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>2016-11-21 04:30:30 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 06:37:16 UTC</tt>.

: The original revision id was <tt>~~599948016~~</tt>.

: The original revision id was <tt>599957202</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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==Representations of Just Intervals==

|| Degree || Cents

coarse/fine

DMS ||= 5L3s Notation ||||= [[Ups and Downs Notation|up/down ]]

DMS ||= 5L3s Notation ||||||= [[Ups and Downs Notation|up/down ]][[Ups and Downs Notation|notation]]

[[Ups and Downs Notation|notation]] ** || Nearest Ratio || Error (cents

based on 18b-edo, with

sharp lower than flat || Nearest Ratio || Error (cents

coarse/fine)

(DMS) ||< 17-Limit Ratios* ||

|| 0 || 0 ||= **C** ||= C ||= P1 || 1/1 || 0 ||< **1/1** ||

|| 0 || 0 ||= C ||= C || unison ||= P1 || 1/1 || 0 ||< 1/1 ||

|| 1 || 66.667

80

20° ||= Db ||= C^,

Dv ||= ^P1,

Dv || up-unison,

downmajor 2nd ||= ^P1,

vM2 || 27/26 || +1.329

+1.595

Line 39:

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|| 2 || 133.333

160

40° ||= C# ||= D ||= M2 || 27/25 || +0.096

40° ||= C# ||= D || major 2nd ||= M2 || 27/25 || +0.096

+0.115

+1'43" ||< 51/55, 42/39 ||

|| 3 || 200

240

60° ||= **D** ||= D^,

60° ||= D ||= D^,

Ev ||= ~2 || 9/8 || -3.910

Ev || mid 2nd ||= ~2 || 9/8 || -3.910

-4.692

-1°10'23" ||< **9/8** ||

-1°10'23" ||< 9/8 ||

|| 4 || 266.667

320

80° ||= Eb ||= E ||= m2,

80° ||= Eb ||= E || minor 2nd,

major 3rd ||= m2,

M3 || 7/6 || -0.204

-0.245

-1"50" ||< **75/64** ||

-1"50" ||< 75/64 ||

|| 5 || 333.333

400

100° ||= D# ||= E^ ||= ~3 || 17/14 or 40/33 || -2.796 +0.293

100° ||= D# ||= E^ || mid 3rd ||= ~3 || 17/14 or 40/33 || -2.796 +0.293

-3.355 +0.351

-50'20" +5'16" ||< **39/32** ||

-50'20" +5'16" ||< 39/32 ||

|| 6 || 400

480

120° ||= **E** ||= Eb,

120° ||= E ||= Eb,

F# ||= m3,

F# || minor 3rd,

augmented 4th ||= m3,

A4 || 5/4 or 44/35 || +13.686 +3.822

+16.4235 +4.586

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|| 7 || 466.667

560

140° ||= **F** ||= Fv ||= ^m3,

140° ||= F ||= Fv || upminor 3rd,

down-fourth ||= ^m3,

vP4 || 21/16 || -4.114

-4.937

-1°14'3" ||< **21/16** ||

-1°14'3" ||< 21/16 ||

|| 8 || 533.333

640

160° ||= Gb ||= F ||= P4 || 15/11 || -3.617

160° ||= Gb ||= F || fourth ||= P4 || 15/11 || -3.617

-4.341

-1°5'7" ||< 102/75 ||

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720

180° ||= F# ||= F^,

Gv ||= ^P4,

Gv || upfourth,

downfifth ||= ^P4,

vP5 || 17/12 or 24/17 || -3.000 +3.000

-3.6005 +3.6005

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|| 10 || 666.667

800

200° ||= **G** ||= G ||= P5 || 22/15 || +3.617

200° ||= G ||= G || fifthj ||= P5 || 22/15 || +3.617

+4.341

+1°5'7" ||< 75/51 ||

|| 11 || 733.333

880

220° ||= Hb ||= G^ ||= ^P5,

220° ||= Hb ||= G^ || upfifth,

downmajor 6th ||= ^P5,

vM6 || 32/21 || +4.114

+4.937

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|| 12 || 800

960

240° ||= G# ||= A ||= d5,

240° ||= G# ||= A || diminished 5th,

major 6th ||= d5,

M6 || 8/5 or 35/22 || -13.686 -3.822

-16.4235 -4.586

-4°6'21" -1°8'47" ||< **51/32** ||

-4°6'21" -1°8'47" ||< 51/32 ||

|| 13 || 866.667

1040

260° ||= **H** ||= A^,

260° ||= H ||= A^,

Bv ||= ~6 || 28/17 or 33/20 || +2.796 -0.293

Bv || mid 6th ||= ~6 || 28/17 or 33/20 || +2.796 -0.293

+3.355 -0.351

+50'20" -5'16" ||< 64/39 ||

|| 14 || 933.333

1120

280° ||= **A** ||= B ||= m6,

280° ||= A ||= B || minor 6th,

major 7th ||= m6,

M7 || 12/7 || +0.204

+0.245

+1"50" ||< **55/32** ||

+1"50" ||< 55/32 ||

|| 15 || 1000

1200

300° ||= Bb ||= B^ ||= ~7 || 16/9 || +3.910

300° ||= Bb ||= B^ || mid 7th ||= ~7 || 16/9 || +3.910

+4.692

+1°10'23" ||< 16/9 ||

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1280

320° ||= A# ||= Bb,

C# ||= m7 || 50/27 || -0.096

C# || minor 7th ||= m7 || 50/27 || -0.096

-0.115

-1'43" ||< 39/21 ||

|| 17 || 1133.333

1360

340° ||= **B** ||= Cv ||= ^m7,

340° ||= B ||= Cv || upminor 7th,

down-octave ||= ^m7,

vP8 || 52/27 || -1.329

-1.595

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|| 18 || 1200

1440

360° ||= **C** ||= C ||= P8 || 2/1 || 0 ||< **2/1** ||

360° ||= 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 18b-edo with sharp lower than flat and major narrower than minor

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

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/vM2 - M2 - ~2 - m2/M3 - ~3 - m3 - ^m3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vM6 - M6 - ~6 - m6/M7 - ~7 - m7 - ^m7/d8 - P8

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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<td>Degree

</td>

<td>Cents

<td>Cents

coarse/fine

DMS

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<td style="text-align: center;">5L3s Notation

</td>

<td colspan="2" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down </a>~~ ~~

<td colspan="3" style="text-align: center;"><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">up/down </a><a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a>

<a class="wiki_link" href="/Ups%20and%20Downs%20Notation">notation</a> <~~strong~~>

based on 18b-edo, with

sharp lower than flat

</td>

<td>Nearest Ratio

</td>

<td>Error (cents

<td>Error (cents

coarse/fine)

(DMS)

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<td>0

</td>

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

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

</td>

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

</td>

<td>unison

</td>

<td style="text-align: center;">P1

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Line 264:

<td>0

</td>

<td style="text-align: left;"~~></strong~~>1/1~~~~

<td style="text-align: left;">1/1

</td>

</tr>

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

Dv

</td>

<td>up-unison,

downmajor 2nd

</td>

<td style="text-align: center;">^P1,

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Line 304:

</td>

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

</td>

<td>major 2nd

</td>

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

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Line 325:

60°

</td>

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

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

</td>

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

Ev

</td>

<td>mid 2nd

</td>

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

Line 310:

Line 340:

-1°10'23&quot;

</td>

<td style="text-align: left;"~~></strong~~>9/8~~~~

<td style="text-align: left;">9/8

</td>

</tr>

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Line 353:

</td>

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

</td>

<td>minor 2nd,

major 3rd

</td>

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

Line 333:

Line 366:

-1&quot;50&quot;

</td>

<td style="text-align: left;"~~></strong~~>75/64~~~~

<td style="text-align: left;">75/64

</td>

</tr>

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Line 379:

</td>

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

</td>

<td>mid 3rd

</td>

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

Line 355:

Line 390:

-50'20&quot; +5'16&quot;

</td>

<td style="text-align: left;"~~></strong~~>39/32~~~~

<td style="text-align: left;">39/32

</td>

</tr>

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Line 400:

120°

</td>

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

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

</td>

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

F#

</td>

<td>minor 3rd,

augmented 4th

</td>

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

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Line 427:

140°

</td>

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

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

</td>

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

</td>

<td>upminor 3rd,

down-fourth

</td>

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

Line 402:

Line 443:

-1°14'3&quot;

</td>

<td style="text-align: left;"~~></strong~~>21/16~~~~

<td style="text-align: left;">21/16

</td>

</tr>

Line 415:

Line 456:

</td>

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

</td>

<td>fourth

</td>

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

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Line 481:

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

Gv

</td>

<td>upfourth,

downfifth

</td>

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

Line 458:

Line 504:

200°

</td>

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

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

</td>

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

</td>

<td>fifthj

</td>

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

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Line 531:

</td>

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

</td>

<td>upfifth,

downmajor 6th

</td>

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

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Line 557:

</td>

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

</td>

<td>diminished 5th,

major 6th

</td>

<td style="text-align: center;">d5,

Line 516:

Line 570:

-4°6'21&quot; -1°8'47&quot;

</td>

<td style="text-align: left;"~~></strong~~>51/32~~~~

<td style="text-align: left;">51/32

</td>

</tr>

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Line 580:

260°

</td>

<td style="text-align: center;"~~></strong~~>H~~~~

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

</td>

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

Bv

</td>

<td>mid 6th

</td>

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

Line 549:

Line 605:

280°

</td>

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

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

</td>

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

</td>

<td>minor 6th,

major 7th

</td>

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

Line 562:

Line 621:

+1&quot;50&quot;

</td>

<td style="text-align: left;"~~></strong~~>55/32~~~~

<td style="text-align: left;">55/32

</td>

</tr>

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Line 634:

</td>

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

</td>

<td>mid 7th

</td>

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

Line 598:

Line 659:

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

C#

</td>

<td>minor 7th

</td>

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

Line 617:

Line 680:

340°

</td>

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

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

</td>

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

</td>

<td>upminor 7th,

down-octave

</td>

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

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Line 706:

360°

</td>

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

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

</td>

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

</td>

<td>octave

</td>

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

Line 650:

Line 718:

<td>0

</td>

<td style="text-align: left;"~~></strong~~>2/1**

<td style="text-align: left;">2/1**

</td>

</tr>

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<ul><ul><li>based on 18b-edo with sharp lower than flat and major narrower than minor</li></ul></ul>

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

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/vM2 - M2 - ~2 - m2/M3 - ~3 - m3 - ^m3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vM6 - M6 - ~6 - m6/M7 - ~7 - m7 - ^m7/d8 - P8

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>.

@@ 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>2016-11-21 04:30:30 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-21 06:37:16 UTC</tt>.<br>
-: The original revision id was <tt>599948016</tt>.<br>
+: The original revision id was <tt>599957202</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 23: / Line 23: @@
 ==Representations of Just Intervals==
 || Degree || Cents
 coarse/fine
-DMS ||= 5L3s Notation ||||= [[Ups and Downs Notation|up/down ]]
+DMS ||= 5L3s Notation ||||||= [[Ups and Downs Notation|up/down ]][[Ups and Downs Notation|notation]]
-[[Ups and Downs Notation|notation]] ** || Nearest Ratio || Error (cents
+based on 18b-edo, with
+sharp lower than flat || Nearest Ratio || Error (cents
 coarse/fine)
 (DMS) ||&lt; 17-Limit Ratios* ||
-|| 0 || 0 ||= **C** ||= C ||= P1 || 1/1 || 0 ||&lt; **1/1** ||
+|| 0 || 0 ||= C ||= C || unison ||= P1 || 1/1 || 0 ||&lt; 1/1 ||
 || 1 || 66.667
 ° ||= Db ||= C^,
-Dv ||= ^P1,
+Dv || up-unison,
+downmajor 2nd ||= ^P1,
 vM2 || 27/26 || +1.329
 +1.595
@@ Line 39: / Line 41: @@
 || 2 || 133.333
-° ||= C# ||= D ||= M2 || 27/25 || +0.096
+° ||= C# ||= D || major 2nd ||= M2 || 27/25 || +0.096
 +0.115
 +1'43" ||&lt; 51/55, 42/39 ||
 || 3 || 200
-° ||= **D** ||= D^,
+° ||= D ||= D^,
-Ev ||= ~2 || 9/8 || -3.910
+Ev || mid 2nd ||= ~2 || 9/8 || -3.910
 -4.692
--1°10'23" ||&lt; **9/8** ||
+-1°10'23" ||&lt; 9/8 ||
 || 4 || 266.667
-° ||= Eb ||= E ||= m2,
+° ||= Eb ||= E || minor 2nd,
+major 3rd ||= m2,
 M3 || 7/6 || -0.204
 -0.245
--1"50" ||&lt; **75/64** ||
+-1"50" ||&lt; 75/64 ||
 || 5 || 333.333
-° ||= D# ||= E^ ||= ~3 || 17/14 or 40/33 || -2.796 +0.293
+° ||= D# ||= E^ || mid 3rd ||= ~3 || 17/14 or 40/33 || -2.796 +0.293
 -3.355 +0.351
--50'20" +5'16" ||&lt; **39/32** ||
+-50'20" +5'16" ||&lt; 39/32 ||
 || 6 || 400
-° ||= **E** ||= Eb,
+° ||= E ||= Eb,
-F# ||= m3,
+F# || minor 3rd,
+augmented 4th ||= m3,
 A4 || 5/4 or 44/35 || +13.686 +3.822
 +16.4235 +4.586
@@ Line 68: / Line 72: @@
 || 7 || 466.667
-° ||= **F** ||= Fv ||= ^m3,
+° ||= F ||= Fv || upminor 3rd,
+down-fourth ||= ^m3,
 vP4 || 21/16 || -4.114
 -4.937
--1°14'3" ||&lt; **21/16** ||
+-1°14'3" ||&lt; 21/16 ||
 || 8 || 533.333
-° ||= Gb ||= F ||= P4 || 15/11 || -3.617
+° ||= Gb ||= F || fourth ||= P4 || 15/11 || -3.617
 -4.341
 -1°5'7" ||&lt; 102/75 ||
@@ Line 80: / Line 85: @@
 ° ||= F# ||= F^,
-Gv ||= ^P4,
+Gv || upfourth,
+downfifth ||= ^P4,
 vP5 || 17/12 or 24/17 || -3.000 +3.000
 -3.6005 +3.6005
@@ Line 86: / Line 92: @@
 || 10 || 666.667
-° ||= **G** ||= G ||= P5 || 22/15 || +3.617
+° ||= G ||= G || fifthj ||= P5 || 22/15 || +3.617
 +4.341
 +1°5'7" ||&lt; 75/51 ||
 || 11 || 733.333
-° ||= Hb ||= G^ ||= ^P5,
+° ||= Hb ||= G^ || upfifth,
+downmajor 6th ||= ^P5,
 vM6 || 32/21 || +4.114
 +4.937
@@ Line 97: / Line 104: @@
 || 12 || 800
-° ||= G# ||= A ||= d5,
+° ||= G# ||= A || diminished 5th,
+major 6th ||= d5,
 M6 || 8/5 or 35/22 || -13.686 -3.822
 -16.4235 -4.586
--4°6'21" -1°8'47" ||&lt; **51/32** ||
+-4°6'21" -1°8'47" ||&lt; 51/32 ||
 || 13 || 866.667
-° ||= **H** ||= A^,
+° ||= H ||= A^,
-Bv ||= ~6 || 28/17 or 33/20 || +2.796 -0.293
+Bv || mid 6th ||= ~6 || 28/17 or 33/20 || +2.796 -0.293
 +3.355 -0.351
 &lt;span style="line-height: 15.6000003814697px;"&gt;+&lt;/span&gt;50'20" &lt;span style="line-height: 15.6000003814697px;"&gt;-&lt;/span&gt;&lt;span style="line-height: 1.5;"&gt;5'16"&lt;/span&gt; ||&lt; 64/39 ||
 || 14 || 933.333
-° ||= **A** ||= B ||= m6,
+° ||= A ||= B || minor 6th,
+major 7th ||= m6,
 M7 || 12/7 || +0.204
 +0.245
-+1"50" ||&lt; **55/32** ||
++1"50" ||&lt; 55/32 ||
 || 15 || 1000
-° ||= Bb ||= B^ ||= ~7 || 16/9 || +3.910
+° ||= Bb ||= B^ || mid 7th ||= ~7 || 16/9 || +3.910
 +4.692
 +1°10'23" ||&lt; 16/9 ||
@@ Line 121: / Line 130: @@
 ° ||= A# ||= Bb,
-C# ||= m7 || 50/27 || -0.096
+C# || minor 7th ||= m7 || 50/27 || -0.096
 -0.115
 -1'43" ||&lt; 39/21 ||
 || 17 || 1133.333
-° ||= **B** ||= Cv ||= ^m7,
+° ||= B ||= Cv || upminor 7th,
+down-octave ||= ^m7,
 vP8 || 52/27 || -1.329
 -1.595
@@ Line 132: / Line 142: @@
 || 18 || 1200
-° ||= **C** ||= C ||= P8 || 2/1 || 0 ||&lt; **2/1** ||
+° ||= C ||= C || octave ||= P8 || 2/1 || 0 ||&lt; 2/1** ||
 *based on the above description of 18-EDO as a 2.9.75.21.55.39.51 subgroup temperament
 ** based on 18b-edo with sharp lower than flat and major narrower than minor
+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
+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/vM2 - M2 - ~2 - m2/M3 - ~3 - m3 - ^m3/vP4 - P4 - ^P4/vP5 - P5 - ^P5/vM6 - M6 - ~6 - m6/M7 - ~7 - m7 - ^m7/d8 - P8
 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]].
@@ Line 208: / Line 228: @@
          &lt;td&gt;Degree&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Cents &lt;br /&gt;
+         &lt;td&gt;Cents&lt;br /&gt;
 coarse/fine&lt;br /&gt;
 DMS&lt;br /&gt;
@@ Line 214: / Line 234: @@
          &lt;td style="text-align: center;"&gt;5L3s Notation&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td colspan="2" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down &lt;/a&gt;&lt;br /&gt;
+         &lt;td colspan="3" style="text-align: center;"&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;up/down &lt;/a&gt;&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt; &lt;strong&gt;&lt;br /&gt;
+based on 18b-edo, with &lt;br /&gt;
+sharp lower than flat&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;Nearest Ratio&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;Error (cents &lt;br /&gt;
+         &lt;td&gt;Error (cents&lt;br /&gt;
 coarse/fine)&lt;br /&gt;
 (DMS)&lt;br /&gt;
@@ Line 231: / Line 252: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;C&lt;strong&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;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;unison&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
@@ Line 241: / Line 264: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;1/1&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 255: / Line 278: @@
          &lt;td style="text-align: center;"&gt;C^,&lt;br /&gt;
 Dv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;up-unison,&lt;br /&gt;
+downmajor 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^P1,&lt;br /&gt;
@@ Line 278: / Line 304: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;major 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
@@ Line 297: / Line 325: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;D&lt;strong&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;D^,&lt;br /&gt;
 Ev&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mid 2nd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;~2&lt;br /&gt;
@@ Line 310: / Line 340: @@
 -1°10'23&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;9/8&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;9/8&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 323: / Line 353: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;minor 2nd,&lt;br /&gt;
+major 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m2,&lt;br /&gt;
@@ Line 333: / Line 366: @@
 -1&amp;quot;50&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;75/64&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;75/64&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 346: / Line 379: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mid 3rd&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;~3&lt;br /&gt;
@@ Line 355: / Line 390: @@
 -50'20&amp;quot; +5'16&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;39/32&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;39/32&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 365: / Line 400: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;E&lt;strong&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;Eb,&lt;br /&gt;
 F#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;minor 3rd,&lt;br /&gt;
+augmented 4th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m3,&lt;br /&gt;
@@ Line 389: / Line 427: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;F&lt;strong&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;Fv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;upminor 3rd,&lt;br /&gt;
+down-fourth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^m3,&lt;br /&gt;
@@ Line 402: / Line 443: @@
 -1°14'3&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;21/16&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;21/16&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 415: / Line 456: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;fourth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
@@ Line 438: / Line 481: @@
          &lt;td style="text-align: center;"&gt;F^,&lt;br /&gt;
 Gv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;upfourth,&lt;br /&gt;
+downfifth&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^P4,&lt;br /&gt;
@@ Line 458: / Line 504: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;G&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;fifthj&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
@@ Line 483: / Line 531: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;upfifth,&lt;br /&gt;
+downmajor 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^P5,&lt;br /&gt;
@@ Line 506: / Line 557: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;diminished 5th,&lt;br /&gt;
+major 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;d5,&lt;br /&gt;
@@ Line 516: / Line 570: @@
 -4°6'21&amp;quot; -1°8'47&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;51/32&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;51/32&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 526: / Line 580: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;H&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;H&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;A^,&lt;br /&gt;
 Bv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mid 6th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;~6&lt;br /&gt;
@@ Line 549: / Line 605: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;A&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;minor 6th,&lt;br /&gt;
+major 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m6,&lt;br /&gt;
@@ Line 562: / Line 621: @@
 +1&amp;quot;50&amp;quot;&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;55/32&lt;strong&gt;&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;55/32&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 575: / Line 634: @@
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;mid 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;~7&lt;br /&gt;
@@ Line 598: / Line 659: @@
          &lt;td style="text-align: center;"&gt;Bb,&lt;br /&gt;
 C#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;minor 7th&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
@@ Line 617: / Line 680: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;B&lt;strong&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;Cv&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;upminor 7th,&lt;br /&gt;
+down-octave&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;^m7,&lt;br /&gt;
@@ Line 640: / Line 706: @@
 °&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: center;"&gt;&lt;/strong&gt;C&lt;strong&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;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;octave&lt;br /&gt;
 &lt;/td&gt;
          &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
@@ Line 650: / Line 718: @@
          &lt;td&gt;0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td style="text-align: left;"&gt;&lt;/strong&gt;2/1**&lt;br /&gt;
+         &lt;td style="text-align: left;"&gt;2/1**&lt;br /&gt;
 &lt;/td&gt;
      &lt;/tr&gt;
@@ Line 658: / Line 726: @@
 &lt;br /&gt;
 &lt;ul&gt;&lt;ul&gt;&lt;li&gt;based on 18b-edo with sharp lower than flat and major narrower than minor&lt;/li&gt;&lt;/ul&gt;&lt;/ul&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;
+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 - ^P1/vM2 - M2 - ~2 - m2/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;
 For alternative notations, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Superflat%22%20EDOs"&gt;Ups and Downs Notation -&amp;quot;Superflat&amp;quot; EDOs&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Supersharp%22%20EDOs"&gt;Ups and Downs Notation -&amp;quot;Supersharp&amp;quot; EDOs&lt;/a&gt; and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Natural%20Generators"&gt;Ups and Downs Notation - Natural Generators&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;

18edo: Difference between revisions

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