td style="text-align: center;">dim 3rd, aug 4th<br /> | |||
</td> | |||
<td style="text-align: center;">Fb, G#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 414: | Line 426: | ||
<td>Wide 4th<br /> | <td>Wide 4th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 4th<br /> | ||
</td> | |||
<td style="text-align: center;">perf 4th<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | </td> | ||
<td>perf 4th<br /> | <td style="text-align: center;">perf 4th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">G<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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<td>Tritone<br /> | <td>Tritone<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">aug 4th,<br /> | ||
dim 5th<br /> | |||
</td> | |||
<td style="text-align: center;">aug 4th, dim 5th<br /> | |||
</td> | |||
<td style="text-align: center;">G#, Ab<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">dim 4th, aug 5th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Gb, A#<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 447: | Line 467: | ||
<td>Narrow 5th<br /> | <td>Narrow 5th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 5th<br /> | ||
</td> | |||
<td style="text-align: center;">perf 5th<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">A<br /> | ||
</td> | </td> | ||
<td>perf 5th<br /> | <td style="text-align: center;">perf 5th<br /> | ||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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Subminor 6th<br /> | Subminor 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 5th<br /> | ||
</td> | </td> | ||
<td>aug 5th, dim 6th<br /> | <td style="text-align: center;">aug 5th, dim 6th<br /> | ||
</td> | </td> | ||
<td>dim 5th, aug 6th<br /> | <td style="text-align: center;">A#, Bb<br /> | ||
</td> | |||
<td style="text-align: center;">dim 5th, aug 6th<br /> | |||
</td> | |||
<td style="text-align: center;">Ab, B#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 480: | Line 508: | ||
<td>Minor 6th<br /> | <td>Minor 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 6th<br /> | ||
</td> | |||
<td style="text-align: center;">min 6th<br /> | |||
</td> | |||
<td style="text-align: center;">B<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">B<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 496: | Line 528: | ||
<td>Major 6th<br /> | <td>Major 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 6th<br /> | ||
</td> | |||
<td style="text-align: center;">maj 6th<br /> | |||
</td> | |||
<td style="text-align: center;">B#<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 6th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">Bb<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 513: | Line 549: | ||
Septimal Minor 7th<br /> | Septimal Minor 7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">perf 7th<br /> | ||
</td> | </td> | ||
<td>min 7th<br /> | <td style="text-align: center;">min 7th<br /> | ||
</td> | </td> | ||
<td>maj 7th<br /> | <td style="text-align: center;">Cb<br /> | ||
</td> | |||
<td style="text-align: center;">maj 7th<br /> | |||
</td> | |||
<td style="text-align: center;">C#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 529: | Line 569: | ||
<td>Neutral 7th<br /> | <td>Neutral 7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">min 7th<br /> | ||
</td> | </td> | ||
<td>maj 7th<br /> | <td style="text-align: center;">maj 7th<br /> | ||
</td> | </td> | ||
<td>min 7th<br /> | <td style="text-align: center;">C<br /> | ||
</td> | |||
<td style="text-align: center;">min 7th<br /> | |||
</td> | |||
<td style="text-align: center;">C<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 545: | Line 589: | ||
<td>Supermajor 7th<br /> | <td>Supermajor 7th<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">maj 7th<br /> | ||
</td> | |||
<td style="text-align: center;">aug 7th, dim 8ve<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">C#<br /> | ||
</td> | </td> | ||
<td>dim 7th, aug 8ve<br /> | <td style="text-align: center;">dim 7th, aug 8ve<br /> | ||
</td> | |||
<td style="text-align: center;">D#<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 559: | Line 607: | ||
<td style="text-align: center;">2/1<br /> | <td style="text-align: center;">2/1<br /> | ||
</td> | </td> | ||
<td> | <td>octave<br /> | ||
</td> | |||
<td style="text-align: center;">octave<br /> | |||
</td> | |||
<td style="text-align: center;">8ve<br /> | |||
</td> | </td> | ||
<td> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
<td>8ve<br /> | <td style="text-align: center;">8ve<br /> | ||
</td> | </td> | ||
<td> | <td style="text-align: center;">D<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
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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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<!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Hexadecaphonic Notation"></a><!-- ws:end:WikiTextHeadingRule:11 -->Hexadecaphonic Notation</h1> | <!-- ws:start:WikiTextHeadingRule:11:&lt;h1&gt; --><h1 id="toc4"><a name="Hexadecaphonic Notation"></a><!-- ws:end:WikiTextHeadingRule:11 -->Hexadecaphonic Notation</h1> | ||
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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 black 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 black 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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