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== Notations ==
== Notations ==
From the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]], a diagram of how to notate 31-EDO in the Revo flavor of Sagittal:
'''Quarter-tone notation''' is much like ups and downs notation. Between C and D (do and re) for example, we have the following notes:
{| class="wikitable"
|-
| |'''Degree'''
| |'''Letter'''
| |'''Name'''
| |'''English full name'''
|-
| |0
| |C
| |do
| | C
|-
| |1
| |C+
| |do+
| |C half-sharp
|-
| |2
| |C#
| |do#
| |C sharp
|-
| | 3
| |Db
| |re b
| |D flat
|-
| |4
| | Dd
| |re d
| |D half-flat
|-
| |5
| |D
| |re
| |D
|}'''Extended pythagorean notation''' uses double sharps and double flats:
{| class="wikitable"
|-
| |'''Degree'''
| |'''Letter'''
| |'''Name'''
| |'''English full name'''
|-
| |0
| |C
| |do
| |C
|-
| |1
| |Dbb
| |re bb
| |D double flat
|-
| |2
| |C#
| |do #
| |C sharp
|-
| |3
| | Db
| |re b
| |D flat
|-
| |4
| |Cx
| |do x
| |C double sharp
|-
| | 5
| |D
| |re
| |D
|}While using double sharp and double flat may seem confusing because it alternates between C and D, it provides a way of writing chords that is consistent with traditional notation. For example, the subminor7 chord 12:14:18:21 is written like so:
* C / D# / G / A#
*C# / Dx / G# / Ax
*Db / E / Ab / B
* D / E# / A / B#
In 12-edo, we have the enharmonic equivalences C# = Db and E# = F. But in 31-edo we have:
*Cx = Dd
*C+ = Dbb
*E# = Fd
*E+ = Fb
*Ex = F+
*Ed = Fbb
'''Revo Sagittal notation''', from the appendix to [[The Sagittal Songbook]] by [[Jacob Barton|Jacob A. Barton]]:


[[File:31edo Sagittal.png|800px]]
[[File:31edo Sagittal.png|800px]]
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{{See also|:Category:31edo tracks}}
{{See also|:Category:31edo tracks}}
* [[31-edo compositions|An alphabetical list of Tricesimoprimal Compositions]].
* [[31-edo compositions|An alphabetical list of Tricesimoprimal Compositions]].
* [http://archive.org/download/Aire2In31-equalTemperament/Aire2In31.mp3 Aire #2 in 31-equal temperament] by [[Jon Lyle Smith]] {{dead link}}
* [https://archive.org/download/Aire2In31-equalTemperament/Aire2In31.mp3 Aire #2 in 31-equal temperament] by [[Jon Lyle Smith]] {{dead link}}
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2031-tET-I%20Stand%20Hopeless%20Before%20the%20Gray%20Sea.mp3 I Stand Hopeless Before the Gray Sea] by [[Chuckles McGee]]
* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2031-tET-I%20Stand%20Hopeless%20Before%20the%20Gray%20Sea.mp3 I Stand Hopeless Before the Gray Sea] by [[Chuckles McGee]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3 Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)] by [[Claudi Meneghin]]
* [http://soonlabel.com/xenharmonic/wp-content/uploads/2012/03/Claudi_Meneghin_Chaconne_G_001.mp3 Chaconna en G=, La Padana, ou la septimala (‘The Padanian, or the septimal’)] by [[Claudi Meneghin]]
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=== Articles ===
=== Articles ===
* [http://www.huygens-fokker.org/docs/beerart.html de Beer, Anton, ''The Development of 31-tone Music''] [http://www.webcitation.org/5xeFzBM9b Permalink]
* [http://www.huygens-fokker.org/docs/beerart.html de Beer, Anton, ''The Development of 31-tone Music''] [https://www.webcitation.org/5xeFzBM9b Permalink]
* [http://www.huygens-fokker.org/docs/fokkerorg.html Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ''] [http://www.webcitation.org/5xeG6Tmli Permalink]
* [http://www.huygens-fokker.org/docs/fokkerorg.html Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ''] [https://www.webcitation.org/5xeG6Tmli Permalink]
* Fokker, A.D., "New Music with 31 Notes" translated by Leigh Gerdine
* Fokker, A.D., "New Music with 31 Notes" translated by Leigh Gerdine
* [http://www.huygens-fokker.org/docs/rap31.html Rapoport, Paul, ''About 31-tone Equal Temperament''] [http://www.webcitation.org/5xeGH4uBH Permalink]
* [http://www.huygens-fokker.org/docs/rap31.html Rapoport, Paul, ''About 31-tone Equal Temperament''] [https://www.webcitation.org/5xeGH4uBH Permalink]
* [http://www.huygens-fokker.org/docs/terp31.html Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''] [http://www.webcitation.org/5xeGMeCMd Permalink]
* [http://www.huygens-fokker.org/docs/terp31.html Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''] [https://www.webcitation.org/5xeGMeCMd Permalink]
* [http://tonalsoft.com/enc/number/31edo.aspx Tonalsoft Encyclopedia article] [http://www.webcitation.org/5xeGYj7QU Permalink]
* [http://tonalsoft.com/enc/number/31edo.aspx Tonalsoft Encyclopedia article] [https://www.webcitation.org/5xeGYj7QU Permalink]


=== Videos ===
=== Videos ===
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