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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
__FORCETOC__
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
<span style="display: block; text-align: right;">Other languages: [[:de:53edo Deutsch]]</span>
: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-11-11 21:13:14 UTC</tt>.<br>
: The original revision id was <tt>621464553</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>
<h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]]
&lt;span style="display: block; text-align: right;"&gt;Other languages: [[xenharmonie/53edo|Deutsch]]
&lt;/span&gt;


=Theory=  
=Theory=
The famous //53 equal division// divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[xenharmonic/5-limit|5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[xenharmonic/optimal patent val|optimal patent val]] for [[xenharmonic/Nuwell family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[xenharmonic/Semicomma family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[xenharmonic/Marvel family|athene temperament]]. It is the eighth [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]] and the 16th [[xenharmonic/prime numbers|prime]] edo, following [[xenharmonic/47edo|47edo]] and coming before [[xenharmonic/59edo|59edo]].
The famous ''53 equal division'' divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a [[5-limit|5-limit]] system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the [[Optimal_patent_val|optimal patent val]] for [[Nuwell_family|Big Brother]] temperament, which tempers out both, as well as 11-limit [[Semicomma_family|orwell temperament]], which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for [[Marvel_family|athene temperament]]. It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]] and the 16th [[prime_numbers|prime]] edo, following [[47edo|47edo]] and coming before [[59edo|59edo]].


53EDO has also found a certain dissemination as an EDO tuning for [[Arabic, Turkish, Persian|Arabic/Turkish/Persian music]].
53EDO has also found a certain dissemination as an EDO tuning for [[Arabic,_Turkish,_Persian|Arabic/Turkish/Persian music]].


It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.
It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.


[[http://en.wikipedia.org/wiki/53_equal_temperament|Wikipeda article about 53edo]]
[http://en.wikipedia.org/wiki/53_equal_temperament Wikipeda article about 53edo]


=Linear temperaments=  
=Linear temperaments=
[[List of edo-distinct 53et rank two temperaments]]
[[List_of_edo-distinct_53et_rank_two_temperaments|List of edo-distinct 53et rank two temperaments]]


=Just Approximation=  
=Just Approximation=
53edo provides excellent approximations for the classic 5-limit [[xenharmonic/just|just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.
53edo provides excellent approximations for the classic 5-limit [[just|just]] chords and scales, such as the Ptolemy-Zarlino "just major" scale.
||~ interval ||~ ratio ||~ size ||~ difference ||
 
|| perfect fifth || 3/2 ||= 31 || −0.07 cents ||
{| class="wikitable"
|| major third || 5/4 ||= 17 || −1.40 cents ||
|-
|| minor third || 6/5 ||= 14 || +1.34 cents ||
! | interval
|| major tone || 9/8 ||= 9 || −0.14 cents ||
! | ratio
|| minor tone || 10/9 ||= 8 || −1.27 cents ||
! | size
|| diat. semitone || 16/15 ||= 5 || +1.48 cents ||
! | difference
|-
| | perfect fifth
| | 3/2
| style="text-align:center;" | 31
| | −0.07 cents
|-
| | major third
| | 5/4
| style="text-align:center;" | 17
| | −1.40 cents
|-
| | minor third
| | 6/5
| style="text-align:center;" | 14
| | +1.34 cents
|-
| | major tone
| | 9/8
| style="text-align:center;" | 9
| | −0.14 cents
|-
| | minor tone
| | 10/9
| style="text-align:center;" | 8
| | −1.27 cents
|-
| | diat. semitone
| | 16/15
| style="text-align:center;" | 5
| | +1.48 cents
|}


One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.


The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[xenharmonic/septimal kleisma|septimal kleisma]], 225/224.
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the [[septimal_kleisma|septimal kleisma]], 225/224.


=Intervals=  
=Intervals=
||~ degree ||~ solfege ||~ cents ||~ approximate ratios ||||||~ [[xenharmonic/Ups and Downs Notation|ups and downs ]][[xenharmonic/Ups and Downs Notation|notation]] ||~ generator for ||
 
||= 0 ||= do ||= 0.00 ||= 1/1 ||= P1 ||= unison ||= D ||   ||
{| class="wikitable"
||= 1 ||= di ||= 22.64 ||= 81/80, 64/63, 50/49 ||= ^1 ||= up unison ||= D^ ||   ||
|-
||= 2 ||= daw ||= 45.28 ||= 49/48, 36/35, 33/32, 128/125 ||= ^^1,
! | degree
vvm2 ||= double-up unison,
! | solfege
double-down minor 2nd ||= D^^,
! | cents
Ebvv || [[xenharmonic/Quartonic|Quartonic]] ||
! | approximate ratios
||= 3 ||= ro ||= 67.92 ||= 27/26, 26/25, 25/24, 22/21 ||= vm2 ||= downminor 2nd ||= Ebv ||   ||
! colspan="3" | [[Ups_and_Downs_Notation|ups and downs ]][[Ups_and_Downs_Notation|notation]]
||= 4 ||= rih ||= 90.57 ||= 21/20, 256/243 ||= m2 ||= minor 2nd ||= Eb ||   ||
! | generator for
||= 5 ||= ra ||= 113.21 ||= 16/15, 15/14 ||= ^m2 ||= upminor 2nd ||= Eb^ ||   ||
|-
||= 6 ||= ru ||= 135.85 ||= 14/13, 13/12, 27/25 ||= v~2 ||= downmid 2nd ||= Eb^^ ||   ||
| style="text-align:center;" | 0
||= 7 ||= ruh ||= 158.49 ||= 12/11, 11/10, 800/729 ||= ^~2 ||= upmid 2nd ||= Evv || [[xenharmonic/Hemikleismic|Hemikleismic]] ||
| style="text-align:center;" | do
||= 8 ||= reh ||= 181.13 ||= 10/9 ||= vM2 ||= downmajor 2nd ||= Ev ||   ||
| style="text-align:center;" | 0.00
||= 9 ||= re ||= 203.77 ||= 9/8 ||= M2 ||= major 2nd ||= E ||   ||
| style="text-align:center;" | 1/1
||= 10 ||= ri ||= 226.42 ||= 8/7, 256/225 ||= ^M2 ||= upmajor 2nd ||= E^ ||   ||
| style="text-align:center;" | P1
||= 11 ||= raw ||= 249.06 ||= 15/13, 144/125 ||= ^^M2,
| style="text-align:center;" | unison
vvm3 ||= double-up major 2nd,
| style="text-align:center;" | D
double-down minor 3rd ||= E^^,
| |  
Fvv || [[xenharmonic/Hemischis|Hemischis]] ||
|-
||= 12 ||= ma ||= 271.70 ||= 7/6, 75/64 ||= vm3 ||= downminor 3rd ||= Fv || [[xenharmonic/Orwell|Orwell]] ||
| style="text-align:center;" | 1
||= 13 ||= meh ||= 294.34 ||= 13/11, 32/27 ||= m3 ||= minor 3rd ||= F ||   ||
| style="text-align:center;" | di
||= 14 ||= me ||= 316.98 ||= 6/5 ||= ^m3 ||= upminor 3rd ||= F^ || [[xenharmonic/Hanson|Hanson]]/[[xenharmonic/Catakleismic|Catakleismic]] ||
| style="text-align:center;" | 22.64
||= 15 ||= mu ||= 339.62 ||= 11/9, 243/200 ||= v~3 ||= downmid 3rd ||= F^^ || [[xenharmonic/Amity|Amity]]/[[xenharmonic/Hitchcock|Hitchcock]] ||
| style="text-align:center;" | 81/80, 64/63, 50/49
||= 16 ||= muh ||= 362.26 ||= 16/13, 100/81 ||= ^~3 ||= upmid 3rd ||= F#vv ||  ||
| style="text-align:center;" | ^1
||= 17 ||= mi ||= 384.91 ||= 5/4 ||= vM3 ||= downmajor 3rd ||= F#v ||   ||
| style="text-align:center;" | up unison
||= 18 ||= maa ||= 407.55 ||= 81/64 ||= M3 ||= major 3rd ||= F# ||   ||
| style="text-align:center;" | D^
||= 19 ||= mo ||= 430.19 ||= 9/7, 14/11 ||= ^M3 ||= upmajor 3rd ||= F#^ || [[Hamity]] ||
| |  
||= 20 ||= maw ||= 452.83 ||= 13/10, 125/96 ||= ^^M3,
|-
vv4 ||= double-up major 3rd,
| style="text-align:center;" | 2
double-down 4th ||= F#^^,
| style="text-align:center;" | daw
Gvv ||   ||
| style="text-align:center;" | 45.28
||= 21 ||= fe ||= 475.47 ||= 21/16, 675/512, 320/243 ||= v4 ||= down 4th ||= Gv || [[xenharmonic/Vulture|Vulture]]/[[xenharmonic/Buzzard|Buzzard]] ||
| style="text-align:center;" | 49/48, 36/35, 33/32, 128/125
||= 22 ||= fa ||= 498.11 ||= 4/3 ||= P4 ||= perfect 4th ||= G ||   ||
| style="text-align:center;" | ^^1,
||= 23 ||= fih ||= 520.75 ||= 27/20 ||= ^4 ||= up 4th ||= G^ ||   ||
 
||= 24 ||= fu ||= 543.40 ||= 11/8, 15/11 ||= ^^4 ||= double-up 4th ||= G^^ ||   ||
vvm2
||= 25 ||= fuh ||= 566.04 ||= 18/13 ||= vvA4,
| style="text-align:center;" | double-up unison,
vd5 ||= double-down aug 4th,
 
downdim 5th ||= G#vv,
double-down minor 2nd
Abv || [[xenharmonic/Tricot|Tricot]] ||
| style="text-align:center;" | D^^,
||= 26 ||= fi ||= 588.68 ||= 7/5, 45/32 ||= vA4,
 
d5 ||= downaug 4th,
Ebvv
dim 5th ||= G#v,
| | [[Quartonic|Quartonic]]
Ab ||   ||
|-
||= 27 ||= se ||= 611.32 ||= 10/7, 64/45 ||= A4,
| style="text-align:center;" | 3
^d5 ||= aug 4th,
| style="text-align:center;" | ro
updim 5th ||= G#,
| style="text-align:center;" | 67.92
Ab^ ||   ||
| style="text-align:center;" | 27/26, 26/25, 25/24, 22/21
||= 28 ||= suh ||= 633.96 ||= 13/9 ||= ^A4,
| style="text-align:center;" | vm2
^^d5 ||= upaug 4th,
| style="text-align:center;" | downminor 2nd
double-up dim 5th ||= G#^,
| style="text-align:center;" | Ebv
Ab^^ ||   ||
| |  
||= 29 ||= su ||= 656.60 ||= 16/11, 22/15 ||= vv5 ||= double-down 5th ||= Avv ||   ||
|-
||= 30 ||= sih ||= 679.25 ||= 40/27 ||= v5 ||= down 5th ||= Av ||   ||
| style="text-align:center;" | 4
||= 31 ||= sol ||= 701.89 ||= 3/2 ||= P5 ||= perfect 5th ||= A || [[xenharmonic/Helmholtz|Helmholtz]]/[[xenharmonic/Garibaldi|Garibaldi]] ||
| style="text-align:center;" | rih
||= 32 ||= si ||= 724.53 ||= 32/21, 243/160, 1024/675 ||= ^5 ||= up 5th ||= A^ ||   ||
| style="text-align:center;" | 90.57
||= 33 ||= saw ||= 747.17 ||= 20/13, 192/125 ||= ^^5,
| style="text-align:center;" | 21/20, 256/243
vvm6 ||= double-up 5th,
| style="text-align:center;" | m2
double-down minor 6th ||= A^^,
| style="text-align:center;" | minor 2nd
Bbvv ||   ||
| style="text-align:center;" | Eb
||= 34 ||= lo ||= 769.81 ||= 14/9, 25/16, 11/7 ||= vm6 ||= downminor 6th ||= Bbv ||   ||
| |  
||= 35 ||= leh ||= 792.45 ||= 128/81 ||= m6 ||= minor 6th ||= Bb ||   ||
|-
||= 36 ||= le ||= 815.09 ||= 8/5 ||= ^m6 ||= upminor 6th ||= Bb^ ||   ||
| style="text-align:center;" | 5
||= 37 ||= lu ||= 837.74 ||= 13/8, 81/50 ||= v~6 ||= downmid 6th ||= Bb^^ ||   ||
| style="text-align:center;" | ra
||= 38 ||= luh ||= 860.38 ||= 18/11, 400/243 ||= ^~6 ||= upmid 6th ||= Bvv ||   ||
| style="text-align:center;" | 113.21
||= 39 ||= la ||= 883.02 ||= 5/3 ||= vM6 ||= downmajor 6th ||= Bv ||   ||
| style="text-align:center;" | 16/15, 15/14
||= 40 ||= laa ||= 905.66 ||= 22/13, 27/16 ||= M6 ||= major 6th ||= B ||   ||
| style="text-align:center;" | ^m2
||= 41 ||= lo ||= 928.30 ||= 12/7 ||= ^M6 ||= upmajor 6th ||= B^ ||   ||
| style="text-align:center;" | upminor 2nd
||= 42 ||= law ||= 950.94 ||= 26/15, 125/72 ||= ^^M6
| style="text-align:center;" | Eb^
vvm7 ||= double-up major 6th,
| |  
double-down minor 7th ||= B^^,
|-
Cvv ||   ||
| style="text-align:center;" | 6
||= 43 ||= ta ||= 973.58 ||= 7/4 ||= vm7 ||= downminor 7th ||= Cv ||   ||
| style="text-align:center;" | ru
||= 44 ||= teh ||= 996.23 ||= 16/9 ||= m7 ||= minor 7th ||= C ||   ||
| style="text-align:center;" | 135.85
||= 45 ||= te ||= 1018.87 ||= 9/5 ||= ^m7 ||= upminor 7th ||= C^ ||   ||
| style="text-align:center;" | 14/13, 13/12, 27/25
||= 46 ||= tu ||= 1041.51 ||= 11/6, 20/11, 729/400 ||= v~7 ||= downmid 7th ||= C^^ ||   ||
| style="text-align:center;" | v~2
||= 47 ||= tuh ||= 1064.15 ||= 13/7, 24/13, 50/27 ||= ^~7 ||= upmid 7th ||= C#vv ||   ||
| style="text-align:center;" | downmid 2nd
||= 48 ||= ti ||= 1086.79 ||= 15/8 ||= vM7 ||= downmajor 7th ||= C#v ||   ||
| style="text-align:center;" | Eb^^
||= 49 ||= tih ||= 1109.43 ||= 40/21, 243/128 ||= M7 ||= major 7th ||= C# ||  ||
| |  
||= 50 ||= to ||= 1132.08 ||= 48/25, 27/14 ||= ^M7 ||= upmajor 7th ||= C#^ ||   ||
|-
||= 51 ||= taw ||= 1154.72 ||= 125/64 ||= ^^M7,
| style="text-align:center;" | 7
vv8 ||= double-up major 7th,
| style="text-align:center;" | ruh
double-down 8ve ||= C#^^,
| style="text-align:center;" | 158.49
Dvv ||  ||
| style="text-align:center;" | 12/11, 11/10, 800/729
||= 52 ||= da ||= 1177.36 ||= 160/81 ||= v8 ||= down 8ve ||= Dv ||  ||
| style="text-align:center;" | ^~2
||= 53 ||= do ||= 1200 ||= 2/1 ||= P8 ||= perfect 8ve ||= D ||  ||
| style="text-align:center;" | upmid 2nd
Combining ups and downs notation with [[Kite's color notation|color notation]], qualities can be loosely associated with colors:
| style="text-align:center;" | Evv
||~ quality ||~ color ||~ monzo format ||~ examples ||
| | [[Hemikleismic|Hemikleismic]]
||= downminor ||= blue ||= {a, b, 0, 1} ||= 7/6, 7/4 ||
|-
||= minor ||= fourthward white ||= {a, b}, b &lt; -1 ||= 32/27, 16/9 ||
| style="text-align:center;" | 8
||= upminor ||= green ||= {a, b, -1} ||= 6/5, 9/5 ||
| style="text-align:center;" | reh
||= downmid ||= jade ||= {a, b, 0, 0, 1} ||= 11/9, 11/6 ||
| style="text-align:center;" | 181.13
||= upmid ||= amber ||= {a, b, 0, 0, -1} ||= 12/11, 18/11 ||
| style="text-align:center;" | 10/9
||= downmajor ||= yellow ||= {a, b, 1} ||= 5/4, 5/3 ||
| style="text-align:center;" | vM2
||= major ||= fifthward white ||= {a, b}, b &gt; 1 ||= 9/8, 27/16 ||
| style="text-align:center;" | downmajor 2nd
||= upmajor ||= red ||= {a, b, 0, -1} ||= 9/7, 12/7 ||
| style="text-align:center;" | Ev
All 53edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:
| |  
||~ color of the 3rd ||~ JI chord ||~ notes as edosteps ||~ notes of C chord ||~ written name ||~ spoken name ||
|-
||= blue ||= 6:7:9 ||= 0-12-31 ||= C Ebv G ||= C.vm ||= C downminor ||
| style="text-align:center;" | 9
||= green ||= 10:12:15 ||= 0-14-31 ||= C Eb^ G ||= C.^m ||= C upminor ||
| style="text-align:center;" | re
||= jade ||= 18:22:27 ||= 0-15-31 ||= C Eb^^ G ||= C.v~ ||= C downmid ||
| style="text-align:center;" | 203.77
||= yellow ||= 4:5:6 ||= 0-17-31 ||= C Ev G ||= C.v ||= C downmajor or C dot down ||
| style="text-align:center;" | 9/8
||= red ||= 14:18:27 ||= 0-19-31 ||= C E^ G ||= C.^ ||= C upmajor or C dot up ||
| style="text-align:center;" | M2
For a more complete list, see [[xenharmonic/Ups and Downs Notation#Chord%20names%20in%20other%20EDOs|Ups and Downs Notation - Chord names in other EDOs]].
| style="text-align:center;" | major 2nd
| style="text-align:center;" | E
| |  
|-
| style="text-align:center;" | 10
| style="text-align:center;" | ri
| style="text-align:center;" | 226.42
| style="text-align:center;" | 8/7, 256/225
| style="text-align:center;" | ^M2
| style="text-align:center;" | upmajor 2nd
| style="text-align:center;" | E^
| |  
|-
| style="text-align:center;" | 11
| style="text-align:center;" | raw
| style="text-align:center;" | 249.06
| style="text-align:center;" | 15/13, 144/125
| style="text-align:center;" | ^^M2,
 
vvm3
| style="text-align:center;" | double-up major 2nd,
 
double-down minor 3rd
| style="text-align:center;" | E^^,
 
Fvv
| | [[Hemischis|Hemischis]]
|-
| style="text-align:center;" | 12
| style="text-align:center;" | ma
| style="text-align:center;" | 271.70
| style="text-align:center;" | 7/6, 75/64
| style="text-align:center;" | vm3
| style="text-align:center;" | downminor 3rd
| style="text-align:center;" | Fv
| | [[Orwell|Orwell]]
|-
| style="text-align:center;" | 13
| style="text-align:center;" | meh
| style="text-align:center;" | 294.34
| style="text-align:center;" | 13/11, 32/27
| style="text-align:center;" | m3
| style="text-align:center;" | minor 3rd
| style="text-align:center;" | F
| |  
|-
| style="text-align:center;" | 14
| style="text-align:center;" | me
| style="text-align:center;" | 316.98
| style="text-align:center;" | 6/5
| style="text-align:center;" | ^m3
| style="text-align:center;" | upminor 3rd
| style="text-align:center;" | F^
| | [[Hanson|Hanson]]/[[catakleismic|Catakleismic]]
|-
| style="text-align:center;" | 15
| style="text-align:center;" | mu
| style="text-align:center;" | 339.62
| style="text-align:center;" | 11/9, 243/200
| style="text-align:center;" | v~3
| style="text-align:center;" | downmid 3rd
| style="text-align:center;" | F^^
| | [[Amity|Amity]]/[[Hitchcock|Hitchcock]]
|-
| style="text-align:center;" | 16
| style="text-align:center;" | muh
| style="text-align:center;" | 362.26
| style="text-align:center;" | 16/13, 100/81
| style="text-align:center;" | ^~3
| style="text-align:center;" | upmid 3rd
| style="text-align:center;" | F#vv
| |  
|-
| style="text-align:center;" | 17
| style="text-align:center;" | mi
| style="text-align:center;" | 384.91
| style="text-align:center;" | 5/4
| style="text-align:center;" | vM3
| style="text-align:center;" | downmajor 3rd
| style="text-align:center;" | F#v
| |  
|-
| style="text-align:center;" | 18
| style="text-align:center;" | maa
| style="text-align:center;" | 407.55
| style="text-align:center;" | 81/64
| style="text-align:center;" | M3
| style="text-align:center;" | major 3rd
| style="text-align:center;" | F#
| |  
|-
| style="text-align:center;" | 19
| style="text-align:center;" | mo
| style="text-align:center;" | 430.19
| style="text-align:center;" | 9/7, 14/11
| style="text-align:center;" | ^M3
| style="text-align:center;" | upmajor 3rd
| style="text-align:center;" | F#^
| | [[Hamity|Hamity]]
|-
| style="text-align:center;" | 20
| style="text-align:center;" | maw
| style="text-align:center;" | 452.83
| style="text-align:center;" | 13/10, 125/96
| style="text-align:center;" | ^^M3,
 
vv4
| style="text-align:center;" | double-up major 3rd,
 
double-down 4th
| style="text-align:center;" | F#^^,
 
Gvv
| |  
|-
| style="text-align:center;" | 21
| style="text-align:center;" | fe
| style="text-align:center;" | 475.47
| style="text-align:center;" | 21/16, 675/512, 320/243
| style="text-align:center;" | v4
| style="text-align:center;" | down 4th
| style="text-align:center;" | Gv
| | [[Vulture|Vulture]]/[[Buzzard|Buzzard]]
|-
| style="text-align:center;" | 22
| style="text-align:center;" | fa
| style="text-align:center;" | 498.11
| style="text-align:center;" | 4/3
| style="text-align:center;" | P4
| style="text-align:center;" | perfect 4th
| style="text-align:center;" | G
| |  
|-
| style="text-align:center;" | 23
| style="text-align:center;" | fih
| style="text-align:center;" | 520.75
| style="text-align:center;" | 27/20
| style="text-align:center;" | ^4
| style="text-align:center;" | up 4th
| style="text-align:center;" | G^
| |  
|-
| style="text-align:center;" | 24
| style="text-align:center;" | fu
| style="text-align:center;" | 543.40
| style="text-align:center;" | 11/8, 15/11
| style="text-align:center;" | ^^4
| style="text-align:center;" | double-up 4th
| style="text-align:center;" | G^^
| |  
|-
| style="text-align:center;" | 25
| style="text-align:center;" | fuh
| style="text-align:center;" | 566.04
| style="text-align:center;" | 18/13
| style="text-align:center;" | vvA4,
 
vd5
| style="text-align:center;" | double-down aug 4th,
 
downdim 5th
| style="text-align:center;" | G#vv,
 
Abv
| | [[Tricot|Tricot]]
|-
| style="text-align:center;" | 26
| style="text-align:center;" | fi
| style="text-align:center;" | 588.68
| style="text-align:center;" | 7/5, 45/32
| style="text-align:center;" | vA4,
 
d5
| style="text-align:center;" | downaug 4th,
 
dim 5th
| style="text-align:center;" | G#v,
 
Ab
| |  
|-
| style="text-align:center;" | 27
| style="text-align:center;" | se
| style="text-align:center;" | 611.32
| style="text-align:center;" | 10/7, 64/45
| style="text-align:center;" | A4,
 
^d5
| style="text-align:center;" | aug 4th,
 
updim 5th
| style="text-align:center;" | G#,
 
Ab^
| |  
|-
| style="text-align:center;" | 28
| style="text-align:center;" | suh
| style="text-align:center;" | 633.96
| style="text-align:center;" | 13/9
| style="text-align:center;" | ^A4,
 
^^d5
| style="text-align:center;" | upaug 4th,
 
double-up dim 5th
| style="text-align:center;" | G#^,
 
Ab^^
| |  
|-
| style="text-align:center;" | 29
| style="text-align:center;" | su
| style="text-align:center;" | 656.60
| style="text-align:center;" | 16/11, 22/15
| style="text-align:center;" | vv5
| style="text-align:center;" | double-down 5th
| style="text-align:center;" | Avv
| |  
|-
| style="text-align:center;" | 30
| style="text-align:center;" | sih
| style="text-align:center;" | 679.25
| style="text-align:center;" | 40/27
| style="text-align:center;" | v5
| style="text-align:center;" | down 5th
| style="text-align:center;" | Av
| |  
|-
| style="text-align:center;" | 31
| style="text-align:center;" | sol
| style="text-align:center;" | 701.89
| style="text-align:center;" | 3/2
| style="text-align:center;" | P5
| style="text-align:center;" | perfect 5th
| style="text-align:center;" | A
| | [[Helmholtz|Helmholtz]]/[[Garibaldi|Garibaldi]]
|-
| style="text-align:center;" | 32
| style="text-align:center;" | si
| style="text-align:center;" | 724.53
| style="text-align:center;" | 32/21, 243/160, 1024/675
| style="text-align:center;" | ^5
| style="text-align:center;" | up 5th
| style="text-align:center;" | A^
| |  
|-
| style="text-align:center;" | 33
| style="text-align:center;" | saw
| style="text-align:center;" | 747.17
| style="text-align:center;" | 20/13, 192/125
| style="text-align:center;" | ^^5,
 
vvm6
| style="text-align:center;" | double-up 5th,
 
double-down minor 6th
| style="text-align:center;" | A^^,
 
Bbvv
| |  
|-
| style="text-align:center;" | 34
| style="text-align:center;" | lo
| style="text-align:center;" | 769.81
| style="text-align:center;" | 14/9, 25/16, 11/7
| style="text-align:center;" | vm6
| style="text-align:center;" | downminor 6th
| style="text-align:center;" | Bbv
| |  
|-
| style="text-align:center;" | 35
| style="text-align:center;" | leh
| style="text-align:center;" | 792.45
| style="text-align:center;" | 128/81
| style="text-align:center;" | m6
| style="text-align:center;" | minor 6th
| style="text-align:center;" | Bb
| |  
|-
| style="text-align:center;" | 36
| style="text-align:center;" | le
| style="text-align:center;" | 815.09
| style="text-align:center;" | 8/5
| style="text-align:center;" | ^m6
| style="text-align:center;" | upminor 6th
| style="text-align:center;" | Bb^
| |  
|-
| style="text-align:center;" | 37
| style="text-align:center;" | lu
| style="text-align:center;" | 837.74
| style="text-align:center;" | 13/8, 81/50
| style="text-align:center;" | v~6
| style="text-align:center;" | downmid 6th
| style="text-align:center;" | Bb^^
| |  
|-
| style="text-align:center;" | 38
| style="text-align:center;" | luh
| style="text-align:center;" | 860.38
| style="text-align:center;" | 18/11, 400/243
| style="text-align:center;" | ^~6
| style="text-align:center;" | upmid 6th
| style="text-align:center;" | Bvv
| |  
|-
| style="text-align:center;" | 39
| style="text-align:center;" | la
| style="text-align:center;" | 883.02
| style="text-align:center;" | 5/3
| style="text-align:center;" | vM6
| style="text-align:center;" | downmajor 6th
| style="text-align:center;" | Bv
| |  
|-
| style="text-align:center;" | 40
| style="text-align:center;" | laa
| style="text-align:center;" | 905.66
| style="text-align:center;" | 22/13, 27/16
| style="text-align:center;" | M6
| style="text-align:center;" | major 6th
| style="text-align:center;" | B
| |  
|-
| style="text-align:center;" | 41
| style="text-align:center;" | lo
| style="text-align:center;" | 928.30
| style="text-align:center;" | 12/7
| style="text-align:center;" | ^M6
| style="text-align:center;" | upmajor 6th
| style="text-align:center;" | B^
| |  
|-
| style="text-align:center;" | 42
| style="text-align:center;" | law
| style="text-align:center;" | 950.94
| style="text-align:center;" | 26/15, 125/72
| style="text-align:center;" | ^^M6
 
vvm7
| style="text-align:center;" | double-up major 6th,
 
double-down minor 7th
| style="text-align:center;" | B^^,
 
Cvv
| |  
|-
| style="text-align:center;" | 43
| style="text-align:center;" | ta
| style="text-align:center;" | 973.58
| style="text-align:center;" | 7/4
| style="text-align:center;" | vm7
| style="text-align:center;" | downminor 7th
| style="text-align:center;" | Cv
| |  
|-
| style="text-align:center;" | 44
| style="text-align:center;" | teh
| style="text-align:center;" | 996.23
| style="text-align:center;" | 16/9
| style="text-align:center;" | m7
| style="text-align:center;" | minor 7th
| style="text-align:center;" | C
| |  
|-
| style="text-align:center;" | 45
| style="text-align:center;" | te
| style="text-align:center;" | 1018.87
| style="text-align:center;" | 9/5
| style="text-align:center;" | ^m7
| style="text-align:center;" | upminor 7th
| style="text-align:center;" | C^
| |  
|-
| style="text-align:center;" | 46
| style="text-align:center;" | tu
| style="text-align:center;" | 1041.51
| style="text-align:center;" | 11/6, 20/11, 729/400
| style="text-align:center;" | v~7
| style="text-align:center;" | downmid 7th
| style="text-align:center;" | C^^
| |  
|-
| style="text-align:center;" | 47
| style="text-align:center;" | tuh
| style="text-align:center;" | 1064.15
| style="text-align:center;" | 13/7, 24/13, 50/27
| style="text-align:center;" | ^~7
| style="text-align:center;" | upmid 7th
| style="text-align:center;" | C#vv
| |  
|-
| style="text-align:center;" | 48
| style="text-align:center;" | ti
| style="text-align:center;" | 1086.79
| style="text-align:center;" | 15/8
| style="text-align:center;" | vM7
| style="text-align:center;" | downmajor 7th
| style="text-align:center;" | C#v
| |  
|-
| style="text-align:center;" | 49
| style="text-align:center;" | tih
| style="text-align:center;" | 1109.43
| style="text-align:center;" | 40/21, 243/128
| style="text-align:center;" | M7
| style="text-align:center;" | major 7th
| style="text-align:center;" | C#
| |  
|-
| style="text-align:center;" | 50
| style="text-align:center;" | to
| style="text-align:center;" | 1132.08
| style="text-align:center;" | 48/25, 27/14
| style="text-align:center;" | ^M7
| style="text-align:center;" | upmajor 7th
| style="text-align:center;" | C#^
| |  
|-
| style="text-align:center;" | 51
| style="text-align:center;" | taw
| style="text-align:center;" | 1154.72
| style="text-align:center;" | 125/64
| style="text-align:center;" | ^^M7,
 
vv8
| style="text-align:center;" | double-up major 7th,
 
double-down 8ve
| style="text-align:center;" | C#^^,


=Compositions=
Dvv
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3|Bach WTC1 Prelude 1 in 53]] by Bach and [[xenharmonic/Mykhaylo Khramov|Mykhaylo Khramov]]
| |  
[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3|Bach WTC1 Fugue 1 in 53]] by Bach and Mykhaylo Khramov
|-
[[http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html|Whisper Song in 53EDO]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3|play]] by [[xenharmonic/Prent Rodgers|Prent Rodgers]]
| style="text-align:center;" | 52
[[http://www.archive.org/details/TrioInOrwell|Trio in Orwell]] [[http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3|play]] by [[xenharmonic/Gene Ward Smith|Gene Ward Smith]]
| style="text-align:center;" | da
[[http://www.akjmusic.com/audio/desert_prayer.mp3|Desert Prayer]] by [[http://www.akjmusic.com/|Aaron Krister Johnson]]
| style="text-align:center;" | 1177.36
[[http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3|Whisper Song in 53 EDO]] by [[Prent Rodgers]]
| style="text-align:center;" | 160/81
[[@http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho|Elf Dine on Ho Ho]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3|play]] and [[@http://andrewheathwaite.bandcamp.com/track/spun|Spun]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3|play]] by [[xenharmonic/Andrew Heathwaite|Andrew Heathwaite]]
| style="text-align:center;" | v8
[[http://chrisvaisvil.com/the-fallen-of-kleismic15/|The Fallen of Kleismic15]][[http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3|play]] by [[Chris Vaisvil]]
| style="text-align:center;" | down 8ve
[[https://soundcloud.com/cam-taylor-2-1/mothers|mothers]] by Cam Taylor</pre></div>
| style="text-align:center;" | Dv
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;53edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:10:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:10 --&gt;&lt;!-- ws:start:WikiTextTocRule:11: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:11 --&gt;&lt;!-- ws:start:WikiTextTocRule:12: --&gt; | &lt;a href="#Linear temperaments"&gt;Linear temperaments&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:12 --&gt;&lt;!-- ws:start:WikiTextTocRule:13: --&gt; | &lt;a href="#Just Approximation"&gt;Just Approximation&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:13 --&gt;&lt;!-- ws:start:WikiTextTocRule:14: --&gt; | &lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:14 --&gt;&lt;!-- ws:start:WikiTextTocRule:15: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:15 --&gt;&lt;!-- ws:start:WikiTextTocRule:16: --&gt;
|-
&lt;!-- ws:end:WikiTextTocRule:16 --&gt;&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/53edo"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
| style="text-align:center;" | 53
&lt;/span&gt;&lt;br /&gt;
| style="text-align:center;" | do
&lt;br /&gt;
| style="text-align:center;" | 1200
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Theory&lt;/h1&gt;
| style="text-align:center;" | 2/1
The famous &lt;em&gt;53 equal division&lt;/em&gt; divides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/5-limit"&gt;5-limit&lt;/a&gt; system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/optimal%20patent%20val"&gt;optimal patent val&lt;/a&gt; for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Nuwell%20family"&gt;Big Brother&lt;/a&gt; temperament, which tempers out both, as well as 11-limit &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Semicomma%20family"&gt;orwell temperament&lt;/a&gt;, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Marvel%20family"&gt;athene temperament&lt;/a&gt;. It is the eighth &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta integral edo&lt;/a&gt; and the 16th &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/prime%20numbers"&gt;prime&lt;/a&gt; edo, following &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/47edo"&gt;47edo&lt;/a&gt; and coming before &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/59edo"&gt;59edo&lt;/a&gt;.&lt;br /&gt;
| style="text-align:center;" | P8
&lt;br /&gt;
| style="text-align:center;" | perfect 8ve
53EDO has also found a certain dissemination as an EDO tuning for &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic/Turkish/Persian music&lt;/a&gt;.&lt;br /&gt;
| style="text-align:center;" | D
&lt;br /&gt;
| |
It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.&lt;br /&gt;
|}
&lt;br /&gt;
Combining ups and downs notation with [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors:
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/53_equal_temperament" rel="nofollow"&gt;Wikipeda article about 53edo&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Linear temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Linear temperaments&lt;/h1&gt;
&lt;a class="wiki_link" href="/List%20of%20edo-distinct%2053et%20rank%20two%20temperaments"&gt;List of edo-distinct 53et rank two temperaments&lt;/a&gt;&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="Just Approximation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Just Approximation&lt;/h1&gt;
53edo provides excellent approximations for the classic 5-limit &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/just"&gt;just&lt;/a&gt; chords and scales, such as the Ptolemy-Zarlino &amp;quot;just major&amp;quot; scale.&lt;br /&gt;


{| class="wikitable"
|-
! | quality
! | color
! | monzo format
! | examples
|-
| style="text-align:center;" | downminor
| style="text-align:center;" | blue
| style="text-align:center;" | {a, b, 0, 1}
| style="text-align:center;" | 7/6, 7/4
|-
| style="text-align:center;" | minor
| style="text-align:center;" | fourthward white
| style="text-align:center;" | {a, b}, b &lt; -1
| style="text-align:center;" | 32/27, 16/9
|-
| style="text-align:center;" | upminor
| style="text-align:center;" | green
| style="text-align:center;" | {a, b, -1}
| style="text-align:center;" | 6/5, 9/5
|-
| style="text-align:center;" | downmid
| style="text-align:center;" | jade
| style="text-align:center;" | {a, b, 0, 0, 1}
| style="text-align:center;" | 11/9, 11/6
|-
| style="text-align:center;" | upmid
| style="text-align:center;" | amber
| style="text-align:center;" | {a, b, 0, 0, -1}
| style="text-align:center;" | 12/11, 18/11
|-
| style="text-align:center;" | downmajor
| style="text-align:center;" | yellow
| style="text-align:center;" | {a, b, 1}
| style="text-align:center;" | 5/4, 5/3
|-
| style="text-align:center;" | major
| style="text-align:center;" | fifthward white
| style="text-align:center;" | {a, b}, b &gt; 1
| style="text-align:center;" | 9/8, 27/16
|-
| style="text-align:center;" | upmajor
| style="text-align:center;" | red
| style="text-align:center;" | {a, b, 0, -1}
| style="text-align:center;" | 9/7, 12/7
|}
All 53edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;th&gt;interval&lt;br /&gt;
! | color of the 3rd
&lt;/th&gt;
! | JI chord
        &lt;th&gt;ratio&lt;br /&gt;
! | notes as edosteps
&lt;/th&gt;
! | notes of C chord
        &lt;th&gt;size&lt;br /&gt;
! | written name
&lt;/th&gt;
! | spoken name
        &lt;th&gt;difference&lt;br /&gt;
|-
&lt;/th&gt;
| style="text-align:center;" | blue
    &lt;/tr&gt;
| style="text-align:center;" | 6:7:9
    &lt;tr&gt;
| style="text-align:center;" | 0-12-31
        &lt;td&gt;perfect fifth&lt;br /&gt;
| style="text-align:center;" | C Ebv G
&lt;/td&gt;
| style="text-align:center;" | C.vm
        &lt;td&gt;3/2&lt;br /&gt;
| style="text-align:center;" | C downminor
&lt;/td&gt;
|-
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
| style="text-align:center;" | green
&lt;/td&gt;
| style="text-align:center;" | 10:12:15
        &lt;td&gt;−0.07 cents&lt;br /&gt;
| style="text-align:center;" | 0-14-31
&lt;/td&gt;
| style="text-align:center;" | C Eb^ G
    &lt;/tr&gt;
| style="text-align:center;" | C.^m
    &lt;tr&gt;
| style="text-align:center;" | C upminor
        &lt;td&gt;major third&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | jade
        &lt;td&gt;5/4&lt;br /&gt;
| style="text-align:center;" | 18:22:27
&lt;/td&gt;
| style="text-align:center;" | 0-15-31
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
| style="text-align:center;" | C Eb^^ G
&lt;/td&gt;
| style="text-align:center;" | C.v~
        &lt;td&gt;−1.40 cents&lt;br /&gt;
| style="text-align:center;" | C downmid
&lt;/td&gt;
|-
    &lt;/tr&gt;
| style="text-align:center;" | yellow
    &lt;tr&gt;
| style="text-align:center;" | 4:5:6
        &lt;td&gt;minor third&lt;br /&gt;
| style="text-align:center;" | 0-17-31
&lt;/td&gt;
| style="text-align:center;" | C Ev G
        &lt;td&gt;6/5&lt;br /&gt;
| style="text-align:center;" | C.v
&lt;/td&gt;
| style="text-align:center;" | C downmajor or C dot down
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
|-
&lt;/td&gt;
| style="text-align:center;" | red
        &lt;td&gt;+1.34 cents&lt;br /&gt;
| style="text-align:center;" | 14:18:27
&lt;/td&gt;
| style="text-align:center;" | 0-19-31
    &lt;/tr&gt;
| style="text-align:center;" | C E^ G
    &lt;tr&gt;
| style="text-align:center;" | C.^
        &lt;td&gt;major tone&lt;br /&gt;
| style="text-align:center;" | C upmajor or C dot up
&lt;/td&gt;
|}
        &lt;td&gt;9/8&lt;br /&gt;
For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;−0.14 cents&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;minor tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;−1.27 cents&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;diat. semitone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;+1.48 cents&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
=Compositions=
One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.&lt;br /&gt;
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3 Bach WTC1 Prelude 1 in 53] by Bach and [[Mykhaylo_Khramov|Mykhaylo Khramov]]
&lt;br /&gt;
The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, 225/224.&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Intervals&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3 Bach WTC1 Fugue 1 in 53] by Bach and Mykhaylo Khramov
    &lt;tr&gt;
        &lt;th&gt;degree&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;solfege&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;cents&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;approximate ratios&lt;br /&gt;
&lt;/th&gt;
        &lt;th colspan="3"&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;ups and downs &lt;/a&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation"&gt;notation&lt;/a&gt;&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;generator for&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0.00&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;di&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22.64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;81/80, 64/63, 50/49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;up unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;daw&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;45.28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;49/48, 36/35, 33/32, 128/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^1,&lt;br /&gt;
vvm2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up unison,&lt;br /&gt;
double-down minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D^^,&lt;br /&gt;
Ebvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Quartonic"&gt;Quartonic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ro&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;67.92&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/26, 26/25, 25/24, 22/21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downminor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ebv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;rih&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;90.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21/20, 256/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;minor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ra&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;113.21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/15, 15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ru&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;135.85&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14/13, 13/12, 27/25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v~2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmid 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ruh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;158.49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/11, 11/10, 800/729&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^~2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmid 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Evv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemikleismic"&gt;Hemikleismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;reh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;181.13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ev&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;re&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;203.77&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ri&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;226.42&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/7, 256/225&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmajor 2nd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;raw&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;249.06&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/13, 144/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^M2,&lt;br /&gt;
vvm3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up major 2nd,&lt;br /&gt;
double-down minor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;E^^,&lt;br /&gt;
Fvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hemischis"&gt;Hemischis&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ma&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;271.70&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/6, 75/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downminor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Fv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Orwell"&gt;Orwell&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;meh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;294.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/11, 32/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;minor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;me&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;316.98&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hanson"&gt;Hanson&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Catakleismic"&gt;Catakleismic&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mu&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;339.62&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/9, 243/200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v~3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmid 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Amity"&gt;Amity&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Hitchcock"&gt;Hitchcock&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;muh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;362.26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/13, 100/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^~3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmid 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#vv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mi&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;384.91&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#v&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;maa&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;407.55&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;81/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;mo&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;430.19&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7, 14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmajor 3rd&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="/Hamity"&gt;Hamity&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;maw&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;452.83&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/10, 125/96&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^M3,&lt;br /&gt;
vv4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up major 3rd,&lt;br /&gt;
double-down 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F#^^,&lt;br /&gt;
Gvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fe&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;475.47&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21/16, 675/512, 320/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;down 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Vulture"&gt;Vulture&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Buzzard"&gt;Buzzard&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fa&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;498.11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;perfect 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fih&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;520.75&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;27/20&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;up 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fu&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;543.40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/8, 15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up 4th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fuh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;566.04&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vvA4,&lt;br /&gt;
vd5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-down aug 4th,&lt;br /&gt;
downdim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#vv,&lt;br /&gt;
Abv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Tricot"&gt;Tricot&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fi&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;588.68&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/5, 45/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vA4,&lt;br /&gt;
d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downaug 4th,&lt;br /&gt;
dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#v,&lt;br /&gt;
Ab&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;se&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;611.32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10/7, 64/45&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A4,&lt;br /&gt;
^d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;aug 4th,&lt;br /&gt;
updim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#,&lt;br /&gt;
Ab^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;suh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;633.96&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^A4,&lt;br /&gt;
^^d5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upaug 4th,&lt;br /&gt;
double-up dim 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;G#^,&lt;br /&gt;
Ab^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;su&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;656.60&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/11, 22/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vv5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-down 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Avv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;sih&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;679.25&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;40/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;down 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Av&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;sol&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;701.89&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;perfect 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Helmholtz"&gt;Helmholtz&lt;/a&gt;/&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Garibaldi"&gt;Garibaldi&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;si&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;724.53&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32/21, 243/160, 1024/675&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;up 5th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;saw&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;747.17&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;20/13, 192/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^5,&lt;br /&gt;
vvm6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up 5th,&lt;br /&gt;
double-down minor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;A^^,&lt;br /&gt;
Bbvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;769.81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14/9, 25/16, 11/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downminor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bbv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;leh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;792.45&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;128/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;minor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;le&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;815.09&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;8/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;lu&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;837.74&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/8, 81/50&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v~6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmid 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;luh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;860.38&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18/11, 400/243&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^~6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmid 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;la&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;883.02&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;laa&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;905.66&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;22/13, 27/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;lo&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;928.30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmajor 6th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;law&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;950.94&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;26/15, 125/72&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^M6&lt;br /&gt;
vvm7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up major 6th,&lt;br /&gt;
double-down minor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;B^^,&lt;br /&gt;
Cvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ta&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;973.58&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vm7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downminor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;teh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;996.23&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;16/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;minor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;te&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1018.87&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^m7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upminor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;tu&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1041.51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/6, 20/11, 729/400&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v~7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmid 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C^^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;tuh&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1064.15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;13/7, 24/13, 50/27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^~7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmid 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#vv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;ti&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1086.79&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;15/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;vM7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;downmajor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#v&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;tih&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1109.43&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;40/21, 243/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;major 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;50&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;to&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1132.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;48/25, 27/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^M7&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;upmajor 7th&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#^&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;taw&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1154.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;125/64&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;^^M7,&lt;br /&gt;
vv8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;double-up major 7th,&lt;br /&gt;
double-down 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C#^^,&lt;br /&gt;
Dvv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;52&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;da&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1177.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;160/81&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;v8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;down 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Dv&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;do&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;P8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;perfect 8ve&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;D&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


Combining ups and downs notation with &lt;a class="wiki_link" href="/Kite%27s%20color%20notation"&gt;color notation&lt;/a&gt;, qualities can be loosely associated with colors:&lt;br /&gt;
[http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html Whisper Song in 53EDO] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3 play] by [[Prent_Rodgers|Prent Rodgers]]


[http://www.archive.org/details/TrioInOrwell Trio in Orwell] [http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]


&lt;table class="wiki_table"&gt;
[http://www.akjmusic.com/audio/desert_prayer.mp3 Desert Prayer] by [http://www.akjmusic.com/ Aaron Krister Johnson]
    &lt;tr&gt;
        &lt;th&gt;quality&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;color&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;monzo format&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;examples&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downminor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/6, 7/4&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fourthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;lt; -1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;32/27, 16/9&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upminor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6/5, 9/5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downmid&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;11/9, 11/6&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upmid&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;amber&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;12/11, 18/11&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;downmajor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;5/4, 5/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;major&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;fifthward white&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b}, b &amp;gt; 1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8, 27/16&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;upmajor&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;{a, b, 0, -1}&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/7, 12/7&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


All 53edo chords can be named using ups and downs. Here are the blue, green, jade, yellow and red triads:&lt;br /&gt;
[http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3 Whisper Song in 53 EDO] by [[Prent_Rodgers|Prent Rodgers]]


[http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho Elf Dine on Ho Ho] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3 play] and [http://andrewheathwaite.bandcamp.com/track/spun Spun] [http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3 play] by [[Andrew_Heathwaite|Andrew Heathwaite]]


&lt;table class="wiki_table"&gt;
[http://chrisvaisvil.com/the-fallen-of-kleismic15/ The Fallen of Kleismic15][http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]]
    &lt;tr&gt;
        &lt;th&gt;color of the 3rd&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;JI chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes as edosteps&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;notes of C chord&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;written name&lt;br /&gt;
&lt;/th&gt;
        &lt;th&gt;spoken name&lt;br /&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;blue&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6:7:9&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-12-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ebv G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.vm&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downminor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;green&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;10:12:15&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-14-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Eb^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.^m&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C upminor&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;jade&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;18:22:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-15-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Eb^^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.v~&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downmid&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;yellow&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4:5:6&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-17-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C Ev G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.v&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C downmajor or C dot down&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;red&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;14:18:27&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0-19-31&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C E^ G&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C.^&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;C upmajor or C dot up&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


For a more complete list, see &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Ups%20and%20Downs%20Notation#Chord%20names%20in%20other%20EDOs"&gt;Ups and Downs Notation - Chord names in other EDOs&lt;/a&gt;.&lt;br /&gt;
[https://soundcloud.com/cam-taylor-2-1/mothers mothers] by Cam Taylor
&lt;br /&gt;
[[Category:amity]]
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Compositions&lt;/h1&gt;
[[Category:athene]]
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/prelude1-53.mp3" rel="nofollow"&gt;Bach WTC1 Prelude 1 in 53&lt;/a&gt; by Bach and &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Mykhaylo%20Khramov"&gt;Mykhaylo Khramov&lt;/a&gt;&lt;br /&gt;
[[Category:big_brother]]
&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Khramov/fugue1-53.mp3" rel="nofollow"&gt;Bach WTC1 Fugue 1 in 53&lt;/a&gt; by Bach and Mykhaylo Khramov&lt;br /&gt;
[[Category:edo]]
&lt;a class="wiki_link_ext" href="http://bumpermusic.blogspot.com/2007/05/whisper-song-in-53-edo-now-526-slower.html" rel="nofollow"&gt;Whisper Song in 53EDO&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prent/sing53-c5-slow.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Prent%20Rodgers"&gt;Prent Rodgers&lt;/a&gt;&lt;br /&gt;
[[Category:hanson]]
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/TrioInOrwell" rel="nofollow"&gt;Trio in Orwell&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://www.archive.org/download/TrioInOrwell/TrioInOrwell.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Gene%20Ward%20Smith"&gt;Gene Ward Smith&lt;/a&gt;&lt;br /&gt;
[[Category:kleismic]]
&lt;a class="wiki_link_ext" href="http://www.akjmusic.com/audio/desert_prayer.mp3" rel="nofollow"&gt;Desert Prayer&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.akjmusic.com/" rel="nofollow"&gt;Aaron Krister Johnson&lt;/a&gt;&lt;br /&gt;
[[Category:listen]]
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/sing53-c5-slow.mp3" rel="nofollow"&gt;Whisper Song in 53 EDO&lt;/a&gt; by &lt;a class="wiki_link" href="/Prent%20Rodgers"&gt;Prent Rodgers&lt;/a&gt;&lt;br /&gt;
[[Category:marvel]]
&lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/elf-dine-on-ho-ho" rel="nofollow" target="_blank"&gt;Elf Dine on Ho Ho&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2005%20Elf%20Dine%20on%20Ho%20Ho.mp3" rel="nofollow"&gt;play&lt;/a&gt; and &lt;a class="wiki_link_ext" href="http://andrewheathwaite.bandcamp.com/track/spun" rel="nofollow" target="_blank"&gt;Spun&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Heathwaite/Newbeams/Andrew%20Heathwaite%20-%20Newbeams%20-%2008%20Spun.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;&lt;br /&gt;
[[Category:orwell]]
&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/the-fallen-of-kleismic15/" rel="nofollow"&gt;The Fallen of Kleismic15&lt;/a&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/53edo/20130903_Kleismic%5b15%5d.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;&lt;br /&gt;
[[Category:prime_edo]]
&lt;a class="wiki_link_ext" href="https://soundcloud.com/cam-taylor-2-1/mothers" rel="nofollow"&gt;mothers&lt;/a&gt; by Cam Taylor&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:pythagorean]]
[[Category:schismic]]
[[Category:semicomma]]
[[Category:zeta]]
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