18edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 00:10:06 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 00:35:14 UTC</tt>.

: The original revision id was <tt>~~602810378~~</tt>.

: The original revision id was <tt>602810468</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

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*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:~~

~~D * E * * * F * G * A * B * * * C * D~~

~~D - D^/Ev - E - E^ - E#/Fb - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - B#/Cb - Cv - C - C^/Dv - D~~

~~P1 - ^P1/vm2 - m2 - ~2 - mM2/m3 - ~3 - M3 - ^M3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vm6 - m6 - ~6 - M6/m7 - ~7 - M7 - ^M7/d8 - P8~~

~~The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:~~

~~D * E * * * F * G * A * B * * * C * D~~

=[[#Notation]]Notation=

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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~~

~~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^ ||

||= 1 ||= 67 ||= up unison, downminor 2nd ||= ^1, vm2 ||= D^, Ev ||= up unison, downmajor 2nd ||= ^1, vM2 ||= D^, Ev ||

||= 2 ||= 133 ||= minor 2nd ||= ||= ||= ~~aug unison,~~ major 2nd ||= ~~A1,~~ M2 ||= ~~D#,~~ E ||

||= 2 ||= 133 ||= minor 2nd ||= m2 ||= E ||= major 2nd ||= M2 ||= E ||

||= 3 ||= 200 ||= mid 2nd ||= ||= ||= mid 2nd ||= ~2 ||= E^ ||

||= 3 ||= 200 ||= mid 2nd ||= ~2 ||= E^ ||= mid 2nd ||= ~2 ||= E^ ||

||= 4 ||= 267 ||= major 2nd, minor 3rd ||= ||= ||= minor 2nd, major 3rd ||= m2, M3 ||= Eb, F# ||

||= 4 ||= 267 ||= major 2nd, minor 3rd ||= M2, m3 ||= E#, Fb ||= minor 2nd, major 3rd ||= m2, M3 ||= Eb, F# ||

||= 5 ||= 333 ||= mid 3rd ||= ||= ||= mid 3rd ||= ~3 ||= Fv ||

||= 5 ||= 333 ||= mid 3rd ||= ~3 ||= Fv ||= mid 3rd ||= ~3 ||= Fv ||

||= 6 ||= 400 ||= major 3rd ||= ||= ||= minor 3rd ||= m3 ||= F ||

||= 6 ||= 400 ||= major 3rd ||= M3 ||= F ||= minor 3rd ||= m3 ||= F ||

||= 7 ||= 467 ||= upmajor 3rd, down 4th ||= ||= ||= upminor 3rd, down 4th ||= ^m3, v4 ||= F^, Gv ||

||= 7 ||= 467 ||= upmajor 3rd, down 4th ||= ^M3, v4 ||= F^, Gv ||= upminor 3rd, down 4th ||= ^m3, v4 ||= F^, Gv ||

||= 8 ||= 533 ||= perfect 4th ||= ||= G ||= perfect 4th ||= P4 ||= G ||

||= 8 ||= 533 ||= perfect 4th ||= P4 ||= G ||= perfect 4th ||= P4 ||= G ||

||= 9 ||= 600 ||= up 4th, down 5th ||= ||= ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||

||= 9 ||= 600 ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||

||= 10 ||= 667 ||= perfect 5th ||= ||= A ||= perfect 5th ||= P5 ||= A ||

||= 10 ||= 667 ||= perfect 5th ||= P5 ||= A ||= perfect 5th ||= P5 ||= A ||

||= 11 ||= 733 ||= up 5th ||= ||= ||= up fifth, downmajor 6th ||= ^5, vM6 ||= A^, vB ||

||= 11 ||= 733 ||= up 5th ||= ^5, vm6 ||= A^, Bv ||= up fifth, downmajor 6th ||= ^5, vM6 ||= A^, Bv ||

||= 12 ||= 800 ||= minor 6th ||= ||= ||= major 6th ||= M6 ||= B ||

||= 12 ||= 800 ||= minor 6th ||= m6 ||= B ||= major 6th ||= M6 ||= B ||

||= 13 ||= 867 ||= mid 6th ||= ||= ||= mid 6th ||= ~6 ||= Bv ||

||= 13 ||= 867 ||= mid 6th ||= ~6 ||= B^ ||= mid 6th ||= ~6 ||= B^ ||

||= 14 ||= 933 ||= major 6th, minor 7th ||= ||= ||= minor 6th, major 7th ||= m6, M7 ||= Bb, C# ||

||= 14 ||= 933 ||= major 6th, minor 7th ||= M6, m7 ||= B#, Cb ||= minor 6th, major 7th ||= m6, M7 ||= Bb, C# ||

||= 15 ||= 1000 ||= mid 7th ||= ||= ||= mid 7th ||= ~7 ||= Cv ||

||= 15 ||= 1000 ||= mid 7th ||= ~7 ||= Cv ||= mid 7th ||= ~7 ||= Cv ||

||= 16 ||= 1067 ||= major 7th ||= ||= ||= minor 7th~~, dim 8ve~~ ||= m7, d8 ||= C~~, Db~~ ||

||= 16 ||= 1067 ||= major 7th ||= M7 ||= C ||= minor 7th ||= m7, d8 ||= C ||

||= 17 ||= 1133 ||= down 8ve ||= ||= ||= down 8ve ||= v8 ||= Dv ||

||= 17 ||= 1133 ||= upmajor 7th, down 8ve ||= ^M7, v8 ||= C^, Dv ||= upminor 7th, down 8ve ||= ^m7, v8 ||= C^, Dv ||

||= 18 ||= 1200 ||= perfect 8ve ||= ||= ||= perfect 8ve ||= P8 ||= D ||

||= 18 ||= 1200 ||= perfect 8ve ||= P8 ||= D ||= perfect 8ve ||= P8 ||= D ||

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*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: ~~

~~D * E * * * F * G * A * B * * * C * D ~~

~~D - D^/Ev - E - E^ - E#/Fb - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - B#/Cb - Cv - C - C^/Dv - D ~~

~~P1 - ^P1/vm2 - m2 - ~2 - mM2/m3 - ~3 - M3 - ^M3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vm6 - m6 - ~6 - M6/m7 - ~7 - M7 - ^M7/d8 - P8 ~~

~~ ~~

~~The second way is with sharp lower than flat, to preserve interval arithmetic and chord names: ~~

~~D * E * * * F * G * A * B * * * C * D ~~

<h1 id="toc2"><a name="Notation"></a><a name="Notation"></a>Notation</h1>

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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 &quot;on the fly&quot;.

~~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 - ^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 ~~

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<td style="text-align: center;">67

</td>

<td style="text-align: center;">up unison

<td style="text-align: center;">up unison, downminor 2nd

</td>

<td style="text-align: center;">^1

<td style="text-align: center;">^1, vm2

</td>

<td style="text-align: center;">D^, Ev

</td>

<td style="text-align: center;">up unison

<td style="text-align: center;">up unison, downmajor 2nd

</td>

<td style="text-align: center;">^1

<td style="text-align: center;">^1, vM2

</td>

<td style="text-align: center;">D^

<td style="text-align: center;">D^, Ev

</td>

</tr>

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<td style="text-align: center;">minor 2nd

</td>

<td style="text-align: center;">m2

</td>

<td style="text-align: center;">E

</td>

<td style="text-align: center;">~~aug unison,~~ major 2nd

<td style="text-align: center;">major 2nd

</td>

<td style="text-align: center;">~~A1,~~ M2

<td style="text-align: center;">M2

</td>

<td style="text-align: center;">~~D#,~~ E

<td style="text-align: center;">E

</td>

</tr>

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<td style="text-align: center;">mid 2nd

</td>

<td style="text-align: center;">~2

</td>

<td style="text-align: center;">E^

</td>

<td style="text-align: center;">mid 2nd

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<td style="text-align: center;">major 2nd, minor 3rd

</td>

<td style="text-align: center;">M2, m3

</td>

<td style="text-align: center;">E#, Fb

</td>

<td style="text-align: center;">minor 2nd, major 3rd

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<td style="text-align: center;">mid 3rd

</td>

<td style="text-align: center;">~3

</td>

<td style="text-align: center;">Fv

</td>

<td style="text-align: center;">mid 3rd

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<td style="text-align: center;">major 3rd

</td>

<td style="text-align: center;">M3

</td>

<td style="text-align: center;">F

</td>

<td style="text-align: center;">minor 3rd

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<td style="text-align: center;">upmajor 3rd, down 4th

</td>

<td style="text-align: center;">^M3, v4

</td>

<td style="text-align: center;">F^, Gv

</td>

<td style="text-align: center;">upminor 3rd, down 4th

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<td style="text-align: center;">perfect 4th

</td>

<td style="text-align: center;">P4

</td>

<td style="text-align: center;">G

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<td style="text-align: center;">up 4th, down 5th

</td>

<td style="text-align: center;">^4, v5

</td>

<td style="text-align: center;">G^, Av

</td>

<td style="text-align: center;">up 4th, down 5th

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<td style="text-align: center;">perfect 5th

</td>

<td style="text-align: center;">P5

</td>

<td style="text-align: center;">A

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<td style="text-align: center;">up 5th

</td>

<td style="text-align: center;">^5, vm6

</td>

<td style="text-align: center;">A^, Bv

</td>

<td style="text-align: center;">up fifth, downmajor 6th

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<td style="text-align: center;">^5, vM6

</td>

<td style="text-align: center;">A^, vB

<td style="text-align: center;">A^, Bv

</td>

</tr>

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<td style="text-align: center;">minor 6th

</td>

<td style="text-align: center;">m6

</td>

<td style="text-align: center;">B

</td>

<td style="text-align: center;">major 6th

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<td style="text-align: center;">mid 6th

</td>

<td style="text-align: center;">~6

</td>

<td style="text-align: center;">B^

</td>

<td style="text-align: center;">mid 6th

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<td style="text-align: center;">~6

</td>

<td style="text-align: center;">Bv

<td style="text-align: center;">B^

</td>

</tr>

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<td style="text-align: center;">major 6th, minor 7th

</td>

<td style="text-align: center;">M6, m7

</td>

<td style="text-align: center;">B#, Cb

</td>

<td style="text-align: center;">minor 6th, major 7th

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<td style="text-align: center;">mid 7th

</td>

<td style="text-align: center;">~7

</td>

<td style="text-align: center;">Cv

</td>

<td style="text-align: center;">mid 7th

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<td style="text-align: center;">major 7th

</td>

<td style="text-align: center;">M7

</td>

<td style="text-align: center;">C

</td>

<td style="text-align: center;">minor 7th~~, dim 8ve~~

<td style="text-align: center;">minor 7th

</td>

<td style="text-align: center;">m7, d8

</td>

<td style="text-align: center;">C~~, Db~~

<td style="text-align: center;">C

</td>

</tr>

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<td style="text-align: center;">1133

</td>

<td style="text-align: center;">down 8ve

<td style="text-align: center;">upmajor 7th, down 8ve

</td>

<td style="text-align: center;">^M7, v8

</td>

<td style="text-align: center;">C^, Dv

</td>

<td style="text-align: center;">down 8ve

<td style="text-align: center;">upminor 7th, down 8ve

</td>

<td style="text-align: center;">v8

<td style="text-align: center;">^m7, v8

</td>

<td style="text-align: center;">Dv

<td style="text-align: center;">C^, Dv

</td>

</tr>

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<td style="text-align: center;">perfect 8ve

</td>

<td style="text-align: center;">P8

</td>

<td style="text-align: center;">D

</td>

<td style="text-align: center;">perfect 8ve

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</table>

~~ ~~

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2016-12-26 00:10:06 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-26 00:35:14 UTC</tt>.<br>
-: The original revision id was <tt>602810378</tt>.<br>
+: The original revision id was <tt>602810468</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>
@@ Line 56: / Line 56: @@
 *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:
-D * E * * * F * G * A * B * * * C * D
-D - D^/Ev - E - E^ - E#/Fb - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - B#/Cb - Cv - C - C^/Dv - D
-P1 - ^P1/vm2 - m2 - ~2 - mM2/m3 - ~3 - M3 - ^M3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vm6 - m6 - ~6 - M6/m7 - ~7 - M7 - ^M7/d8 - P8
-The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:
-D * E * * * F * G * A * B * * * C * D
 =[[#Notation]]Notation=
@@ Line 70: / Line 63: @@
 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
-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^ ||
+||= 1 ||= 67 ||= up unison, downminor 2nd ||= ^1, vm2 ||= D^, Ev ||= up unison, downmajor 2nd ||= ^1, vM2 ||= D^, Ev ||
-||= 2 ||= 133 ||= minor 2nd ||=   ||=   ||= aug unison, major 2nd ||= A1, M2 ||= D#, E ||
+||= 2 ||= 133 ||= minor 2nd ||= m2 ||= E ||= major 2nd ||= M2 ||= E ||
-||= 3 ||= 200 ||= mid 2nd ||=   ||=   ||= mid 2nd ||= ~2 ||= E^ ||
+||= 3 ||= 200 ||= mid 2nd ||= ~2 ||= E^ ||= mid 2nd ||= ~2 ||= E^ ||
-||= 4 ||= 267 ||= major 2nd, minor 3rd ||=   ||=   ||= minor 2nd, major 3rd ||= m2, M3 ||= Eb, F# ||
+||= 4 ||= 267 ||= major 2nd, minor 3rd ||= M2, m3 ||= E#, Fb ||= minor 2nd, major 3rd ||= m2, M3 ||= Eb, F# ||
-||= 5 ||= 333 ||= mid 3rd ||=   ||=   ||= mid 3rd ||= ~3 ||= Fv ||
+||= 5 ||= 333 ||= mid 3rd ||= ~3 ||= Fv ||= mid 3rd ||= ~3 ||= Fv ||
-||= 6 ||= 400 ||= major 3rd ||=   ||=   ||= minor 3rd ||= m3 ||= F ||
+||= 6 ||= 400 ||= major 3rd ||= M3 ||= F ||= minor 3rd ||= m3 ||= F ||
-||= 7 ||= 467 ||= upmajor 3rd, down 4th ||=   ||=   ||= upminor 3rd, down 4th ||= ^m3, v4 ||= F^, Gv ||
+||= 7 ||= 467 ||= upmajor 3rd, down 4th ||= ^M3, v4 ||= F^, Gv ||= upminor 3rd, down 4th ||= ^m3, v4 ||= F^, Gv ||
-||= 8 ||= 533 ||= perfect 4th ||=   ||= G ||= perfect 4th ||= P4 ||= G ||
+||= 8 ||= 533 ||= perfect 4th ||= P4 ||= G ||= perfect 4th ||= P4 ||= G ||
-||= 9 ||= 600 ||= up 4th, down 5th ||=   ||=   ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||
+||= 9 ||= 600 ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||= up 4th, down 5th ||= ^4, v5 ||= G^, Av ||
-||= 10 ||= 667 ||= perfect 5th ||=   ||= A ||= perfect 5th ||= P5 ||= A ||
+||= 10 ||= 667 ||= perfect 5th ||= P5 ||= A ||= perfect 5th ||= P5 ||= A ||
-||= 11 ||= 733 ||= up 5th ||=   ||=   ||= up fifth, downmajor 6th ||= ^5, vM6 ||= A^, vB ||
+||= 11 ||= 733 ||= up 5th ||= ^5, vm6 ||= A^, Bv ||= up fifth, downmajor 6th ||= ^5, vM6 ||= A^, Bv ||
-||= 12 ||= 800 ||= minor 6th ||=   ||=   ||= major 6th ||= M6 ||= B ||
+||= 12 ||= 800 ||= minor 6th ||= m6 ||= B ||= major 6th ||= M6 ||= B ||
-||= 13 ||= 867 ||= mid 6th ||=   ||=   ||= mid 6th ||= ~6 ||= Bv ||
+||= 13 ||= 867 ||= mid 6th ||= ~6 ||= B^ ||= mid 6th ||= ~6 ||= B^ ||
-||= 14 ||= 933 ||= major 6th, minor 7th ||=   ||=   ||= minor 6th, major 7th ||= m6, M7 ||= Bb, C# ||
+||= 14 ||= 933 ||= major 6th, minor 7th ||= M6, m7 ||= B#, Cb ||= minor 6th, major 7th ||= m6, M7 ||= Bb, C# ||
-||= 15 ||= 1000 ||= mid 7th ||=   ||=   ||= mid 7th ||= ~7 ||= Cv ||
+||= 15 ||= 1000 ||= mid 7th ||= ~7 ||= Cv ||= mid 7th ||= ~7 ||= Cv ||
-||= 16 ||= 1067 ||= major 7th ||=   ||=   ||= minor 7th, dim 8ve ||= m7, d8 ||= C, Db ||
+||= 16 ||= 1067 ||= major 7th ||= M7 ||= C ||= minor 7th ||= m7, d8 ||= C ||
-||= 17 ||= 1133 ||= down 8ve ||=   ||=   ||= down 8ve ||= v8 ||= Dv ||
+||= 17 ||= 1133 ||= upmajor 7th, down 8ve ||= ^M7, v8 ||= C^, Dv ||= upminor 7th, down 8ve ||= ^m7, v8 ||= C^, Dv ||
-||= 18 ||= 1200 ||= perfect 8ve ||=   ||=   ||= perfect 8ve ||= P8 ||= D ||
+||= 18 ||= 1200 ||= perfect 8ve ||= P8 ||= D ||= perfect 8ve ||= P8 ||= D ||
@@ Line 580: / Line 568: @@
 *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament&lt;br /&gt;
 &lt;br /&gt;
-Like 16edo, 18b-edo can be notated two ways. The first is with sharp higher than flat, to preserve melodic contour:&lt;br /&gt;
-D * E * * * F * G * A * B * * * C * D&lt;br /&gt;
-D - D^/Ev - E - E^ - E#/Fb - Fv - F - F^/Gv - G - G^/Av - A - A^/Bv - B - B^ - B#/Cb - Cv - C - C^/Dv - D&lt;br /&gt;
-P1 - ^P1/vm2 - m2 - ~2 - mM2/m3 - ~3 - M3 - ^M3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vm6 - m6 - ~6 - M6/m7 - ~7 - M7 - ^M7/d8 - P8&lt;br /&gt;
-&lt;br /&gt;
-The second way is with sharp lower than flat, to preserve interval arithmetic and chord names:&lt;br /&gt;
-D * E * * * F * G * A * B * * * C * D&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;!-- ws:start:WikiTextAnchorRule:38:&amp;lt;img src=&amp;quot;/i/anchor.gif&amp;quot; class=&amp;quot;WikiAnchor&amp;quot; alt=&amp;quot;Anchor&amp;quot; id=&amp;quot;wikitext@@anchor@@Notation&amp;quot; title=&amp;quot;Anchor: Notation&amp;quot;/&amp;gt; --&gt;&lt;a name="Notation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextAnchorRule:38 --&gt;Notation&lt;/h1&gt;
@@ Line 594: / Line 575: @@
 The second approach preserves the &lt;u&gt;harmonic&lt;/u&gt; 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 &amp;quot;on the fly&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
-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&lt;br /&gt;
-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&lt;br /&gt;
@@ Line 634: / Line 613: @@
          &lt;td style="text-align: center;"&gt;67&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up unison, downminor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^1, vm2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^, Ev&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;up unison, downmajor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^1, vM2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D^, Ev&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 654: / Line 633: @@
          &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;aug unison, major 2nd&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A1, M2&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;D#, E&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 672: / Line 651: @@
          &lt;td style="text-align: center;"&gt;mid 2nd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mid 2nd&lt;br /&gt;
@@ Line 690: / Line 669: @@
          &lt;td style="text-align: center;"&gt;major 2nd, minor 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M2, m3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;E#, Fb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;minor 2nd, major 3rd&lt;br /&gt;
@@ Line 708: / Line 687: @@
          &lt;td style="text-align: center;"&gt;mid 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Fv&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mid 3rd&lt;br /&gt;
@@ Line 726: / Line 705: @@
          &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
@@ Line 744: / Line 723: @@
          &lt;td style="text-align: center;"&gt;upmajor 3rd, down 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M3, v4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;F^, Gv&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;upminor 3rd, down 4th&lt;br /&gt;
@@ Line 762: / Line 741: @@
          &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
@@ Line 780: / Line 759: @@
          &lt;td style="text-align: center;"&gt;up 4th, down 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^4, v5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G^, Av&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up 4th, down 5th&lt;br /&gt;
@@ Line 798: / Line 777: @@
          &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
@@ Line 816: / Line 795: @@
          &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^5, vm6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^, Bv&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;up fifth, downmajor 6th&lt;br /&gt;
@@ Line 824: / Line 803: @@
          &lt;td style="text-align: center;"&gt;^5, vM6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;A^, vB&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A^, Bv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 834: / Line 813: @@
          &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
@@ Line 852: / Line 831: @@
          &lt;td style="text-align: center;"&gt;mid 6th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mid 6th&lt;br /&gt;
@@ Line 860: / Line 839: @@
          &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 870: / Line 849: @@
          &lt;td style="text-align: center;"&gt;major 6th, minor 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M6, m7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;B#, Cb&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;minor 6th, major 7th&lt;br /&gt;
@@ Line 888: / Line 867: @@
          &lt;td style="text-align: center;"&gt;mid 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;mid 7th&lt;br /&gt;
@@ Line 906: / Line 885: @@
          &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;minor 7th, dim 8ve&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m7, d8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;C, Db&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 922: / Line 901: @@
          &lt;td style="text-align: center;"&gt;1133&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upmajor 7th, down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^M7, v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^, Dv&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;upminor 7th, down 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;^m7, v8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;C^, Dv&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 942: / Line 921: @@
          &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
@@ Line 955: / Line 934: @@
 &lt;/table&gt;
-&lt;br /&gt;
-&lt;br /&gt;
-&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;