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{{Wikipedia|15 equal temperament}}
'''15 equal temperament''' or 15-edo is a tuning which divides the octave into 15 equally spaced pitches.  
'''15 equal divisions of the octave''' ('''15edo'''), or '''15(-tone) equal temperament''' ('''15tet''', '''15et''') when viewed from a [[regular temperament]] perspective, is the [[tuning system]] derived by dividing the [[octave]] into 15 [[equal]]ly large steps.


== Theory ==
== Theory ==
{{Odd harmonics in edo|edo=15}}
{{Harmonics in equal|15}}
 
15-edo can be thought of as three sets of 5-edo which do not connect by fifths. The fifth at 720 cents is quite wide yet still useable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15-edo returns to the octave if stacked five times which is radically different than a meantone system.
 
From [[Wikipedia:15_equal_temperament|Wikipedia]]:


"In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2<sup>1/15</sup>, or 80 [[cent|cents]]. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]])."
15edo can be thought of as three sets of [[5edo]] which do not connect by fifths. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. The perfect fifth of 15edo returns to the octave if stacked five times which is radically different than a meantone system. Additionally, 15 being equal to 3 × 5 also implies that 15edo contains five sets of [[3edo]].


15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, 6/5, and their octave inverses) that has a positive [[81/80|syntonic comma]].
15edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, 6/5, and their octave inverses) that has a positive [[81/80|syntonic comma]].


In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in xenharmony, due to its manageable number of tones and for containing the relatively popular 5-edo.
In the 15edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in xenharmony, due to its manageable number of tones and for containing the relatively popular 5edo.


A recommended method to the notation of 15-edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15-edo while the "small quill" (80¢) is the chroma of 15-edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15-edo into a seven nominal based framework.
A recommended method to the notation of 15edo by some is a system based on porcupine[8] in which eight nominals form the base diatonic scale. In this sense, the "quill" is the name given to the two step interval (160¢) of 15edo while the "small quill" (80¢) is the chroma of 15edo. This produces a very consistent notation for both porcupine[8] and Blackwood[10] and seems to work much better than attempting to put 15edo into a seven nominal based framework.


<gallery widths=300px>
<gallery widths=300px>
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<nowiki>*</nowiki> based on treating 15-EDO as an 11-limit temperament; other approaches are possible
<nowiki>*</nowiki> based on treating 15edo as an 11-limit temperament; other approaches are possible


In [[Ups_and_Downs_Notation# Summary of EDO notation-"Pentatonic" EDOs|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names. 15edo can also be notated using the [[Ups_and_Downs_Notation #Natural Generators|natural generator]], which is not the 9\15 5th but the 2\15 2nd. For 15edo, this is also known as porcupine notation. The 15edo porcupine genchain in both absolute and relative notation:
In [[Ups_and_Downs_Notation# Summary of EDO notation-"Pentatonic" EDOs|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names. 15edo can also be notated using the [[Ups_and_Downs_Notation #Natural Generators|natural generator]], which is not the 9\15 5th but the 2\15 2nd. For 15edo, this is also known as porcupine notation. The 15edo porcupine genchain in both absolute and relative notation:
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== Just approximation ==
== Just approximation ==
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[http://www.cityoftheasleep.com/etc/5nEDOs.pdf Five is Not an Odd Number]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[Harmony_in_15edo_Blacksmith|Harmony in 15edo Blacksmith[10]]].
15edo offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[http://www.cityoftheasleep.com/etc/5nEDOs.pdf Five is Not an Odd Number]". For an in-depth treatment of harmony in 15edo based on this temperament (and its 7- and 11-limit extensions), see [[Harmony_in_15edo_Blacksmith|Harmony in 15edo Blacksmith[10]]].


=== Selected just intervals ===
=== Selected just intervals ===
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== Notation ==
== Notation ==
There are a variety of other ways to notate 15-edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15-edo composition.
There are a variety of other ways to notate 15edo, and the choice of notation depends heavily which rank-2 temperament or MOS scale one wishes to treat as being the "main focus" of 15edo composition.


=== Blackwood Notation ===
=== Blackwood Notation ===
* '''Decimal Version:''' Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5-edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
* '''Decimal Version:''' Using the nominals 1-0 (with 0 representing "10"), one of the three chains of 5edo is represented by the odd numbers, the second by the even numbers, and the third by numbers with accidentals (either odd numbers with sharps, or even numbers with flats).
* '''Guitar Version:''' On a 15-edo guitar, because the "perfect fourth" comes from 5-edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the circle of fourths on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15-edo, it is necessary to use accidentals to notate intervals on the other two chains of 5-edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15-edo on the guitar, since 5-edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.
* '''Guitar Version:''' On a 15edo guitar, because the "perfect fourth" comes from 5edo, all of the open strings can be tuned a perfect fourth apart and still span exactly two octaves. If one starts the circle of fourths on B — B-E-A-D-G-(B) — then the open strings of the guitar can be notated as usual (E-A-D-G-B-E). However, because the circle of fourths closes at five, and does not continue to circulate through the other 10 notes of 15edo, it is necessary to use accidentals to notate intervals on the other two chains of 5edo. This notation is not particularly ideal as a basis for a staff notation (as it requires all non-5edo chords to be notated with accidentals). It is nevertheless useful because it reflects an intuitive approach to 15edo on the guitar, since 5edo provides a useful set of 3-limit landmarks (or "perfect fourths" and "perfect fifths") that can be used to navigate the fretboard. It's especially convenient for writing chord charts, where the funky accidental-laden spellings can be more or less ignored.


=== Porcupine Notation ===
=== Porcupine Notation ===
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=== Guitar ===
=== Guitar ===
[http://www.swordguitars.com Sword, Ronald. "Pendecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.] - A large repository of all known scales and temperament families in the 15-edo system. 300+ examples /w chord-scale progressions.
[http://www.swordguitars.com Sword, Ronald. "Pendecaphonic Scales for Guitar" IAAA Press, UK-USA. First Ed: June 2009.] - A large repository of all known scales and temperament families in the 15edo system. 300+ examples /w chord-scale progressions.


=== Keyboard ===
=== Keyboard ===
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{{See also|:Category:15edo tracks}}
{{See also|:Category:15edo tracks}}
* [http://micro.soonlabel.com/15-ET/ XA 15-ET Directory]  
* [http://micro.soonlabel.com/15-ET/ XA 15-ET Directory]  
* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)], an album of xenharmonic Christmas covers played by [https://www.stephenweigelcomposerperformer.com/ Stephen Weigel], many are in 15edo
* [https://stephenweigel.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)], an album of xenharmonic Christmas covers played by [[Stephen Weigel]], many are in 15edo
* [https://soundcloud.com/overtoneshock/keep-out-of-my-psyche-15-edo Keep out of my Psyche] by Stephen Weigel
* [https://soundcloud.com/overtoneshock/keep-out-of-my-psyche-15-edo Keep out of my Psyche] by Stephen Weigel
* [https://sites.google.com/site/teamouse/home Mizarian Porcupine Overture] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/MizarianPorcupineOverture.mp3 play]'' by [[Herman_Miller|Herman Miller]] ([http://teamouse.googlepages.com/home Herman Miller]) ([[Regular_Temperaments#porcupine|porcupine]] chord progressions; this is the song that 'porcupine' is named after)
* [https://sites.google.com/site/teamouse/home Mizarian Porcupine Overture] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/MizarianPorcupineOverture.mp3 play]''{{dead link}} by [[Herman Miller]] ([[porcupine]] chord progressions; this is the song that 'porcupine' is named after)
* ''[http://www.microtonalmusic.net/audio/15edostudy.mp3 Study for Bells]'' by [[Daniel_Thompson|Daniel Thompson]] ([http://danielthompson.blogspot.com/ Daniel Thompson]) (Jan. 2007)
* ''[http://www.microtonalmusic.net/audio/15edostudy.mp3 Study for Bells]''{{dead link}} by [[Daniel Thompson]] (Jan. 2007)
* [http://www.soundclick.com/bands/songInfo.cfm?bandID=145852&songID=2920478 Hyperimprovisation 3.3] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation3.3.mp3 play]'' by [[Jacob Barton]] (2003)
* [https://www.soundclick.com/music/songInfo.cfm?songID=2920478 Hyperimprovisation 3.3] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/Hyperimprovisation3.3.mp3 play]''{{dead link}} by [[Jacob Barton]] (2003)
* [http://www.soundclick.com/bands/page_songInfo.cfm?bandID=145852&songID=5483130+OFOIOB OFOIOB] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/OFOIOB.mp3 play]'' by Jacob Barton
* [https://www.soundclick.com/music/songInfo.cfm?songID=5483130 OFOIOB] ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Barton/OFOIOB.mp3 play]''{{dead link}} by Jacob Barton
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/15%20tone%20E.T.Improvisationn.mp3 15 Tone ET Improvisationn]'' by [[Norbert Oldani]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Oldani/15%20tone%20E.T.Improvisationn.mp3 15 Tone ET Improvisationn]''{{dead link}} by [[Norbert Oldani]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/15ET.mp3 Elegy in 15ET]'' by [[Aaron Andrew Hunt]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/15ET.mp3 Elegy in 15ET]''{{dead link}} by [[Aaron Andrew Hunt]]
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/15ETa3fugue2.mp3 Fugue a3 in 15ET]'' by Aaron Andrew Hunt
* ''[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Hunt/15ETa3fugue2.mp3 Fugue a3 in 15ET]''{{dead link}} by Aaron Andrew Hunt
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/12%20-%2012.%2015%20octave.mp3 Comets Over Flatland 12]'' by [[Randy Winchester]]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/12%20-%2012.%2015%20octave.mp3 Comets Over Flatland 12]''{{dead link}} by [[Randy Winchester]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/13%20-%2013.%2015%20octave.mp3 Comets Over Flatland 13] by [[Randy Winchester]]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/13%20-%2013.%2015%20octave.mp3 Comets Over Flatland 13]''{{dead link}} by Randy Winchester
* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/16%20-%2016.%2015%20octave.mp3 Comets Over Flatland 16] by [[Randy Winchester]]
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/16%20-%2016.%2015%20octave.mp3 Comets Over Flatland 16]''{{dead link}} by Randy Winchester
* Study for Kyle Gann by [http://www.akjmusic.com/works.html Aaron K. Johnson] (12-out-of-15)
* ''Study for Kyle Gann'' by [[Aaron Krister Johnson]] (12-out-of-15)
* [http://azuma-asobi.com/Music/index.html Rick McGowan]: [http://azuma-asobi.com/Music/Music-FullWorks.html Four Ballet Scenes]
* [http://azuma-asobi.com/Music/Music-FullWorks.html Four Ballet Scenes]{{dead link}} by [[Rick McGowan]]
* "[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3 Gently Playing With Miller's Porcupine]" by [http://www.chrisvaisvil.com Chris Vaisvil] (uses Miller's Porcupine-7 mode 2 2 2 3 2 2 2)
* "[http://micro.soonlabel.com/15-ET/daily20110619_millers_porcupine_7a.mp3 Gently Playing With Miller's Porcupine]" by [[Chris Vaisvil]] - [http://chrisvaisvil.com/?p=1983 details] (uses Miller's Porcupine-7 mode 2 2 2 3 2 2 2)
* [http://micro.soonlabel.com/15-ET/daily20110619_15edo_after_dark_in_the_pedway.mp3 After Dark on the Pedway] by [http://chrisvaisvil.com/?p=969 Chris Vaisvil]
* [http://micro.soonlabel.com/15-ET/daily20110619_15edo_after_dark_in_the_pedway.mp3 After Dark on the Pedway] by Chris Vaisvil - [http://chrisvaisvil.com/?p=969 details]
* [http://micro.soonlabel.com/15-ET/15_sandles.mp3 15 Sandles] by [http://chrisvaisvil.com/?p=722 Chris Vaisvil] [http://micro.soonlabel.com/15-ET/15_sandles.mid scordatura midi file]
* [http://micro.soonlabel.com/15-ET/15_sandles.mp3 15 Sandles] by Chris Vaisvil - [http://chrisvaisvil.com/?p=722 details], [http://micro.soonlabel.com/15-ET/15_sandles.mid scordatura midi file]
* [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.mp3 Improv on 15 EDO] by [http://www.chrisvaisvil.com Chris Vaisvil] [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.mid scordatura midi file] and [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.pdf scordatura PDF score]
* [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.mp3 Improv on 15 EDO] by Chris Vaisvil - [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.mid scordatura midi file], [http://micro.soonlabel.com/15-ET/Improv_on_15edo/Improv_on_15.pdf scordatura PDF score]
* [http://micro.soonlabel.com/15-ET/20120317-synth-15edo-trolls.mp3 15 edo Trolls] by [[Chris_Vaisvil|Chris Vaisvil]] - [http://chrisvaisvil.com/?p=2206 details]
* [http://micro.soonlabel.com/15-ET/20120317-synth-15edo-trolls.mp3 15 edo Trolls] by Chris Vaisvil - [http://chrisvaisvil.com/?p=2206 details]
* ''[http://micro.soonlabel.com/15-ET/20120903_15edo_through_the_fire_of_the_sun.mp3 Through the Fire of the Sun (15 edo rock band)]'' by [http://chrisvaisvil.com Chris Vaisvil]
* ''[http://micro.soonlabel.com/15-ET/20120903_15edo_through_the_fire_of_the_sun.mp3 Through the Fire of the Sun (15 edo rock band)]'' by Chris Vaisvil - [http://chrisvaisvil.com/?p=2656 details]
* [http://chrisvaisvil.com/2-2-1-2-2-1-2-2-1-mode-of-15-edo/ 2-2-1-2-2-1-2-2-1 mode of 15 edo] [http://micro.soonlabel.com/15-ET/20130831_221of15.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]]
* [http://micro.soonlabel.com/15-ET/20130831_221of15.mp3 2-2-1-2-2-1-2-2-1 mode of 15 edo] by Chris Vaisvil - [http://chrisvaisvil.com/?p=3619 details]
* [http://youtu.be/6TyQ9kDm2fk Ode For Ada] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html blog entry])
* [http://youtu.be/6TyQ9kDm2fk Ode For Ada] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/5f07ebbdf8b4ba8ef067ed3d00a38357-158.html blog entry])
* [http://www.seraph.it/dep/det/Sahara.mp3 Sahara] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/152ffe3684d7a11a91e5bc6c92a5bc9a-271.html blog entry])
* [http://www.seraph.it/dep/det/Sahara.mp3 Sahara] by Carlo Serafini ([http://www.seraph.it/blog_files/152ffe3684d7a11a91e5bc6c92a5bc9a-271.html blog entry])
* Suite in 15-Note Equal Tuning, opus 33 by [[Easley Blackwood]] (as well as one of the Twelve Microtonal Etudes, opus 28)
* Suite in 15-Note Equal Tuning, opus 33 by [[Easley Blackwood]] (as well as one of the Twelve Microtonal Etudes, opus 28)
* [[:File:15edo-Chords.ogg|15edo-Chords.ogg]] Some nice sounds I found in 15 EDO
* [[:File:15edo-Chords.ogg|15edo-Chords.ogg]] Some nice sounds I found in 15 EDO
* [[:File:happenstance15.ogg|happenstance15.ogg]] Sonic experiment in 15. Somewhat familiar tonality.
* [[:File:happenstance15.ogg|happenstance15.ogg]] Sonic experiment in 15. Somewhat familiar tonality.
* [http://www.youtube.com/watch?v=kQECU5ecCd4 Portrait of insects with 15-tone equal tempered guitar music]
* [http://www.youtube.com/watch?v=kQECU5ecCd4 Portrait of insects with 15-tone equal tempered guitar music] by Jonathan Rabson
* [http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et PentadecafoniCoda (15et)] by F.F.F. Fiale
* [http://www.reverbnation.com/ffffiale/song/3073160-pentadecafonicoda-15et PentadecafoniCoda (15et)] by F.F.F. Fiale
* [http://soonlabel.com/xenharmonic/archives/1946 Cuckoo-Rag Fugue by Claudi Meneghin]
* [http://soonlabel.com/xenharmonic/archives/1946 Cuckoo-Rag Fugue]{{dead link}} by [[Claudi Meneghin]]
* [http://soonlabel.com/xenharmonic/archives/2313 15-penny jingle, by Claudi Meneghin]
* [http://soonlabel.com/xenharmonic/archives/2313 15-penny jingle]{{dead link}} by Claudi Meneghin
* [http://soonlabel.com/xenharmonic/archives/2710 Tocada in 15edo, by Claudi Meneghin]
* [http://soonlabel.com/xenharmonic/archives/2710 Tocada in 15edo]{{dead link}} by Claudi Meneghin
* [https://soundcloud.com/andrew-j-milne/a-broken-stern-2012 A Broken Stern (2012) by Andrew J Milne on SoundCloud]
* [https://soundcloud.com/andrew-j-milne/a-broken-stern-2012 A Broken Stern (2012) by Andrew J Milne on SoundCloud]
* [https://youtu.be/wrLfJ8j2Kt0 Canada Geese by Diamond Doll (punk song)]
* [https://youtu.be/wrLfJ8j2Kt0 Canada Geese by Diamond Doll (punk song)]
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[[Category:15edo| ]] <!-- main article -->
[[Category:15edo| ]] <!-- main article -->
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:guitar]]
[[Category:Guitar]]
[[Category:listen]]
[[Category:Listen]]
[[Category:teentuning]]
[[Category:Teentuning]]
[[Category:theory]]
 
[[Category:todo:unify_precision]]
{{todo|unify precision}}
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