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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2014-03-11 13:33:00 UTC</tt>.<br>
: The original revision id was <tt>495066470</tt>.<br>
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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]]
//50edo// divides the [[octave]] into 50 equal parts of precisely 24 [[cent]]s each. In the [[5-limit]], it tempers out 81/80, making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In [[http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf|"Harmonics or the Philosophy of Musical Sounds"]] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the [[Target tunings|least squares]] tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7_4|7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11_8|11/8]] and [[13_8|13/8]] are nearly pure.


50 tempers out 126/125 in the [[7-limit]], indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the [[11-limit]] and 105/104, 144/143 and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the 15&amp;50 temperament. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], 6115295232/6103515625 = |23 6 -14&gt;, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.
== Theory ==
As an equal temperament, 50et [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a [[meantone]] system, and in that capacity has historically drawn some notice; it is a somewhat sharp approximation of [[2/7-comma meantone]] (and is almost exactly 5/18-comma meantone). In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts &ndash; 50edo, in one word. Later, {{w|W. S. B. Woolhouse}} noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher-limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is also the highest edo where the mapping of [[9/8]] and [[10/9]] to the same interval is [[consistent]], with two stacked fifths falling almost exactly 3/7-syntonic-comma sharp of 10/9 and 4/7-comma flat of 9/8. It also maps all [[15-odd-limit]] intervals consistently, with the sole exceptions of 11/9 and 18/11.


[[http://www.archive.org/details/harmonicsorphilo00smit|Robert Smith's book online]]
It tempers out [[126/125]], [[225/224]] and [[3136/3125]] in the [[7-limit]], indicating it [[support]]s septimal meantone; [[245/242]], [[385/384]] and [[540/539]] in the [[11-limit]] and [[105/104]], [[144/143]] and 196/195 in the [[13-limit]], and can be used for even higher limits. Aside from meantone and its extension [[meanpop]], it can be used to advantage for the [[coblack]] temperament (15 &amp; 50), and provides the optimal patent val for 11- and 13-limit [[Meantone family #Bimeantone|bimeantone]]. It is also the unique equal temperament tempering out both 81/80 and the [[vishnuzma]], {{monzo| 23 6 -14 }}, so that in 50edo seven chromatic semitones stack to a perfect fourth. By comparison, this gives a perfect fifth in 12edo, a doubly diminished fifth in 31edo, and a diminished fourth in 19edo.
[[http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html|More information about Robert Smith's temperament]]


=Relations=  
=== Odd harmonics ===
The 50-edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "Golden Tone System" ([[Das Goldene Tonsystem]]) of Thorvald Kornerup.
{{Harmonics in equal|50|columns=15}}


=Intervals=  
=== Relations ===
|| Degrees of 50-EDO || Cents value ||
The 50edo system is related to [[7edo]], [[12edo]], [[19edo]], [[31edo]] as the next approximation to the "[[Golden meantone|Golden Tone System]]" ([[Das Goldene Tonsystem]]) of [[Thorvald Kornerup]] (and similarly as the next step from 31edo in [[Joseph Yasser]]'s "[https://books.google.com.au/books/about/A_theory_of_evolving_tonality.html?id=-XUsAAAAMAAJ&redir_esc=y A Theory of Evolving Tonality]").
|| 0 || 0 ||
|| 1 || 24 ||
|| 2 || 48 ||
|| 3 || 72 ||
|| 4 || 96 ||
|| 5 || 120 ||
|| 6 || 144 ||
|| 7 || 168 ||
|| 8 || 192 ||
|| 9 || 216 ||
|| 10 || 240 ||
|| 11 || 264 ||
|| 12 || 288 ||
|| 13 || 312 ||
|| 14 || 336 ||
|| 15 || 360 ||
|| 16 || 384 ||
|| 17 || 408 ||
|| 18 || 432 ||
|| 19 || 456 ||
|| 20 || 480 ||
|| 21 || 504 ||
|| 22 || 528 ||
|| 23 || 552 ||
|| 24 || 576 ||
|| 25 || 600 ||
|| 26 || 624 ||
|| 27 || 648 ||
|| 28 || 672 ||
|| 29 || 696 ||
|| 30 || 720 ||
|| 31 || 744 ||
|| 32 || 768 ||
|| 33 || 792 ||
|| 34 || 816 ||
|| 35 || 840 ||
|| 36 || 864 ||
|| 37 || 888 ||
|| 38 || 912 ||
|| 39 || 936 ||
|| 40 || 960 ||
|| 41 || 984 ||
|| 42 || 1008 ||
|| 43 || 1032 ||
|| 44 || 1056 ||
|| 45 || 1080 ||
|| 46 || 1104 ||
|| 47 || 1128 ||
|| 48 || 1152 ||
|| 49 || 1176 ||


==Intervals by patent val error==  
== Intervals ==
|| Interval || Error ||
{| class="wikitable center-all right-2 left-3"
|| 16/13 || 0.528 ||
|-
|| 15/14 || 0.557 ||
! &#35;
|| 11/8 || 0.682 ||
! Cents
|| 13/11 || -1.210 ||
! Ratios<ref group="note">{{sg|13-limit}}</ref>
|| 13/10 || 1.786 ||
! colspan="3" | [[Ups and downs notation]]
|| 5/4 || -2.314 ||
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and vvd2)
|| 7/6 || -2.871 ||
|-
|| 11/10 || 2.996 ||
| 0
|| 9/7 || -3.084 ||
| 0
|| 6/5 || -3.641 ||
| 1/1
|| 13/12 || 5.427 ||
| Perfect 1sn
|| 4/3 || 5.955 ||
| P1
|| 7/5 || -6.512 ||
| D
|| 12/11 || -6.637 ||
|-
|| 15/13 || -7.741 ||
| 1
|| 16/15 || 8.269 ||
| 24
|| 14/13 || -8.298 ||
| 45/44, 49/48, 56/55, 65/64, 66/65, 78/77, 91/90, 99/98, 100/99, 121/120, 169/168
|| 8/7 || 8.826 ||
| Up 1sn
|| 15/11 || -8.951 ||
| ^1
|| 14/11 || -9.508 ||
| ^D
|| 10/9 || 9.596 ||
|-
|| 18/13 || -11.382 ||
| 2
|| 9/8 || -11.910 ||
| 48
|| 11/9 || 12.592 ||
| 27/26, 33/32, 36/35, 50/49, 55/54, 64/63
| Dim 2nd, Downaug 1sn
| d2, vA1
| Ebb, vD#
|-
| 3
| 72
| 21/20, 25/24, 26/25, 28/27
| Aug 1sn, Updim 2nd
| A1, ^d2
| D#, ^Ebb
|-
| 4
| 96
| 22/21
| Downminor 2nd
| vm2
| vEb
|-
| 5
| 120
| 16/15, 15/14, 14/13
| Minor 2nd
| m2
| Eb
|-
| 6
| 144
| 13/12, 12/11
| Upminor 2nd
| ^m2
| ^Eb
|-
| 7
| 168
| 11/10
| Downmajor 2nd
| vM2
| vE
|-
| 8
| 192
| 9/8, 10/9
| Major 2nd
| M2
| E
|-
| 9
| 216
| 25/22
| Upmajor 2nd
| ^M2
| ^E
|-
| 10
| 240
| 8/7, 15/13
| Downaug 2nd, Dim 3rd
| vA2, d3
| vE#, Fb
|-
| 11
| 264
| 7/6
| Updim 3rd, Aug 2nd
| ^d3, A2
| ^Fb, E#
|-
| 12
| 288
| 13/11
| Downminor 3rd
| vm3
| vF
|-
| 13
| 312
| 6/5
| Minor 3rd
| m3
| F
|-
| 14
| 336
| 27/22, 39/32, 40/33, 49/40
| Upminor 3rd
| ^m3
| ^F
|-
| 15
| 360
| 16/13, 11/9
| Downmajor 3rd
| vM3
| vF#
|-
| 16
| 384
| 5/4
| Major 3rd
| M3
| F#
|-
| 17
| 408
| 14/11
| Upmajor 3rd
| ^M3
| ^F#
|-
| 18
| 432
| 9/7
| Downaug 3rd, Dim 4th
| vA3, d4
| vFx, Gb
|-
| 19
| 456
| 13/10
| Updim 4th, Aug 3rd
| A3, ^d4
| ^Gb, Fx
|-
| 20
| 480
| 33/25, 55/42, 64/49
| Down 4th
| v4
| vG
|-
| 21
| 504
| 4/3
| Perfect 4th
| P4
| G
|-
| 22
| 528
| 15/11
| Up 4th
| ^4
| ^G
|-
| 23
| 552
| 11/8, 18/13
| Downaug 4th
| vA4
| vG#
|-
| 24
| 576
| 7/5
| Aug 4th
| A4
| G#
|-
| 25
| 600
| 63/44, 88/63, 78/55, 55/39
| Upaug 4th, Downdim 5th
| ^A4, vd5
| ^G#, vAb
|-
| 26
| 624
| 10/7
| Dim 5th
| d5
| Ab
|-
| 27
| 648
| 16/11, 13/9
| Updim 5th
| ^d5
| ^Ab
|-
| 28
| 672
| 22/15
| Down 5th
| v5
| vA
|-
| 29
| 696
| 3/2
| Perfect 5th
| P5
| A
|-
| 30
| 720
| 50/33, 84/55, 49/32
| Up 5th
| ^5
| ^A
|-
| 31
| 744
| 20/13
| Downaug 5th, Dim 6th
| vA5, d6
| vA#, Bbb
|-
| 32
| 768
| 14/9
| Updim 6th, Aug 5th
| ^d6, A5
| ^Bbb, A#
|-
| 33
| 792
| 11/7
| Downminor 6th
| vm6
| vBb
|-
| 34
| 816
| 8/5
| Minor 6th
| m6
| Bb
|-
| 35
| 840
| 13/8, 18/11
| Upminor 6th
| ^m6
| ^Bb
|-
| 36
| 864
| 44/27, 64/39, 33/20, 80/49
| Downmajor 6th
| vM6
| vB
|-
| 37
| 888
| 5/3
| Major 6th
| M6
| B
|-
| 38
| 912
| 22/13
| Upmajor 6th
| ^M6
| ^B
|-
| 39
| 936
| 12/7
| Downaug 6th, Dim 7th
| vA6, d7
| vB#, Cb
|-
| 40
| 960
| 7/4
| Updim 7th, Aug 6th
| ^d7, A6
| ^Cb, B#
|-
| 41
| 984
| 44/25
| Downminor 7th
| vm7
| vC
|-
| 42
| 1008
| 16/9, 9/5
| Minor 7th
| m7
| C
|-
| 43
| 1032
| 20/11
| Upminor 7th
| ^m7
| ^C
|-
| 44
| 1056
| 24/13, 11/6
| Downmajor 7th
| vM7
| vC#
|-
| 45
| 1080
| 15/8, 28/15, 13/7
| Major 7th
| M7
| C#
|-
| 46
| 1104
| 21/11
| Upmajor 7th
| ^M7
| ^C#
|-
| 47
| 1128
| 40/21, 48/25, 25/13, 27/14
| Downaug 7th, Dim 8ve
| vA7, d8
| vCx, Db
|-
| 48
| 1152
| 52/27, 64/33, 35/18, 49/25, 108/55, 63/32
| Updim 8ve, Aug 7th
| ^d8, A7
| ^Db, Cx
|-
| 49
| 1176
| 88/45, 96/49, 55/28, 128/65, 65/33, 77/39, 180/91, 196/99, 99/50, 240/121, 336/169
| Down 8ve
| v8
| vD
|-
| 50
| 1200
| 2/1
| Perfect 8ve
| P8
| D
|}


=Commas=  
== Notation ==
50 EDO tempers out the following commas. (Note: This assumes the val &lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
=== Ups and downs notation ===
||~ ===In ket format=== ||~ ===In cents=== ||~ ===Ratio=== ||~ ===Name 1=== ||~ ===Name2=== ||
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
|| | -4 4 -1 &gt; ||&gt; 21.51 ||= 81/80 || Syntonic comma || Didymus comma ||
{{sharpness-sharp3a}}
|| | 23 6 -14 &gt; ||&gt; 3.34 ||= 6115295232/6103515625 || Vishnu comma ||  ||
|| | 1 2 -3 1 &gt; ||&gt; 13.79 ||= 126/125 || Starling comma || Small septimal comma ||
|| | -5 2 2 -1 &gt; ||&gt; 7.71 ||= 225/224 || Septimal kleisma || Marvel comma ||
|| | 6 0 -5 2 &gt; ||&gt; 6.08 ||= 3136/3125 || Hemimean || Middle second comma ||
|| | -6 -8 2 5 &gt; ||&gt; 1.12 ||= 420175/419904 || Wizma ||  ||
|| |-11 2 7 -3 &gt; ||&gt; 1.63 ||= 703125/702464 || Meter ||  ||
|| | 11 -10 -10 10 &gt; ||&gt; 5.57 ||= 578509309952/576650390625 || Linus ||  ||
|| |-13 10 0 -1 &gt; ||&gt; 50.72 ||= 59049/57344 || Harrison's comma ||  ||
|| | 2 3 1 -2 -1 &gt; ||&gt; 3.21 ||= 540/539 || Swets' comma || Swetisma ||
|| | -3 4 -2 -2 2 &gt; ||&gt; 0.18 ||= 9801/9800 || Kalisma || Gauss' comma ||
|| | 5 -1 3 0 -3 &gt; ||&gt; 3.03 ||= 4000/3993 || Wizardharry || Undecimal schisma ||
|| | -7 -1 1 1 1 &gt; ||&gt; 4.50 ||= 385/384 || Keenanisma || Undecimal kleisma ||
|| | -1 0 1 2 -2 &gt; ||&gt; 21.33 ||= 245/242 || Cassacot ||  ||
|| | 2 -1 0 1 -2 1 &gt; ||&gt; 4.76 ||= 364/363 || Gentle comma ||  ||
|| | 2 -1 -1 2 0 -1 &gt; ||&gt; 8.86 ||= 196/195 || Mynucuma ||  ||
|| | 2 3 0 -1 1 -2 &gt; ||&gt; 7.30 ||= 1188/1183 || Kestrel Comma ||  ||
|| | 3 0 2 0 1 -3 &gt; ||&gt; 2.36 ||= 2200/2197 || Petrma || Parizek comma ||
|| | -3 1 1 1 0 -1 &gt; ||&gt; 16.57 ||= 105/104 || Animist comma || Small tridecimal comma ||  ||
|| | 4 2 0 0 -1 -1 &gt; ||&gt; 12.06 ||= 144/143 || Grossma ||  ||
|| | 3 -2 0 1 -1 -1 0 0 1 &gt; ||&gt; 1.34 ||= 1288/1287 || Triaphonisma ||  ||


[[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3|Twinkle canon – 50 edo]] by [[http://soonlabel.com/xenharmonic/archives/573|Claudi Meneghin]]
Using [[Helmholtz–Ellis]] accidentals, 50edo can also be notated using [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]:
[[@http://soonlabel.com/xenharmonic/archives/1118|Fantasia Catalana by Claudi Meneghin]]
{{Sharpness-sharp3}}
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;
Here, a sharp raises by three steps, and a flat lowers by three steps, so arrows can be used to fill in the gap. If the arrows are taken to have their own layer of enharmonic spellings, some notes may be best spelled with double arrows.
[[http://soonlabel.com/xenharmonic/archives/1929|Fugue on the Dragnet theme by Claudi Meneghin]]
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -8 8 -2 &gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 23 6 -14 &gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 1 2 -3 1 &gt; 13.79 126/125 small septimal comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -5 2 2 -1 &gt; 7.71 225/224 septimal kleisma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 6 0 -5 2 &gt; 6.08 3136/3125 middle second comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -6 -8 2 5 &gt; 1.12 420175/419904&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-11 2 7 -3 &gt; 1.63 703125/702464&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 11 -10 -10 10 &gt; 5.57 6772805/6751042&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-13 10 0 -1 &gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 1 -2 -1 &gt; 3.21 540/539 Swets' comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 4 -2 -2 2 &gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 5 -1 3 0 -3 &gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -7 -1 1 1 1 &gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 -1 0 1 -2 1 &gt; 4.76 364/363&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 0 -1 1 -2 &gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 -2 0 1 -1 -1 0 0 1 &gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;
</pre></div>
<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;50edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:18:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Relations"&gt;Relations&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Intervals"&gt;Intervals&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Intervals-Intervals by patent val error"&gt;Intervals by patent val error&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Commas"&gt;Commas&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Commas--In ket format"&gt;In ket format&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Commas--In cents"&gt;In cents&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Commas--Ratio"&gt;Ratio&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Commas--Name 1"&gt;Name 1&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Commas--Name2"&gt;Name2&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;em&gt;50edo&lt;/em&gt; divides the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 50 equal parts of precisely 24 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s each. In the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, it tempers out 81/80, making it a &lt;a class="wiki_link" href="/meantone"&gt;meantone&lt;/a&gt; system, and in that capacity has historically has drawn some notice. In &lt;a class="wiki_link_ext" href="http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf" rel="nofollow"&gt;&amp;quot;Harmonics or the Philosophy of Musical Sounds&amp;quot;&lt;/a&gt; (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts - 50edo, in one word. Later W. S. B. Woolhouse noted it was fairly close to the &lt;a class="wiki_link" href="/Target%20tunings"&gt;least squares&lt;/a&gt; tuning for 5-limit meantone. 50, however, is especially interesting from a higher limit point of view. While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; extends meantone with a &lt;a class="wiki_link" href="/7_4"&gt;7/4&lt;/a&gt; which is nearly pure, 50 has a flat 7/4 but both &lt;a class="wiki_link" href="/11_8"&gt;11/8&lt;/a&gt; and &lt;a class="wiki_link" href="/13_8"&gt;13/8&lt;/a&gt; are nearly pure.&lt;br /&gt;
&lt;br /&gt;
50 tempers out 126/125 in the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, indicating it supports septimal meantone; 245/242, 385/384 and 540/539 in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt; and 105/104, 144/143 and 196/195 in the &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;, and can be used for even higher limits. Aside from meantone and its extension meanpop, it can be used to advantage for the 15&amp;amp;50 temperament. It is also the unique equal temperament tempering out both 81/80 and the &lt;a class="wiki_link" href="/vishnuzma"&gt;vishnuzma&lt;/a&gt;, 6115295232/6103515625 = |23 6 -14&amp;gt;, so that in 50et seven chromatic semitones are a perfect fourth. In 12et by comparison this gives a fifth, in 31et a doubly diminished fifth, and in 19et a diminished fourth.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.archive.org/details/harmonicsorphilo00smit" rel="nofollow"&gt;Robert Smith's book online&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html" rel="nofollow"&gt;More information about Robert Smith's temperament&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Relations"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Relations&lt;/h1&gt;
The 50-edo system is related to &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;, &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; as the next approximation to the &amp;quot;Golden Tone System&amp;quot; (&lt;a class="wiki_link" href="/Das%20Goldene%20Tonsystem"&gt;Das Goldene Tonsystem&lt;/a&gt;) of Thorvald Kornerup.&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="Intervals"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Intervals&lt;/h1&gt;


&lt;table class="wiki_table"&gt;
=== Sagittal notation ===
    &lt;tr&gt;
This notation uses the same sagittal sequence as EDOs [[57edo#Sagittal notation|57]], [[64edo#Sagittal notation|64]], and [[71edo#Second-best fifth notation|71b]].
        &lt;td&gt;Degrees of 50-EDO&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cents value&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;48&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;72&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;96&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;120&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;144&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;168&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;192&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;216&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;240&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;264&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;288&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;312&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;336&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;360&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;384&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;408&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;432&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;456&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;20&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;480&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;504&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;22&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;528&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;552&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;24&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;576&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;600&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;624&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;648&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;28&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;672&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;696&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;30&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;720&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;744&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;768&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;792&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;34&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;816&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;36&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;864&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;888&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;38&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;912&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;936&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;40&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;960&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;984&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;42&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1008&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1032&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;44&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1056&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1080&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;46&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1104&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1128&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1152&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1176&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
==== Evo flavor ====
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Intervals-Intervals by patent val error"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Intervals by patent val error&lt;/h2&gt;
<imagemap>
File:50-EDO_Evo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 599 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[1053/1024]]
default [[File:50-EDO_Evo_Sagittal.svg]]
</imagemap>


&lt;table class="wiki_table"&gt;
==== Revo flavor ====
    &lt;tr&gt;
<imagemap>
        &lt;td&gt;Interval&lt;br /&gt;
File:50-EDO_Revo_Sagittal.svg
&lt;/td&gt;
desc none
        &lt;td&gt;Error&lt;br /&gt;
rect 80 0 300 50 [[Sagittal_notation]]
&lt;/td&gt;
rect 300 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
    &lt;/tr&gt;
rect 20 80 160 106 [[1053/1024]]
    &lt;tr&gt;
default [[File:50-EDO_Revo_Sagittal.svg]]
        &lt;td&gt;16/13&lt;br /&gt;
</imagemap>
&lt;/td&gt;
        &lt;td&gt;0.528&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/14&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.557&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.682&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-1.210&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1.786&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2.314&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/6&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-2.871&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/10&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2.996&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3.084&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-3.641&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13/12&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.427&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5.955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6.512&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-6.637&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-7.741&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.269&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-8.298&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8/7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;8.826&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-8.951&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-9.508&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9.596&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;18/13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-11.382&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;-11.910&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11/9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;12.592&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Commas"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Commas&lt;/h1&gt;
50 EDO tempers out the following commas. (Note: This assumes the val &amp;lt; 50 79 116 140 173 185 204 212 226 |, comma values rounded to 2 decimal places.) This list is not all-inclusive, and is based on the interval table from Scala version 2.2.&lt;br /&gt;


== Approximation to JI ==
[[File:50ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 29-limit intervals approximated in 50edo]]


&lt;table class="wiki_table"&gt;
=== 15-odd-limit interval mappings ===
    &lt;tr&gt;
{{Q-odd-limit intervals|50|15}}
        &lt;th&gt;&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Commas--In ket format"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;In ket format&lt;/h3&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Commas--In cents"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;In cents&lt;/h3&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Commas--Ratio"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Ratio&lt;/h3&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="Commas--Name 1"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Name 1&lt;/h3&gt;
&lt;/th&gt;
        &lt;th&gt;&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="Commas--Name2"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Name2&lt;/h3&gt;
&lt;/th&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -4 4 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;21.51&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;81/80&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Syntonic comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Didymus comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 23 6 -14 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;6115295232/6103515625&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Vishnu comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 1 2 -3 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;13.79&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;126/125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Starling comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Small septimal comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -5 2 2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;7.71&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;225/224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Septimal kleisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Marvel comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 6 0 -5 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;6.08&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3136/3125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Hemimean&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Middle second comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -6 -8 2 5 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1.12&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;420175/419904&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Wizma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|-11 2 7 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1.63&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;703125/702464&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Meter&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 11 -10 -10 10 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;5.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;578509309952/576650390625&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Linus&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;|-13 10 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;50.72&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;59049/57344&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Harrison's comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 2 3 1 -2 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.21&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;540/539&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Swets' comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Swetisma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -3 4 -2 -2 2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;0.18&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9801/9800&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Kalisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gauss' comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 5 -1 3 0 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;3.03&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;4000/3993&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Wizardharry&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Undecimal schisma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -7 -1 1 1 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.50&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;385/384&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Keenanisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Undecimal kleisma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -1 0 1 2 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;21.33&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;245/242&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Cassacot&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 2 -1 0 1 -2 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;4.76&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;364/363&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Gentle comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 2 -1 -1 2 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;8.86&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;196/195&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Mynucuma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 2 3 0 -1 1 -2 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;7.30&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1188/1183&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Kestrel Comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 3 0 2 0 1 -3 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;2.36&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2200/2197&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Petrma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Parizek comma&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| -3 1 1 1 0 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;16.57&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;105/104&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Animist comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Small tridecimal comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 4 2 0 0 -1 -1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;12.06&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;144/143&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Grossma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;| 3 -2 0 1 -1 -1 0 0 1 &amp;gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: right;"&gt;1.34&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1288/1287&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Triaphonisma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;br /&gt;
== Regular temperament properties ==
&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3" rel="nofollow"&gt;Twinkle canon – 50 edo&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow"&gt;Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
=== Temperament measures ===
&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1118" rel="nofollow" target="_blank"&gt;Fantasia Catalana by Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
{| class="wikitable center-4 center-5 center-6"
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -4 4 -1 &amp;gt; 21.51 81/80 syntonic comma, Didymus comma&lt;/span&gt;&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/1929" rel="nofollow"&gt;Fugue on the Dragnet theme by Claudi Meneghin&lt;/a&gt;&lt;br /&gt;
! rowspan="2" | [[Subgroup]]
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -8 8 -2 &amp;gt; 43.01 6561/6400 Mathieu superdiesis&lt;/span&gt;&lt;br /&gt;
! rowspan="2" | [[Comma list]]
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 23 6 -14 &amp;gt; 3.34 1212717/1210381 Vishnu comma&lt;/span&gt;&lt;br /&gt;
! rowspan="2" | [[Mapping]]
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 1 2 -3 1 &amp;gt; 13.79 126/125 small septimal comma&lt;/span&gt;&lt;br /&gt;
! rowspan="2" | Optimal<br>8ve stretch (¢)
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -5 2 2 -1 &amp;gt; 7.71 225/224 septimal kleisma&lt;/span&gt;&lt;br /&gt;
! colspan="2" | Tuning error
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 6 0 -5 2 &amp;gt; 6.08 3136/3125 middle second comma&lt;/span&gt;&lt;br /&gt;
|-
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -6 -8 2 5 &amp;gt; 1.12 420175/419904&lt;/span&gt;&lt;br /&gt;
! [[TE error|Absolute]] (¢)
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-11 2 7 -3 &amp;gt; 1.63 703125/702464&lt;/span&gt;&lt;br /&gt;
! [[TE simple badness|Relative]] (%)
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 11 -10 -10 10 &amp;gt; 5.57 6772805/6751042&lt;/span&gt;&lt;br /&gt;
|-
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;|-13 10 0 -1 &amp;gt; 50.72 59049/57344 Harrison's comma&lt;/span&gt;&lt;br /&gt;
| 2.3
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 1 -2 -1 &amp;gt; 3.21 540/539 Swets' comma&lt;/span&gt;&lt;br /&gt;
| {{monzo| -79 50 }}
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 4 -2 -2 2 &amp;gt; 0.18 9801/9800 kalisma, Gauss' comma&lt;/span&gt;&lt;br /&gt;
| {{mapping| 50 79 }}
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 5 -1 3 0 -3 &amp;gt; 3.03 4000/3993 undecimal schisma&lt;/span&gt;&lt;br /&gt;
| +1.88
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -7 -1 1 1 1 &amp;gt; 4.50 385/384 undecimal kleisma&lt;/span&gt;&lt;br /&gt;
| 1.88
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 -1 0 1 -2 1 &amp;gt; 4.76 364/363&lt;/span&gt;&lt;br /&gt;
| 7.83
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 2 3 0 -1 1 -2 &amp;gt; 7.30 1188/1183 Kestrel Comma&lt;/span&gt;&lt;br /&gt;
|-
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 0 2 0 1 -3 &amp;gt; 2.36 2200/2197 Parizek comma&lt;/span&gt;&lt;br /&gt;
| 2.3.5
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| -3 1 1 1 0 -1 &amp;gt; 16.57 105/104 small tridecimal comma&lt;/span&gt;&lt;br /&gt;
| 81/80, {{monzo| -27 -2 13 }}
&lt;span style="display: block; height: 1px; left: -40px; overflow: hidden; position: absolute; top: 5675.5px; width: 1px;"&gt;| 3 -2 0 1 -1 -1 0 0 1 &amp;gt; 1.34 1288/1287 triaphonisma&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
| {{mapping| 50 79 116 }}
| +1.58
| 1.59
| 6.62
|-
| 2.3.5.7
| 81/80, 126/125, 84035/82944
| {{mapping| 50 79 116 140 }}
| +1.98
| 1.54
| 6.39
|-
| 2.3.5.7.11
| 81/80, 126/125, 245/242, 385/384
| {{mapping| 50 79 116 140 173 }}
| +1.54
| 1.63
| 6.76
|-
| 2.3.5.7.11.13
| 81/80, 105/104, 126/125, 144/143, 245/242
| {{mapping| 50 79 116 140 173 185 }}
| +1.31
| 1.57
| 6.54
|}
 
=== Commas ===
50et [[tempering out|tempers out]] the following [[comma]]s. This assumes the [[val]] {{val| 50 79 116 140 173 185 204 212 226 }}, comma values in cents rounded to 2 decimal places. This list is not all-inclusive, and is based on the interval table from Scala version 2.2.
 
{| class="commatable wikitable center-all left-3 right-4 left-5"
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Cent]]s
! Name
|-
| 3
| <abbr title="717897987691852588770249/604462909807314587353088">(20 digits)</abbr>
| {{monzo| -79 50 }}
| 297.75
| 50-comma
|-
| 5
| [[81/80]]
| {{monzo| -4 4 -1 }}
| 21.51
| Syntonic comma
|-
| 5
| <abbr title="1220703125/1207959552">(20 digits)</abbr>
| {{monzo| -27 -2 13 }}
| 18.17
| [[Ditonma]]
|-
| 5
| [[6115295232/6103515625|(20 digits)]]
| {{monzo| 23 6 -14 }}
| 3.34
| [[Vishnuzma]]
|-
| 7
| [[59049/57344]]
| {{monzo| -13 10 0 -1 }}
| 50.72
| Harrison's comma
|-
| 7
| [[16807/16384]]
| {{monzo| -14 0 0 5}}
| 44.13
| Cloudy comma
|-
| 7
| [[3645/3584]]
| {{monzo| -9 6 1 -1 }}
| 29.22
| Schismean comma
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.79
| Starling comma
|-
| 7
| [[225/224]]
| {{monzo| -5 2 2 -1 }}
| 7.71
| Marvel comma
|-
| 7
| [[3136/3125]]
| {{monzo| 6 0 -5 2 }}
| 6.08
| Hemimean comma
|-
| 7
| <abbr title="578509309952/576650390625">(24 digits)</abbr>
| {{monzo| 11 -10 -10 10 }}
| 5.57
| [[Linus comma]]
|-
| 7
| [[703125/702464|(12 digits)]]
| {{monzo| -11 2 7 -3 }}
| 1.63
| [[Meter]]
|-
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| {{monzo| -6 -8 2 5 }}
| 1.12
| [[Wizma]]
|-
| 11
| [[245/242]]
| {{monzo| -1 0 1 2 -2 }}
| 21.33
| Frostma
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| Keenanisma
|-
| 11
| [[540/539]]
| {{monzo| 2 3 1 -2 -1 }}
| 3.21
| Swetisma
|-
| 11
| [[4000/3993]]
| {{monzo| 5 -1 3 0 -3 }}
| 3.03
| Wizardharry comma
|-
| 11
| [[9801/9800]]
| {{monzo| -3 4 -2 -2 2 }}
| 0.18
| Kalisma
|-
| 13
| [[105/104]]
| {{monzo| -3 1 1 1 0 -1 }}
| 16.57
| Animist comma
|-
| 13
| [[144/143]]
| {{monzo| 4 2 0 0 -1 -1 }}
| 12.06
| Grossma
|-
| 13
| [[196/195]]
| {{monzo| 2 -1 -1 2 0 -1 }}
| 8.86
| Mynucuma
|-
| 13
| [[1188/1183]]
| {{monzo| 2 3 0 -1 1 -2 }}
| 7.30
| Kestrel comma
|-
| 13
| [[31213/31104]]
| {{monzo| -7 -5 0 4 0 1 }}
| 6.06
| Praveensma
|-
| 13
| [[364/363]]
| {{monzo| 2 -1 0 1 -2 1 }}
| 4.76
| Minor minthma
|-
| 13
| [[2200/2197]]
| {{monzo| 3 0 2 0 1 -3 }}
| 2.36
| Petrma
|-
| 17
| [[170/169]]
| {{monzo| 1 0 1 0 0 -2 1 }}
| 10.21
| Major naiadma
|-
| 17
| [[221/220]]
| {{monzo| -2 0 -1 0 -1 1 1 }}
| 7.85
| Minor naiadma
|-
| 17
| [[289/288]]
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| Semitonisma
|-
| 17
| [[375/374]]
| {{monzo| -1 1 3 0 -1 0 -1 }}
| 4.62
| Ursulisma
|-
| 19
| [[153/152]]
| {{monzo| -3 2 0 0 0 0 1 -1 }}
| 11.35
| Ganassisma
|-
| 19
| [[171/170]]
| {{monzo| -1 2 -1 0 0 0 -1 1}}
| 10.15
| Malcolmisma
|-
| 19
| [[210/209]]
| {{monzo| 1 1 1 1 -1 0 0 1}}
| 8.26
| Spleen comma
|-
| 19
| [[324/323]]
| {{monzo| 2 4 0 0 0 0 -1 -1 }}
| 5.35
| Photisma
|-
| 19
| [[361/360]]
| {{monzo| -3 -2 -1 0 0 0 0 2 }}
| 4.80
| Go comma
|-
| 19
| [[495/494]]
| {{monzo| -1 2 1 0 1 -1 0 -1 }}
| 3.50
| Eulalisma
|-
| 23
| [[507/506]]
| 2.3.11.13.23 {{monzo| -1 1 -1 2 -1 }}
| 3.42
| Laodicisma
|-
| 23
| [[529/528]]
| 2.3.11.23 {{monzo| -4 -1 -1 2 }}
| 3.28
| Preziosisma
|-
| 23
| [[576/575]]
| 2.3.5.23 {{monzo| 6 2 -2 -1 }}
| 3.01
| Worcester comma
|-
| 23
| [[1288/1287]]
| {{monzo| 3 -2 0 1 -1 -1 0 0 1 }}
| 1.34
| Triaphonisma
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperament
|-
| 1
| 1\50
| 24.0
| 686/675
| [[Sengagen]]
|-
| 1
| 9\50
| 216.0
| 17/15
| [[Tremka]]
|-
| 1
| 11\50
| 264.0
| 7/6
| [[Septimin]]
|-
| 1
| 13\50
| 312.0
| 6/5
| [[Oolong]]
|-
| 1
| 17\50
| 408.0
| 325/256
| [[Coditone]]
|-
| 1
| 19\50
| 456.0
| 125/96
| [[Qak]]
|-
| 1
| 21\50
| 504.0
| 4/3
| [[Meantone]] / [[meanpop]]
|-
| 1
| 23\50
| 552.0
| 11/8
| [[Emka]]
|-
| 2
| 2\50
| 48.0
| 36/35
| [[Pombe]]
|-
| 2
| 3\50
| 72.0
| 25/24
| [[Vishnu]] / [[vishnean]]
|-
| 2
| 6\50
| 144.0
| 12/11
| [[Bisemidim]]
|-
| 2
| 9\50
| 216.0
| 17/15
| [[Wizard]] / [[lizard]] / [[gizzard]]
|-
| 2
| 12\50
| 288.0
| 13/11
| [[Vines]]
|-
| 2
| 21\50<br>(4\50)
| 504.0<br>(96.0)
| 4/3<br>(35/33)
| [[Bimeantone]]
|-
| 5
| 21\50<br>(1\50)
| 504.0<br>(24.0)
| 4/3<br>(49/48)
| [[Cloudtone]]
|-
| 5
| 23<br>(3\50)
| 552.0<br>(72.0)
| 11/8<br>(21/20)
| [[Coblack]]
|-
| 10
| 7\50<br>(3\50)
| 168.0<br>(72.0)
| 54/49<br>(25/24)
| [[Decavish]]
|-
| 10
| 21\50<br>(1\50)
| 504.0<br>(24.0)
| 4/3<br>(78/77)
| [[Decic]]
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 
== Instruments ==
; Lumatone
 
See [[Lumatone mapping for 50edo]]
 
 
; Piano
 
A [[:Category:Piano|piano]] playing with a 50edo ensemble may wish to use the tuning [[116ed5]]. This tuning is almost exactly the same as 50edo, but with octaves [[octave stretch|stretched]] by 1 cent. Because pianos usually use stretched octaves, this tuning will sit better with the [[timbre]] of the piano, while still being close enough that it sounds perfectly in-tune with the other instruments tuned to 50edo.
 
== Music ==
=== Modern renderings ===
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=RnYqc0NKMLM "Ricercar a 3" from ''The Musical Offering'', BWV 1079] (1747) – rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=e6fMO-sue4Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) &ndash; rendered by Claudi Meneghin (2024)
* [https://www.youtube.com/watch?v=M3wQu4UF1pg "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) &ndash; rendered by Claudi Meneghin (2024, organ sound rendering)
* [https://www.youtube.com/watch?v=qjb9DDM32Ic "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742-1749) &mdash; rendered by Claudi Meneghin (2025, harpsichord sound rendering)
 
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=yrM50pvmD5c ''Prelude in E Minor "The Great"''] &ndash; rendered by Claudi Meneghin (2023)
 
; {{W|Gabriel Fauré}}
* [https://www.youtube.com/watch?v=7djfrUlw2ck  ''Pavane'', op. 50] (1887) &ndash; arranged for harpsichord and rendered by Claudi Meneghin (2020)
 
; {{W|Akira Kamiya}}
* [https://www.youtube.com/watch?v=5UnPAhRqmb4 ''funfunfun ta yo''] (2007) &ndash; rendered by MortisTheneRd (2024)
 
=== 21st century===
; [[Bryan Deister]]
* [https://www.youtube.com/shorts/zCsc5n6dr_I ''microtonal improv in 50edo''] (2024)
* [https://www.youtube.com/shorts/ynz5XvJOHiE ''Piano that may not be played that well - Deltarune (microtonal cover in 50edo)''] (2025)
 
; [[Francium]]
* [https://www.youtube.com/watch?v=pH6E35hwUnM ''On My Way To Somewhere''] (2023)
 
; [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon &ndash; 50 edo] {{dead link}}
* [https://www.youtube.com/watch?v=wcTVED9zFrU ''Blue Fugue for Organ''] (2018)
* [https://www.youtube.com/watch?v=Zh2jWoIXAf8 ''La Petite Poule Grise - Fugue''] (2019)
* [https://www.youtube.com/watch?v=28x3vqw9kDI ''Happy Birthday Canon'', 6-in-1 Canon in 50edo] (2019)
* [https://www.youtube.com/watch?v=szUpO3FAOes ''Fantasia Catalana''] (2020)
* [https://www.youtube.com/watch?v=38UMa3oWSIE ''Preludi Nocturn i Fuga sobre la Lluna la Pruna''] (2020)
* [https://www.youtube.com/watch?v=TRXy0FJOKIA ''Fugue on the Dragnet theme''] (2020)
* [https://www.youtube.com/watch?v=C4EkNEu4EeU ''Canon at the Semitone on The Mother's Malison Theme'', for Organ] (2022)
* [https://www.youtube.com/watch?v=FyDKSjS9Qtg ''Fugue on an Original Theme'', for Baroque Ensemble] (2023) ([https://www.youtube.com/watch?v=TXwlLV2TCsw for Organ])
* [https://www.youtube.com/watch?v=2nD_7Ot8-0A ''Catalan Fugue (La Santa Espina)''] (2023)
* [https://www.youtube.com/watch?v=TBxDmpM9Xa8 ''Canon in C='' for Baroque Wind Ensemble] (2023)
* [https://www.youtube.com/watch?v=sIr394fGEEg ''Fantasia Catalana'', for Baroque Ensemble] (2023)
 
; [[Cam Taylor]]
* [https://soundcloud.com/camtaylor-1/sets/the-late-little-xmas-album ''the late little xmas album''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/harpsichord-meantone ''Harpsichord meantone improvisation 1 in 50EDO''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/long-improvisation-2-in-50edo ''Long improvisation 2 in 50EDO''] (2014)
* [https://soundcloud.com/camtaylor-1/chord-sequence-for-difference ''Chord sequence for Difference tones in 50EDO''] (2014)
* [https://soundcloud.com/camtaylor-1/enharmonic-modulations-in ''Enharmonic Modulations in 50EDO''] (2014)
* [https://soundcloud.com/cam-taylor-2-1/harmonic-clusters-on-50edo-harpsichord-bosanquet-axis-through-pianoteq ''Harmonic Clusters on 50EDO Harpsichord''] (2014)
* [https://soundcloud.com/camtaylor-1/fragment-in-fifty ''Fragment in Fifty''] (2014)
 
== Additional reading ==
* [http://www.archive.org/details/harmonicsorphilo00smit Robert Smith's book online]
* [http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html More information about Robert Smith's temperament]{{Dead link}}
* [https://www.dropbox.com/sh/4x81rzpkot32qzk/MQ3cJljjkh 50EDO Theory - Intervals, Chords and Scales in 50EDO by Cam Taylor]{{Dead link}}
* [http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]   
 
== Notes ==
<references group="note" />
 
[[Category:50edo]]
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Golden meantone]]
[[Category:Historical]]
[[Category:Listen]]
[[Category:Meantone]]
[[Category:Meanpop]]
Retrieved from "https://en.xen.wiki/w/50edo"