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{{Infobox ET}}
{{Infobox ET}}
{{ED intro}}


{{EDO intro|50}}
== Theory ==
== Theory ==
In the [[5-limit]], 50edo tempers out [[81/80]], making it a [[meantone]] system, and in that capacity has historically 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. 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 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.
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 – 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.


50edo 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 [[Starling temperaments #Coblack temperament|coblack (15&50) temperament]], 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.
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 & 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.


=== Odd harmonics ===
=== Odd harmonics ===
{{Harmonics in equal|50}}
{{Harmonics in equal|50|columns=15}}


=== Relations ===
=== Relations ===
Line 16: Line 16:
{| class="wikitable center-all right-2 left-3"
{| class="wikitable center-all right-2 left-3"
|-
|-
! #
! #
! Cents
! Cents
! Ratios*
! Ratios<ref group="note">{{sg|13-limit}}</ref>
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and downs notation]]
([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and vvd2)
|-
|-
| 0
| 0
Line 378: Line 379:
| D
| D
|}
|}
<nowiki>*</nowiki> using the patent val


== JI approximation ==
== Notation ==
=== Ups and downs notation ===
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud.
{{sharpness-sharp3a}}
 
Using [[Helmholtz–Ellis]] accidentals, 50edo can also be notated using [[Alternative symbols for ups and downs notation#Sharp-3|alternative ups and downs]]:
{{Sharpness-sharp3}}
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.
 
=== Sagittal notation ===
This notation uses the same sagittal sequence as EDOs [[57edo#Sagittal notation|57]], [[64edo#Sagittal notation|64]], and [[71edo#Second-best fifth notation|71b]].
 
==== Evo flavor ====
<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>
 
==== Revo flavor ====
<imagemap>
File:50-EDO_Revo_Sagittal.svg
desc none
rect 80 0 300 50 [[Sagittal_notation]]
rect 300 0 583 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation]
rect 20 80 160 106 [[1053/1024]]
default [[File:50-EDO_Revo_Sagittal.svg]]
</imagemap>
 
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.
 
== Approximation to JI ==
[[File:50ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 29-limit intervals approximated in 50edo]]
[[File:50ed2.svg|250px|thumb|right|alt=alt : Your browser has no SVG support.|Selected 29-limit intervals approximated in 50edo]]
=== 15-odd-limit mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 50edo (ordered by absolute error). Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.


{| class="wikitable center-all mw-collapsible mw-collapsed"
=== 15-odd-limit interval mappings ===
|+style=white-space:nowrap| Direct approximation (even if inconsistent)
{{Q-odd-limit intervals|50|15}}
|-
! Interval, complement
! Error (abs, [[cent|¢]])
|-
| '''[[16/13]], [[13/8]]'''
| '''0.528'''
|-
| [[15/14]], [[28/15]]
| 0.557
|-
| '''[[11/8]], [[16/11]]'''
| '''0.682'''
|-
| [[13/11]], [[22/13]]
| 1.210
|-
| [[13/10]], [[20/13]]
| 1.786
|-
| '''[[5/4]], [[8/5]]'''
| '''2.314'''
|-
| [[7/6]], [[12/7]]
| 2.871
|-
| [[11/10]], [[20/11]]
| 2.996
|-
| [[9/7]], [[14/9]]
| 3.084
|-
| [[6/5]], [[5/3]]
| 3.641
|-
| [[13/12]], [[24/13]]
| 5.427
|-
| '''[[4/3]], [[3/2]]'''
| '''5.955'''
|-
| [[7/5]], [[10/7]]
| 6.512
|-
| [[12/11]], [[11/6]]
| 6.637
|-
| [[15/13]], [[26/15]]
| 7.741
|-
| [[16/15]], [[15/8]]
| 8.269
|-
| [[14/13]], [[13/7]]
| 8.298
|-
| '''[[8/7]], [[7/4]]'''
| '''8.826'''
|-
| [[15/11]], [[22/15]]
| 8.951
|-
| [[14/11]], [[11/7]]
| 9.508
|-
| [[10/9]], [[9/5]]
| 9.596
|-
| [[18/13]], [[13/9]]
| 11.382
|-
| ''[[11/9]], [[18/11]]''
| ''11.408''
|-
| [[9/8]], [[16/9]]
| 11.910
|}


== Regular temperament properties ==
== Regular temperament properties ==
=== Temperament measures ===
=== Temperament measures ===
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
Line 478: Line 435:
| 2.3
| 2.3
| {{monzo| -79 50 }}
| {{monzo| -79 50 }}
| [{{val| 50 79 }}]
| {{mapping| 50 79 }}
| +1.88
| +1.88
| 1.88
| 1.88
Line 485: Line 442:
| 2.3.5
| 2.3.5
| 81/80, {{monzo| -27 -2 13 }}
| 81/80, {{monzo| -27 -2 13 }}
| [{{val| 50 79 116 }}]
| {{mapping| 50 79 116 }}
| +1.58
| +1.58
| 1.59
| 1.59
Line 492: Line 449:
| 2.3.5.7
| 2.3.5.7
| 81/80, 126/125, 84035/82944
| 81/80, 126/125, 84035/82944
| [{{val| 50 79 116 140 }}]
| {{mapping| 50 79 116 140 }}
| +1.98
| +1.98
| 1.54
| 1.54
Line 499: Line 456:
| 2.3.5.7.11
| 2.3.5.7.11
| 81/80, 126/125, 245/242, 385/384
| 81/80, 126/125, 245/242, 385/384
| [{{val| 50 79 116 140 173 }}]
| {{mapping| 50 79 116 140 173 }}
| +1.54
| +1.54
| 1.63
| 1.63
Line 506: Line 463:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 81/80, 105/104, 126/125, 144/143, 245/242
| 81/80, 105/104, 126/125, 144/143, 245/242
| [{{val| 50 79 116 140 173 185 }}]
| {{mapping| 50 79 116 140 173 185 }}
| +1.31
| +1.31
| 1.57
| 1.57
Line 513: Line 470:


=== Commas ===
=== Commas ===
50edo [[tempers out]] the following [[comma]]s. (Note: 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.
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"
{| class="commatable wikitable center-all left-3 right-4 left-5"
|-
|-
! [[Harmonic limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
! [[Cent]]s
! [[Cent]]s
! Name
! Name
|-
| 3
| <abbr title="717897987691852588770249/604462909807314587353088">(20 digits)</abbr>
| {{monzo| -79 50 }}
| 297.75
| 50-comma
|-
|-
| 5
| 5
Line 546: Line 509:
| 50.72
| 50.72
| Harrison's comma
| Harrison's comma
|-
| 7
| [[16807/16384]]
| {{monzo| -14 0 0 5}}
| 44.13
| Cloudy comma
|-
|-
| 7
| 7
Line 551: Line 520:
| {{monzo| -9 6 1 -1 }}
| {{monzo| -9 6 1 -1 }}
| 29.22
| 29.22
| Laruyo
| Schismean comma
| Schismean comma
|-
|-
Line 570: Line 538:
| {{monzo| 6 0 -5 2 }}
| {{monzo| 6 0 -5 2 }}
| 6.08
| 6.08
| Hemimean
| Hemimean comma
|-
|-
| 7
| 7
Line 576: Line 544:
| {{monzo| 11 -10 -10 10 }}
| {{monzo| 11 -10 -10 10 }}
| 5.57
| 5.57
| [[Linus]]
| [[Linus comma]]
|-
|-
| 7
| 7
Line 594: Line 562:
| {{monzo| -1 0 1 2 -2 }}
| {{monzo| -1 0 1 2 -2 }}
| 21.33
| 21.33
| Cassacot
| Frostma
|-
|-
| 11
| 11
Line 612: Line 580:
| {{monzo| 5 -1 3 0 -3 }}
| {{monzo| 5 -1 3 0 -3 }}
| 3.03
| 3.03
| Wizardharry
| Wizardharry comma
|-
|-
| 11
| 11
Line 642: Line 610:
| {{monzo| 2 3 0 -1 1 -2 }}
| {{monzo| 2 3 0 -1 1 -2 }}
| 7.30
| 7.30
| Kestrel Comma
| Kestrel comma
|-
|-
| 13
| 13
Line 654: Line 622:
| {{monzo| 2 -1 0 1 -2 1 }}
| {{monzo| 2 -1 0 1 -2 1 }}
| 4.76
| 4.76
| Gentle comma
| Minor minthma
|-
|-
| 13
| 13
Line 678: Line 646:
| {{monzo| -5 -2 0 0 0 0 2 }}
| {{monzo| -5 -2 0 0 0 0 2 }}
| 6.00
| 6.00
| Septendecimal semitones comma
| Semitonisma
|-
|-
| 17
| 17
Line 746: Line 714:
| Triaphonisma
| Triaphonisma
|}
|}
<references/>


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+ Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br> per Octave
! Periods<br>per 8ve
! Generator
! Generator*
! Cents
! Cents*
! Associated<br>Ratio
! Associated<br>ratio*
! Temperament
! Temperament
|-
|-
| 1
| 1
| 1\50
| 1\50
| 24.00
| 24.0
| 686/675
| 686/675
| [[Sengagen]]
| [[Sengagen]]
Line 766: Line 733:
| 1
| 1
| 9\50
| 9\50
| 216.00
| 216.0
| 17/15
| 17/15
| [[Tremka]]
| [[Tremka]]
Line 772: Line 739:
| 1
| 1
| 11\50
| 11\50
| 264.00
| 264.0
| 7/6
| 7/6
| [[Septimin]]
| [[Septimin]]
Line 778: Line 745:
| 1
| 1
| 13\50
| 13\50
| 312.00
| 312.0
| 6/5
| 6/5
| [[Oolong]]
| [[Oolong]]
Line 784: Line 751:
| 1
| 1
| 17\50
| 17\50
| 408.00
| 408.0
| 15625/12288
| 325/256
| [[Ditonic]] / [[coditone]]
| [[Coditone]]
|-
|-
| 1
| 1
| 19\50
| 19\50
| 456.00
| 456.0
| 125/96
| 125/96
| [[Qak]]
| [[Qak]]
Line 796: Line 763:
| 1
| 1
| 21\50
| 21\50
| 504.00
| 504.0
| 4/3
| 4/3
| [[Meantone]] / [[meanpop]]
| [[Meantone]] / [[meanpop]]
Line 802: Line 769:
| 1
| 1
| 23\50
| 23\50
| 552.00
| 552.0
| 11/8
| 11/8
| [[Emka]]
| [[Emka]]
Line 808: Line 775:
| 2
| 2
| 2\50
| 2\50
| 48.00
| 48.0
| 36/35
| 36/35
| [[Pombe]]
| [[Pombe]]
Line 814: Line 781:
| 2
| 2
| 3\50
| 3\50
| 72.00
| 72.0
| 25/24
| 25/24
| [[Vishnu]] / [[vishnean]]
| [[Vishnu]] / [[vishnean]]
|-
| 2
| 4\50
| 96.00
| 35/33
| [[Bimeantone]]
|-
|-
| 2
| 2
| 6\50
| 6\50
| 144.00
| 144.0
| 12/11
| 12/11
| [[Bisemidim]]
| [[Bisemidim]]
Line 832: Line 793:
| 2
| 2
| 9\50
| 9\50
| 216.00
| 216.0
| 17/15
| 17/15
| [[Wizard]] / [[lizard]] / [[gizzard]]
| [[Wizard]] / [[lizard]] / [[gizzard]]
Line 838: Line 799:
| 2
| 2
| 12\50
| 12\50
| 288.00
| 288.0
| 13/11
| 13/11
| [[Vines]]
| [[Vines]]
|-
| 2
| 21\50<br>(4\50)
| 504.0<br>(96.0)
| 4/3<br>(35/33)
| [[Bimeantone]]
|-
|-
| 5
| 5
| 21\50 <br>(1\50)
| 21\50<br>(1\50)
| 504.00 <br>(24.00)
| 504.0<br>(24.0)
| 4/3 <br>&nbsp;
| 4/3<br>(49/48)
| [[Cloudtone]]
| [[Cloudtone]]
|-
|-
| 5
| 5
| 3\50
| 23<br>(3\50)
| 72.00
| 552.0<br>(72.0)
| 21/20, 25/24
| 11/8<br>(21/20)
| [[Coblack]]
| [[Coblack]]
|-
|-
| 10
| 10
| 21\50 <br>(1\50)
| 7\50<br>(3\50)
| 504.00 <br>(24.00)
| 168.0<br>(72.0)
| 4/3 <br>&nbsp;
| 54/49<br>(25/24)
| [[Decic]]
| [[Decavish]]
|-
|-
| 10
| 10
| 2\50 <br>(3\50)
| 21\50<br>(1\50)
| 48.00 <br>(72.00)
| 504.0<br>(24.0)
| 36/35 <br>(25/24)
| 4/3<br>(78/77)
| [[Decavish]]
| [[Decic]]
|}
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct


== Instruments ==
== Instruments ==
'''Lumatone'''
; Lumatone


See [[Lumatone mapping for 50edo]]
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 ==
== Music ==
=== Modern renderings ===
=== Modern renderings ===
; {{W|Johann Sebastian Bach}}
; {{W|Johann Sebastian Bach}}
* [https://www.youtube.com/watch?v=e6fMO-sue4Y "Contrapunctus 4" from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024)
* [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=M3wQu4UF1pg "Contrapunctus 11" from ''The Art of Fugue'', BWV 1080] (1742–1749) – 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}}
; {{W|Nicolaus Bruhns}}
* [https://www.youtube.com/watch?v=yrM50pvmD5c ''Prelude in E Minor "The Great"''] – rendered by Claudi Meneghin (2023)
* [https://www.youtube.com/watch?v=yrM50pvmD5c ''Prelude in E Minor "The Great"''] &ndash; rendered by Claudi Meneghin (2023)


; {{W|Gabriel Fauré}}
; {{W|Gabriel Fauré}}
* [https://www.youtube.com/watch?v=7djfrUlw2ck  ''Pavane'', op. 50] (1887) – arranged for harpsichord and rendered by Claudi Meneghin (2020)
* [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===
=== 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]]
; [[Francium]]
* [https://www.youtube.com/watch?v=pH6E35hwUnM ''On My Way To Somewhere''] (2023)
* [https://www.youtube.com/watch?v=pH6E35hwUnM ''On My Way To Somewhere''] (2023)


; [[Claudi Meneghin]]
; [[Claudi Meneghin]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-50-edo.mp3 Twinkle canon – 50 edo] {{dead link}}
* [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=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=Zh2jWoIXAf8 ''La Petite Poule Grise - Fugue''] (2019)
Line 915: Line 897:
* [http://www.music.ed.ac.uk/russell/conference/robertsmithkirckman.html More information about Robert Smith's temperament]{{Dead link}}
* [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}}
* [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]    
* [http://iamcamtaylor.wordpress.com/ iamcamtaylor - Blog on 50EDO and extended meantone theory by Cam Taylor]    
 
== Notes ==
<references group="note" />


[[Category:50edo]]
[[Category:50edo]]
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Golden meantone]]
[[Category:Golden meantone]]
[[Category:Historical]]
[[Category:Listen]]
[[Category:Meantone]]
[[Category:Meantone]]
[[Category:Meanpop]]
[[Category:Meanpop]]
[[Category:Historical]]
[[Category:Listen]]
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