27edo: Difference between revisions
Cleanup and update the prime error table |
|||
| Line 11: | Line 11: | ||
== Theory == | == Theory == | ||
If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444… [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes harmonics [[3/1|3]], [[5/1|5]], and [[7/1|7]] sharply. | If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444… [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes harmonics [[3/1|3]], [[5/1|5]], and [[7/1|7]] sharply. The optimal step size for octave-shrinking in the 7-limit is 44.3071 cents, which rougly corresponds to 27.0837-edo. | ||
Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13+2/3 cents. The result is that [[6/5]], [[7/5]] and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from 1/3 [[septimal comma]] superpyth in the same way that 19edo is audibly indistinguishable from [[1/3 syntonic comma meantone]], resulting in three of them reaching a near perfect minor third/major sixth in both. | Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13+2/3 cents. The result is that [[6/5]], [[7/5]] and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from 1/3 [[septimal comma]] superpyth in the same way that 19edo is audibly indistinguishable from [[1/3 syntonic comma meantone]], resulting in three of them reaching a near perfect minor third/major sixth in both. | ||
| Line 792: | Line 792: | ||
== Music == | == Music == | ||
* [ | * [https://www.archive.org/details/MusicForYourEars Music For Your Ears] ([https://www.archive.org/download/MusicForYourEars/musicfor.mp3 play]) by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]]. | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [[Igliashon Jones]] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [[Igliashon Jones]] | ||
* [[:File:Superpythagorean_Waltz.mp3|Superpythagorean Waltz]] by [[Igliashon Jones]] | * [[:File:Superpythagorean_Waltz.mp3|Superpythagorean Waltz]] by [[Igliashon Jones]] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [[Joel Taylor]] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [[Joel Taylor]] | ||
* [ | * [https://www.youtube.com/watch?v=7QcwKlK6z4c miniature prelude and fugue] by [[Peter Kosmorsky]] | ||
* [http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 Chicago Pile-1] by [[Chris Vaisvil]] | * [http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 Chicago Pile-1] by [[Chris Vaisvil]] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 Tetracot Perc-Sitar] (on [ | * [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 Tetracot Perc-Sitar] (on [https://soundcloud.com/dustin-schallert/tetracot-perc-sitar SoundCloud]) by [[Dustin Schallert]] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 Tetracot Jam] (on [ | * [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 Tetracot Jam] (on [https://soundcloud.com/dustin-schallert/tetracot-jam SoundCloud]) by [[Dustin Schallert]] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 Tetracot Pump] (on [ | * [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 Tetracot Pump] (on [https://soundcloud.com/dustin-schallert/tetracot-pump SoundCloud]) by [[Dustin Schallert]] | ||
* [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 27-EDO Guitar 1] by [[Dustin Schallert]] | * [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 27-EDO Guitar 1] by [[Dustin Schallert]] | ||