18edo: Difference between revisions
Wikispaces>TallKite **Imported revision 602738708 - Original comment: ** |
Wikispaces>TallKite **Imported revision 602810378 - 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- | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 00:10:06 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>602810378</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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augmented 4th ||= m3, A4 || 5/4 or 44/35 || +13.686 +3.822 ||< 64/55 || | augmented 4th ||= m3, A4 || 5/4 or 44/35 || +13.686 +3.822 ||< 64/55 || | ||
|| 7 || 466.67 ||= F ||= Fv ||= upminor 3rd, | || 7 || 466.67 ||= F ||= Fv ||= upminor 3rd, | ||
down-fourth ||= ^m3, vP4 || 21/16 || -4.114 | down-fourth ||= ^m3, vP4 || 21/16 || -4.114 ||< 21/16 || | ||
|| 8 || 533.33 ||= Gb ||= F ||= fourth ||= P4 || 15/11 || -3.617 ||< 102/75 || | || 8 || 533.33 ||= Gb ||= F ||= fourth ||= P4 || 15/11 || -3.617 ||< 102/75 || | ||
|| 9 || 600 ||= F# ||= F^, Gv ||= upfourth, | || 9 || 600 ||= F# ||= F^, Gv ||= upfourth, | ||
| Line 57: | Line 55: | ||
|| 18 || 1200 ||= C ||= C ||= octave ||= P8 || 2/1 || 0 ||< 2/1** || | || 18 || 1200 ||= C ||= C ||= octave ||= P8 || 2/1 || 0 ||< 2/1** || | ||
*based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament | *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament | ||
Like 16edo, 18b-edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour: | Like 16edo, 18b-edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour: | ||
| Line 67: | Line 63: | ||
The second way is with sharp lower than flat, to preserve interval arithmetic and chord names: | The second way is with sharp lower than flat, to preserve interval arithmetic and chord names: | ||
D * E * * * F * G * A * B * * * C * D | D * E * * * F * G * A * B * * * C * D | ||
=[[#Notation]]Notation= | |||
18edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4¢ worse that the best approximation. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the __melodic__ meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. 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 preserves 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, and major/aug is narrower than minor/dim. 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 18edo "on the fly". | |||
D - D^/Ev - E - E^ - Eb/F# - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - Bb/C# - Cv - C - C^/Dv - D | D - D^/Ev - E - E^ - Eb/F# - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - Bb/C# - Cv - C - C^/Dv - D | ||
P1 - ^ | P1 - ^1/vM2 - M2 - ~2 - m2/M3 - ~3 - m3 - ^m3/v4 - P4 - ^4/vP5 - P5 - ^5/vM6 - M6 - ~6 - m6/M7 - ~7 - m7 - ^m7/d8 - P8 | ||
||= Degree ||= Cents ||||||= [[xenharmonic/Ups and Downs Notation|Up/down notation]] using the narrow 5th of 10\18, | |||
with major wider than minor ||||||= Up/down notation using the narrow 5th of 10\18, | |||
with major wider than minor || | |||
||= 0 ||= 0 ||= perfect unison ||= P1 ||= D ||= perfect unison ||= P1 ||= D || | |||
||= 1 ||= 67 ||= up unison ||= ^1 ||= ||= up unison ||= ^1 ||= D^ || | |||
||= 2 ||= 133 ||= minor 2nd ||= ||= ||= aug unison, major 2nd ||= A1, M2 ||= D#, E || | |||
||= 3 ||= 200 ||= mid 2nd ||= ||= ||= mid 2nd ||= ~2 ||= E^ || | |||
||= 4 ||= 267 ||= major 2nd, minor 3rd ||= ||= ||= minor 2nd, major 3rd ||= m2, M3 ||= Eb, F# || | |||
||= 5 ||= 333 ||= mid 3rd ||= ||= ||= mid 3rd ||= ~3 ||= Fv || | |||
||= 6 ||= 400 ||= major 3rd ||= ||= ||= minor 3rd ||= m3 ||= F || | |||
||= 7 ||= 467 ||= upmajor 3rd, down 4th ||= ||= ||= upminor 3rd, down 4th ||= ^m3, v4 ||= F^, Gv || | |||
||= 8 ||= 533 ||= perfect 4th ||= ||= G ||= perfect 4th ||= P4 ||= G || | |||
||= 9 ||= 600 ||= up 4th, down 5th ||= ||= ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av || | |||
||= 10 ||= 667 ||= perfect 5th ||= ||= A ||= perfect 5th ||= P5 ||= A || | |||
||= 11 ||= 733 ||= up 5th ||= ||= ||= up fifth, downmajor 6th ||= ^5, vM6 ||= A^, vB || | |||
||= 12 ||= 800 ||= minor 6th ||= ||= ||= major 6th ||= M6 ||= B || | |||
||= 13 ||= 867 ||= mid 6th ||= ||= ||= mid 6th ||= ~6 ||= Bv || | |||
||= 14 ||= 933 ||= major 6th, minor 7th ||= ||= ||= minor 6th, major 7th ||= m6, M7 ||= Bb, C# || | |||
||= 15 ||= 1000 ||= mid 7th ||= ||= ||= mid 7th ||= ~7 ||= Cv || | |||
||= 16 ||= 1067 ||= major 7th ||= ||= ||= minor 7th, dim 8ve ||= m7, d8 ||= C, Db || | |||
||= 17 ||= 1133 ||= down 8ve ||= ||= ||= down 8ve ||= v8 ||= Dv || | |||
||= 18 ||= 1200 ||= perfect 8ve ||= ||= ||= perfect 8ve ||= P8 ||= D || | |||
For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] (pentatonic, octotonic and nonatonic fifth-generated) and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]] (heptatonic third-generated). | |||
For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs|Ups and Downs Notation -"Superflat" EDOs]] and [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]]. | For alternative notations, see [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs|Ups and Downs Notation -"Superflat" EDOs]] and [[xenharmonic/Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs|Ups and Downs Notation -"Supersharp" EDOs]] and [[xenharmonic/Ups and Downs Notation#Natural%20Generators|Ups and Downs Notation - Natural Generators]]. | ||
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* [[https://soundcloud.com/tomprice719/composition-of-june-2015|Composition of June 2015 by TomPrice719]]</pre></div> | * [[https://soundcloud.com/tomprice719/composition-of-june-2015|Composition of June 2015 by TomPrice719]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>18edo</title></head><body><!-- ws:start:WikiTextTocRule: | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>18edo</title></head><body><!-- ws:start:WikiTextTocRule:24:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:24 --><!-- ws:start:WikiTextTocRule:25: --><a href="#Basic Properties">Basic Properties</a><!-- ws:end:WikiTextTocRule:25 --><!-- ws:start:WikiTextTocRule:26: --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --> | <a href="#Notation">Notation</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --> | <a href="#Commas">Commas</a><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:37 --><hr /> | ||
<span style="display: block; text-align: right;"><a class="wiki_link" href="/18%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | <span style="display: block; text-align: right;"><a class="wiki_link" href="/18%E5%B9%B3%E5%9D%87%E5%BE%8B">日本語</a><br /> | ||
</span><br /> | </span><br /> | ||
| Line 316: | Line 347: | ||
</td> | </td> | ||
<td>-4.114<br /> | <td>-4.114<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">21/16<br /> | <td style="text-align: left;">21/16<br /> | ||
| Line 551: | Line 580: | ||
*based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament<br /> | *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament<br /> | ||
<br /> | <br /> | ||
Like 16edo, 18b-edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:<br /> | Like 16edo, 18b-edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:<br /> | ||
D * E * * * F * G * A * B * * * C * D<br /> | D * E * * * F * G * A * B * * * C * D<br /> | ||
| Line 559: | Line 587: | ||
The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:<br /> | The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:<br /> | ||
D * E * * * F * G * A * B * * * C * D<br /> | D * E * * * F * G * A * B * * * C * D<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:4 --><!-- ws:start:WikiTextAnchorRule:38:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@Notation&quot; title=&quot;Anchor: Notation&quot;/&gt; --><a name="Notation"></a><!-- ws:end:WikiTextAnchorRule:38 -->Notation</h1> | |||
<br /> | |||
18edo can also be notated with ups and downs. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4¢ worse that the best approximation. Using this 5th allows conventional notation to be used, including the staff, note names, relative notation, etc. There are two ways to do this. The first way preserves the <u>melodic</u> meaning of sharp/flat, major/minor and aug/dim, in that sharp is higher pitched than flat, and major/aug is wider than minor/dim. 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 preserves 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, and major/aug is narrower than minor/dim. 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 18edo &quot;on the fly&quot;.<br /> | |||
<br /> | |||
D - D^/Ev - E - E^ - Eb/F# - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - Bb/C# - Cv - C - C^/Dv - D<br /> | D - D^/Ev - E - E^ - Eb/F# - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - Bb/C# - Cv - C - C^/Dv - D<br /> | ||
P1 - ^ | P1 - ^1/vM2 - M2 - ~2 - m2/M3 - ~3 - m3 - ^m3/v4 - P4 - ^4/vP5 - P5 - ^5/vM6 - M6 - ~6 - m6/M7 - ~7 - m7 - ^m7/d8 - P8<br /> | ||
<table class="wiki_table"> | |||
<tr> | |||
<td style="text-align: center;">Degree<br /> | |||
</td> | |||
<td style="text-align: center;">Cents<br /> | |||
</td> | |||
<td colspan="3" style="text-align: center;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation">Up/down notation</a> using the narrow 5th of 10\18,<br /> | |||
with major wider than minor<br /> | |||
</td> | |||
<td colspan="3" style="text-align: center;">Up/down notation using the narrow 5th of 10\18,<br /> | |||
with major wider than minor<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">0<br /> | |||
</td> | |||
<td style="text-align: center;">0<br /> | |||
</td> | |||
<td style="text-align: center;">perfect unison<br /> | |||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
<td style="text-align: center;">perfect unison<br /> | |||
</td> | |||
<td style="text-align: center;">P1<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">1<br /> | |||
</td> | |||
<td style="text-align: center;">67<br /> | |||
</td> | |||
<td style="text-align: center;">up unison<br /> | |||
</td> | |||
<td style="text-align: center;">^1<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">up unison<br /> | |||
</td> | |||
<td style="text-align: center;">^1<br /> | |||
</td> | |||
<td style="text-align: center;">D^<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">2<br /> | |||
</td> | |||
<td style="text-align: center;">133<br /> | |||
</td> | |||
<td style="text-align: center;">minor 2nd<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">aug unison, major 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">A1, M2<br /> | |||
</td> | |||
<td style="text-align: center;">D#, E<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">3<br /> | |||
</td> | |||
<td style="text-align: center;">200<br /> | |||
</td> | |||
<td style="text-align: center;">mid 2nd<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">mid 2nd<br /> | |||
</td> | |||
<td style="text-align: center;">~2<br /> | |||
</td> | |||
<td style="text-align: center;">E^<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">4<br /> | |||
</td> | |||
<td style="text-align: center;">267<br /> | |||
</td> | |||
<td style="text-align: center;">major 2nd, minor 3rd<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">minor 2nd, major 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">m2, M3<br /> | |||
</td> | |||
<td style="text-align: center;">Eb, F#<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">5<br /> | |||
</td> | |||
<td style="text-align: center;">333<br /> | |||
</td> | |||
<td style="text-align: center;">mid 3rd<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">mid 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">~3<br /> | |||
</td> | |||
<td style="text-align: center;">Fv<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">6<br /> | |||
</td> | |||
<td style="text-align: center;">400<br /> | |||
</td> | |||
<td style="text-align: center;">major 3rd<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">minor 3rd<br /> | |||
</td> | |||
<td style="text-align: center;">m3<br /> | |||
</td> | |||
<td style="text-align: center;">F<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">7<br /> | |||
</td> | |||
<td style="text-align: center;">467<br /> | |||
</td> | |||
<td style="text-align: center;">upmajor 3rd, down 4th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">upminor 3rd, down 4th<br /> | |||
</td> | |||
<td style="text-align: center;">^m3, v4<br /> | |||
</td> | |||
<td style="text-align: center;">F^, Gv<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">8<br /> | |||
</td> | |||
<td style="text-align: center;">533<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 4th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 4th<br /> | |||
</td> | |||
<td style="text-align: center;">P4<br /> | |||
</td> | |||
<td style="text-align: center;">G<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">9<br /> | |||
</td> | |||
<td style="text-align: center;">600<br /> | |||
</td> | |||
<td style="text-align: center;">up 4th, down 5th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">up 4th, down 5th<br /> | |||
</td> | |||
<td style="text-align: center;">^4, v5<br /> | |||
</td> | |||
<td style="text-align: center;">G^, Av<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">10<br /> | |||
</td> | |||
<td style="text-align: center;">667<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 5th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 5th<br /> | |||
</td> | |||
<td style="text-align: center;">P5<br /> | |||
</td> | |||
<td style="text-align: center;">A<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">11<br /> | |||
</td> | |||
<td style="text-align: center;">733<br /> | |||
</td> | |||
<td style="text-align: center;">up 5th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">up fifth, downmajor 6th<br /> | |||
</td> | |||
<td style="text-align: center;">^5, vM6<br /> | |||
</td> | |||
<td style="text-align: center;">A^, vB<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">12<br /> | |||
</td> | |||
<td style="text-align: center;">800<br /> | |||
</td> | |||
<td style="text-align: center;">minor 6th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">major 6th<br /> | |||
</td> | |||
<td style="text-align: center;">M6<br /> | |||
</td> | |||
<td style="text-align: center;">B<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">13<br /> | |||
</td> | |||
<td style="text-align: center;">867<br /> | |||
</td> | |||
<td style="text-align: center;">mid 6th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">mid 6th<br /> | |||
</td> | |||
<td style="text-align: center;">~6<br /> | |||
</td> | |||
<td style="text-align: center;">Bv<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">14<br /> | |||
</td> | |||
<td style="text-align: center;">933<br /> | |||
</td> | |||
<td style="text-align: center;">major 6th, minor 7th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">minor 6th, major 7th<br /> | |||
</td> | |||
<td style="text-align: center;">m6, M7<br /> | |||
</td> | |||
<td style="text-align: center;">Bb, C#<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">15<br /> | |||
</td> | |||
<td style="text-align: center;">1000<br /> | |||
</td> | |||
<td style="text-align: center;">mid 7th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">mid 7th<br /> | |||
</td> | |||
<td style="text-align: center;">~7<br /> | |||
</td> | |||
<td style="text-align: center;">Cv<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">16<br /> | |||
</td> | |||
<td style="text-align: center;">1067<br /> | |||
</td> | |||
<td style="text-align: center;">major 7th<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">minor 7th, dim 8ve<br /> | |||
</td> | |||
<td style="text-align: center;">m7, d8<br /> | |||
</td> | |||
<td style="text-align: center;">C, Db<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">17<br /> | |||
</td> | |||
<td style="text-align: center;">1133<br /> | |||
</td> | |||
<td style="text-align: center;">down 8ve<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">down 8ve<br /> | |||
</td> | |||
<td style="text-align: center;">v8<br /> | |||
</td> | |||
<td style="text-align: center;">Dv<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td style="text-align: center;">18<br /> | |||
</td> | |||
<td style="text-align: center;">1200<br /> | |||
</td> | |||
<td style="text-align: center;">perfect 8ve<br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;"><br /> | |||
</td> | |||
<td style="text-align: center;">perfect 8ve<br /> | |||
</td> | |||
<td style="text-align: center;">P8<br /> | |||
</td> | |||
<td style="text-align: center;">D<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<br /> | |||
<br /> | |||
<br /> | |||
For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> (pentatonic, octotonic and nonatonic fifth-generated) and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a> (heptatonic third-generated).<br /> | |||
<br /> | <br /> | ||
For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs">Ups and Downs Notation -&quot;Superflat&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a>.<br /> | For alternative notations, see <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs">Ups and Downs Notation -&quot;Superflat&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs">Ups and Downs Notation -&quot;Supersharp&quot; EDOs</a> and <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators">Ups and Downs Notation - Natural Generators</a>.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Notation-Useful Moment-of-Symmetry Scales"></a><!-- ws:end:WikiTextHeadingRule:6 --><span style="font-size: 1.3em;">Useful Moment-of-Symmetry Scales</span></h2> | ||
Note: This list excludes scales found in 9-EDO.<br /> | Note: This list excludes scales found in 9-EDO.<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Notation-Useful Moment-of-Symmetry Scales-Pentatonic:"></a><!-- ws:end:WikiTextHeadingRule:8 --><span style="font-size: 1.1em;">Pentatonic:</span></h3> | ||
3L2s Father Pentatonic: 4 4 3 4 3<br /> | 3L2s Father Pentatonic: 4 4 3 4 3<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Notation-Useful Moment-of-Symmetry Scales-Hexatonic:"></a><!-- ws:end:WikiTextHeadingRule:10 --><span style="font-size: 1.1em;">Hexatonic:</span></h3> | ||
4L2s Bicycle: 4 4 1 4 4 1<br /> | 4L2s Bicycle: 4 4 1 4 4 1<br /> | ||
2L4s Rice Hexatonic: 2 5 2 2 5 2<br /> | 2L4s Rice Hexatonic: 2 5 2 2 5 2<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Notation-Useful Moment-of-Symmetry Scales-Heptatonic:"></a><!-- ws:end:WikiTextHeadingRule:12 --><span style="font-size: 1.1em;">Heptatonic:</span></h3> | ||
4L3s Amity/Mish Heptatonic: 3 2 3 2 3 3 2<br /> | 4L3s Amity/Mish Heptatonic: 3 2 3 2 3 3 2<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="Notation-Useful Moment-of-Symmetry Scales-Octatonic:"></a><!-- ws:end:WikiTextHeadingRule:14 --><span style="font-size: 1.1em;">Octatonic:</span></h3> | ||
5L3s Father Octatonic: 3 1 3 3 1 3 3 1<br /> | 5L3s Father Octatonic: 3 1 3 3 1 3 3 1<br /> | ||
2L6s Rice Octatonic: 2 2 3 2 2 2 3 2<br /> | 2L6s Rice Octatonic: 2 2 3 2 2 2 3 2<br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h3&gt; --><h3 id="toc8"><a name="Notation-Useful Moment-of-Symmetry Scales-Decatonic:"></a><!-- ws:end:WikiTextHeadingRule:16 --><span style="font-size: 1.1em;">Decatonic:</span></h3> | ||
8L2s Biggie Decatonic: 2 2 1 2 2 2 2 1 2 2<br /> | 8L2s Biggie Decatonic: 2 2 1 2 2 2 2 1 2 2<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Notation-Application to Guitar"></a><!-- ws:end:WikiTextHeadingRule:18 --><span style="font-size: 1.3em;">Application to Guitar</span></h2> | ||
18-EDO is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you!<br /> | 18-EDO is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you!<br /> | ||
<br /> | <br /> | ||
The &quot;Father Octatonic&quot; scale maps very simply to a 6-string guitar tuned in &quot;reverse-standard&quot; tuning (tune using four 466.667¢ intervals, with one 533.333¢ interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand).<br /> | The &quot;Father Octatonic&quot; scale maps very simply to a 6-string guitar tuned in &quot;reverse-standard&quot; tuning (tune using four 466.667¢ intervals, with one 533.333¢ interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h1&gt; --><h1 id="toc10"><a name="Commas"></a><!-- ws:end:WikiTextHeadingRule:20 -->Commas</h1> | ||
18 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; 18 29 42 51 62 67 |.)<br /> | 18 EDO <a class="wiki_link" href="/tempering%20out">tempers out</a> the following <a class="wiki_link" href="/comma">comma</a>s. (Note: This assumes the <a class="wiki_link" href="/val">val</a> &lt; 18 29 42 51 62 67 |.)<br /> | ||
| Line 772: | Line 1,172: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:22 -->Music</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/18ETPrelude.mp3" rel="nofollow">18ETPrelude</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3" rel="nofollow">Prelude in 18et</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=3" rel="nofollow" target="_blank">composer notes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3" rel="nofollow">Flippertronics</a> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil (in 9 and 18 edo simultaneously)</a></li><li><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DoAndroidsDreamof18ED2.mp3.mp3" rel="nofollow">Do Androids Dream Of 18ED2?</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/fb0306486b51c270607f90a0c795d531-202.html" rel="nofollow">blog entry</a>)</li><li><a class="wiki_link_ext" href="https://soundcloud.com/tomprice719/composition-of-june-2015" rel="nofollow">Composition of June 2015 by TomPrice719</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://www.h-pi.com/mp3/18ETPrelude.mp3" rel="nofollow">18ETPrelude</a> by <a class="wiki_link" href="/Aaron%20Andrew%20Hunt">Aaron Andrew Hunt</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3" rel="nofollow">Prelude in 18et</a> by <a class="wiki_link_ext" href="http://www.chrisvaisvil.com" rel="nofollow" target="_blank">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=3" rel="nofollow" target="_blank">composer notes</a></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3" rel="nofollow">Flippertronics</a> by Chris Vaisvil</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3" rel="nofollow">Gerbils at the Wheel of Government</a> by <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=1402" rel="nofollow" target="_blank">Chris Vaisvil (in 9 and 18 edo simultaneously)</a></li><li><a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DoAndroidsDreamof18ED2.mp3.mp3" rel="nofollow">Do Androids Dream Of 18ED2?</a> by <a class="wiki_link" href="/Carlo%20Serafini">Carlo Serafini</a> (<a class="wiki_link_ext" href="http://www.seraph.it/blog_files/fb0306486b51c270607f90a0c795d531-202.html" rel="nofollow">blog entry</a>)</li><li><a class="wiki_link_ext" href="https://soundcloud.com/tomprice719/composition-of-june-2015" rel="nofollow">Composition of June 2015 by TomPrice719</a></li></ul></body></html></pre></div> | ||