22edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~keenanpepper~~|~~keenanpepper~~]] and made on <tt>2011-12-~~17 23~~:44:31 UTC</tt>.

: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-21 02:34:07 UTC</tt>.

: The original revision id was <tt>~~287117712~~</tt>.

: The original revision id was <tt>287849378</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 10:

=Theory=

In music, //22 equal temperament//, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 [[cent]]s.

In music, //22 equal temperament//, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent]]s.

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of ~~tolerably dealing with~~ [[5-limit]] ~~music, and while~~ not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to ~~do rough justice to~~ the [[7-limit|7-]] and [[11-limit]]s. While [[31edo|31 equal temperament]] does much better, 22-et ~~at least~~ allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit[[consistent| consistent]]ly. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit[[consistent| consistent]]ly. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.

Line 50:

==Properties of 22 equal temperament==

Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. It does, however, temper out the diaschisma, 2048/2025, the magic comma or small diesis, 3125/3072, and the porcupine comma, or maximal diesis, 250/243. In a diaschismic system, such as 12-et or 22-et, the [[diatonic ~~tritone]]~~ [[~~45_32|45/32~~]], which ~~is a major third above a [[major whole tone]] representing [[9_8|~~9/~~8]]~~, ~~is equated to its inverted form, [[64_45|64~~/~~45]]~~. ~~That~~ the ~~magic~~ comma ~~is tempered out means that 22-et is a [[Regular Temperaments#magic|magic]] system~~, ~~where five major thirds make up a perfect fifth. That~~ the ~~porcupine~~ comma is ~~tempered out means that~~ 22-~~et is a [[Regular Temperaments#porcupine|porcupine]] system, where three [[minor whole tone]]s ([[10_9|10/9]] tones) give a fourth, and five give a minor sixth~~.

Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale has thirds of 9/7 and 7/6, rather than of 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO.

In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal ~~tritons~~ of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.

It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22-EDO supports [[porcupine]] temperament. The generator for porcupine is is a flat minor whole tone of [[10_9|10/9]], two of which is a slightly sharp [[6_5|6/5]], and three of which is a slightly flat [[4_3|4/3]]. Porcupine is notable for being the 5-limit temperament lowest in badness which is //not// approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22-EDO. It forms [[MOSScales|MOS]]'s of 7 and 8, which in 22-EDO are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).

Other 5-limit commas 22-EDO tempers out include the diaschisma, 2048/2025 and the magic comma or small diesis, 3125/3072. In a diaschismic system, such as 12-et or 22-et, the [[diatonic tritone]] [[45_32|45/32]], which is a major third above a [[major whole tone]] representing [[9_8|9/8]], is equated to its inverted form, [[64_45|64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.

In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.

===Linear Temperaments===

Line 125:

Line 129:

=Compositions=

* [[http://music.columbia.edu/~~%7Echris~~/sounds/TIBIA.mp3|Tibia]] by [[Paul Erlich]]

* [[http://music.columbia.edu/~chris/sounds/TIBIA.mp3|Tibia]] by [[Paul Erlich]]

* [[http://lumma.org/music/theory/tctmo/glassic.mp3|Glassic]] by Paul Erlich and [[Ara Sarkissian]]

* [[http://lumma.org/music/theory/tctmo/glassic.mp3|Glassic]] by Paul Erlich and [[Ara Sarkissian]]

* [[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]] by Paul Erlich and Ara Sarkissian (jazz)

* [[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]] by Paul Erlich and Ara Sarkissian (jazz)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3|Dragged by a Storm Across the Desert Years]] by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3|Dragged by a Storm Across the Desert Years]] by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]] by Iglashion Jones (progressive metal)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]] by Iglashion Jones (progressive metal)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3|Revenge of the inorganic compounds]] by Iglashion Jones (progressive metal)

* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3|Revenge of the inorganic compounds]] by Iglashion Jones (progressive metal)

* [[http://chrisvaisvil.com/?p=267|My Crazy Aunt Sophie]] [[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]] by [[Chris Vaisvil]]. Blatantly xenharmonic piano.

* [[http://chrisvaisvil.com/?p=267|My Crazy Aunt Sophie]] [[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]] by [[Chris Vaisvil]]. Blatantly xenharmonic piano.

* [[http://soundclick.com/share?songid=8839058|where words are said to mean]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]] by [[Andrew Heathwaite]], a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This & the following pieces by Andrew are for 22-tone guitar & voice.

* [[http://soundclick.com/share?songid=8839058|where words are said to mean]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]] by [[Andrew Heathwaite]], a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This & the following pieces by Andrew are for 22-tone guitar & voice.

* [[http://soundclick.com/share?songid=9101704|I've come with a bucket of roses]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]] by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).

* [[http://soundclick.com/share?songid=9101704|I've come with a bucket of roses]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]] by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).

* [[http://soundclick.com/share?songid=9101705|one drop of rain]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]] by Andrew Heathwaite (orwell-9).

* [[http://soundclick.com/share?songid=9101705|one drop of rain]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]] by Andrew Heathwaite (orwell-9).

* [[http://soundclick.com/share?songid=8839060|being a]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]] by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).

* [[http://soundclick.com/share?songid=8839060|being a]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]] by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).

* [[http://soundclick.com/share?songid=8839071|my own house]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]] by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).

* [[http://soundclick.com/share?songid=8839071|my own house]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]] by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).

* [[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]] by [[Randy Winchester]]

* [[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]] by [[Randy Winchester]]

* [[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith

* [[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith

* [[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]] - youtube

* [[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]] - youtube

* [[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]], Mike Battaglia - youtube

* [[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]], Mike Battaglia - youtube

* Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - [[http://www.angelfire.com/mo/oljare/midicomp.html|MIDI files]]

** [[http://xenharmonic.wikispaces.com/file/view/sunday3.pdf|Sagittal score of Sunday Pipes]]

Line 152:

Line 156:

<h1 id="toc0"><a name="Theory"></a>Theory</h1>

In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 <a class="wiki_link" href="/cent">cent</a>s.

In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 <a class="wiki_link" href="/cent">cent</a>s.

The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the <a class="wiki_link" href="/Indian">music theory of India</a>, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after <a class="wiki_link" href="/19edo">19 equal temperament</a>, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of ~~tolerably dealing with~~ <a class="wiki_link" href="/5-limit">5-limit</a> ~~music, and while~~ not an integral or gap edo it at least qualifies as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak</a>. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to ~~do rough justice to~~ the <a class="wiki_link" href="/7-limit">7-</a> and <a class="wiki_link" href="/11-limit">11-limit</a>s. While <a class="wiki_link" href="/31edo">31 equal temperament</a> does much better, 22-et ~~at least~~ allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit<a class="wiki_link" href="/consistent"> consistent</a>ly. Furthermore, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the <a class="wiki_link" href="/5-limit">5-limit</a> to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta peak</a>. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the <a class="wiki_link" href="/7-limit">7-</a> and <a class="wiki_link" href="/11-limit">11-limit</a>s to within 3 cents/oct of error. While <a class="wiki_link" href="/31edo">31 equal temperament</a> does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit<a class="wiki_link" href="/consistent"> consistent</a>ly. Furthermore, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.

22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.

Line 365:

Line 369:

<h2 id="toc1"><a name="Theory-Properties of 22 equal temperament"></a>Properties of 22 equal temperament</h2>

Possibly the most striking characteristic of 22-et to those not used to it is that it does not &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. ~~It does~~, ~~however~~, ~~temper out~~ the ~~diaschisma, 2048~~/~~2025~~, the ~~magic~~ comma ~~or small diesis~~, ~~3125~~/~~3072, and~~ the porcupine comma, or maximal diesis, 250/243~~. In a diaschismic system~~, ~~such as 12-et or~~ 22-~~et, the~~ <a class="wiki_link" href="/~~diatonic%20tritone~~">~~diatonic tritone~~</a> <a class="wiki_link" href="/~~45_32~~">45/32</a>, which is a ~~major third above a~~ <a class="wiki_link" href="/~~major%20whole%20tone~~">~~major whole tone~~</a> ~~representing~~ <a class="wiki_link" href="/~~9_8~~">9/8</a>, is ~~equated to its inverted form~~, <a class="wiki_link" href="/~~64_45~~">~~64/45~~</a>. ~~That~~ the magic comma ~~is tempered out means that~~ 22-et ~~is a~~ <a class="wiki_link" href="/~~Regular~~%~~20Temperaments#magic~~">~~magic~~</a> ~~system, where five major thirds make up a perfect fifth. That the porcupine comma is tempered out means that 22-et is a~~ <a class="wiki_link" href="/~~Regular%20Temperaments#porcupine~~">~~porcupine~~</a> ~~system~~, ~~where three~~ <a class="wiki_link" href="/~~minor~~%20whole%20tone">~~minor~~ whole tone</a>~~s (~~<a class="wiki_link" href="/~~10_9~~">10/9</a> ~~tones) give~~ a ~~fourth~~, ~~and~~ five ~~give~~ a ~~minor sixth~~.

Possibly the most striking characteristic of 22-et to those not used to it is that it does not &quot;temper out&quot; the syntonic comma of 81/80, and therefore is not a system of <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> temperament. The diatonic scale it produces is instead derived from <a class="wiki_link" href="/superpyth">superpyth</a> temperament, which despite having the same melodic structure as meantone's diatonic scale has thirds of 9/7 and 7/6, rather than of 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO.

It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22-EDO supports <a class="wiki_link" href="/porcupine">porcupine</a> temperament. The generator for porcupine is is a flat minor whole tone of <a class="wiki_link" href="/10_9">10/9</a>, two of which is a slightly sharp <a class="wiki_link" href="/6_5">6/5</a>, and three of which is a slightly flat <a class="wiki_link" href="/4_3">4/3</a>. Porcupine is notable for being the 5-limit temperament lowest in badness which is not approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22-EDO. It forms <a class="wiki_link" href="/MOSScales">MOS</a>'s of 7 and 8, which in 22-EDO are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).

Other 5-limit commas 22-EDO tempers out include the diaschisma, 2048/2025 and the magic comma or small diesis, 3125/3072. In a diaschismic system, such as 12-et or 22-et, the <a class="wiki_link" href="/diatonic%20tritone">diatonic tritone</a> <a class="wiki_link" href="/45_32">45/32</a>, which is a major third above a <a class="wiki_link" href="/major%20whole%20tone">major whole tone</a> representing <a class="wiki_link" href="/9_8">9/8</a>, is equated to its inverted form, <a class="wiki_link" href="/64_45">64/45</a>. That the magic comma is tempered out means that 22-et is a <a class="wiki_link" href="/Regular%20Temperaments#magic">magic</a> system, where five major thirds make up a perfect fifth.

In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both <a class="wiki_link" href="/50_49">50/49</a>, (the <a class="wiki_link" href="/jubilee%20comma">jubilee comma</a>), and <a class="wiki_link" href="/64_63">64/63</a>, (the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal ~~tritons~~ of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the <a class="wiki_link" href="/orwell%20comma">orwell comma</a>; and the <a class="wiki_link" href="/orwell%20tetrad">orwell tetrad</a> is also a chord of 22-et.

In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both <a class="wiki_link" href="/50_49">50/49</a>, (the <a class="wiki_link" href="/jubilee%20comma">jubilee comma</a>), and <a class="wiki_link" href="/64_63">64/63</a>, (the <a class="wiki_link" href="/septimal%20comma">septimal comma</a>), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the <a class="wiki_link" href="/septimal%20kleisma">septimal kleisma</a>, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the <a class="wiki_link" href="/orwell%20comma">orwell comma</a>; and the <a class="wiki_link" href="/orwell%20tetrad">orwell tetrad</a> is also a chord of 22-et.

<h3 id="toc2"><a name="Theory-Properties of 22 equal temperament-Linear Temperaments"></a>Linear Temperaments</h3>

Line 911:

Line 919:

<h1 id="toc9"><a name="Compositions"></a>Compositions</h1>

<ul><li><a class="wiki_link_ext" href="http://music.columbia.edu/~~%7Echris~~/sounds/TIBIA.mp3" rel="nofollow">Tibia</a> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a></li><li><a class="~~wiki_link_ext~~" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow">Glassic</a> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><a class="~~wiki_link_ext"~~ href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a> by Paul Erlich and Ara Sarkissian (jazz)</li><li><a class="~~wiki_link_ext~~" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow">Dragged by a Storm Across the Desert Years</a> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><a class="~~wiki_link_ext"~~ href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow">Numerology</a> by Iglashion Jones (progressive metal)</li><li><a class="~~wiki_link_ext~~" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow">Revenge of the inorganic compounds</a> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <a class="~~wiki_link_ext"~~ href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <a class="~~wiki_link_ext~~" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <a class="~~wiki_link_ext"~~ href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <a class="~~wiki_link_ext~~" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <a class="~~wiki_link_ext"~~ href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <a class="~~wiki_link_ext~~" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><a class="~~wiki_link_ext"~~ href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow">Comets Over Flatland 17</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><a class="~~wiki_link_ext~~" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith</li><li><a class="~~wiki_link_ext"~~ href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a> - youtube</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a><ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf">Sagittal score of Sunday Pipes</a></li></ul></li></ul>

<ul><li><a class="wiki_link_ext" href="http://music.columbia.edu/~chris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a></li><li><a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow">Glassic</a> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a> by Paul Erlich and Ara Sarkissian (jazz)</li><li><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow">Dragged by a Storm Across the Desert Years</a> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow">Numerology</a> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow">Revenge of the inorganic compounds</a> by Iglashion Jones (progressive metal)</li><li><a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow">My Crazy Aunt Sophie</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a>. Blatantly xenharmonic piano.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow">where words are said to mean</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow">play</a> by <a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a>, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow">I've come with a bucket of roses</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow">one drop of rain</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a> by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow">my own house</a> <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow">Comets Over Flatland 17</a> by <a class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a> Mussorgsky-Smith</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a> - youtube</li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a>, Mike Battaglia - youtube</li><li>Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - <a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow">MIDI files</a><ul><li><a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf">Sagittal score of Sunday Pipes</a></li></ul></li></ul>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-12-17 23:44:31 UTC</tt>.<br>
+: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-21 02:34:07 UTC</tt>.<br>
-: The original revision id was <tt>287117712</tt>.<br>
+: The original revision id was <tt>287849378</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 10: / Line 10: @@
 =Theory=
-In music, //22 equal temperament//, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 [[cent]]s.
+In music, //22 equal temperament//, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent]]s.
 The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the [[Indian|music theory of India]], Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after [[19edo|19 equal temperament]], and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.
-The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with [[5-limit]] music, and while not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to do rough justice to the [[7-limit|7-]] and [[11-limit]]s. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit[[consistent| consistent]]ly. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
+The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the [[5-limit]] to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta peak]]. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the [[7-limit|7-]] and [[11-limit]]s to within 3 cents/oct of error. While [[31edo|31 equal temperament]] does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit[[consistent| consistent]]ly. Furthermore, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.
 -et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.
@@ Line 50: / Line 50: @@
 ==Properties of 22 equal temperament==
-Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. It does, however, temper out the diaschisma, 2048/2025, the magic comma or small diesis, 3125/3072, and the porcupine comma, or maximal diesis, 250/243. In a diaschismic system, such as 12-et or 22-et, the [[diatonic tritone]] [[45_32|45/32]], which is a major third above a [[major whole tone]] representing [[9_8|9/8]], is equated to its inverted form, [[64_45|64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth. That the porcupine comma is tempered out means that 22-et is a [[Regular Temperaments#porcupine|porcupine]] system, where three [[minor whole tone]]s ([[10_9|10/9]] tones) give a fourth, and five give a minor sixth.
+Possibly the most striking characteristic of 22-et to those not used to it is that it does **not** "temper out" the syntonic comma of 81/80, and therefore is not a system of [[Regular Temperaments#meantone|meantone]] temperament. The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale has thirds of 9/7 and 7/6, rather than of 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO.
-In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritons of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.
+It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22-EDO supports [[porcupine]] temperament. The generator for porcupine is is a flat minor whole tone of [[10_9|10/9]], two of which is a slightly sharp [[6_5|6/5]], and three of which is a slightly flat [[4_3|4/3]]. Porcupine is notable for being the 5-limit temperament lowest in badness which is //not// approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22-EDO. It forms [[MOSScales|MOS]]'s of 7 and 8, which in 22-EDO are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).
+Other 5-limit commas 22-EDO tempers out include the diaschisma, 2048/2025 and the magic comma or small diesis, 3125/3072. In a diaschismic system, such as 12-et or 22-et, the [[diatonic tritone]] [[45_32|45/32]], which is a major third above a [[major whole tone]] representing [[9_8|9/8]], is equated to its inverted form, [[64_45|64/45]]. That the magic comma is tempered out means that 22-et is a [[Regular Temperaments#magic|magic]] system, where five major thirds make up a perfect fifth.
+In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both [[50_49|50/49]], (the [[jubilee comma]]), and [[64_63|64/63]], (the [[septimal comma]]), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the [[septimal kleisma]], so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the [[orwell comma]]; and the [[orwell tetrad]] is also a chord of 22-et.
 ===Linear Temperaments===
@@ Line 125: / Line 129: @@
 =Compositions=
-* [[http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3|Tibia]] by [[Paul Erlich]]
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://music.columbia.edu/~chris/sounds/TIBIA.mp3|Tibia]]&lt;/span&gt; by [[Paul Erlich]]
-* [[http://lumma.org/music/theory/tctmo/glassic.mp3|Glassic]] by Paul Erlich and [[Ara Sarkissian]]
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://lumma.org/music/theory/tctmo/glassic.mp3|Glassic]]&lt;/span&gt; by Paul Erlich and [[Ara Sarkissian]]
-* [[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]] by Paul Erlich and Ara Sarkissian (jazz)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]]&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)
-* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3|Dragged by a Storm Across the Desert Years]] by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3|Dragged by a Storm Across the Desert Years]]&lt;/span&gt; by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)
-* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]] by Iglashion Jones (progressive metal)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]]&lt;/span&gt; by Iglashion Jones (progressive metal)
-* [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3|Revenge of the inorganic compounds]] by Iglashion Jones (progressive metal)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3|Revenge of the inorganic compounds]]&lt;/span&gt; by Iglashion Jones (progressive metal)
-* [[http://chrisvaisvil.com/?p=267|My Crazy Aunt Sophie]] [[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]] by [[Chris Vaisvil]]. Blatantly xenharmonic piano.
+* [[http://chrisvaisvil.com/?p=267|My Crazy Aunt Sophie]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]]&lt;/span&gt; by [[Chris Vaisvil]]. Blatantly xenharmonic piano.
-* [[http://soundclick.com/share?songid=8839058|where words are said to mean]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]] by [[Andrew Heathwaite]], a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.
+* [[http://soundclick.com/share?songid=8839058|where words are said to mean]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]]&lt;/span&gt; by [[Andrew Heathwaite]], a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp; the following pieces by Andrew are for 22-tone guitar &amp; voice.
-* [[http://soundclick.com/share?songid=9101704|I've come with a bucket of roses]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]] by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).
+* [[http://soundclick.com/share?songid=9101704|I've come with a bucket of roses]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]]&lt;/span&gt; by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).
-* [[http://soundclick.com/share?songid=9101705|one drop of rain]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]] by Andrew Heathwaite (orwell-9).
+* [[http://soundclick.com/share?songid=9101705|one drop of rain]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]]&lt;/span&gt; by Andrew Heathwaite (orwell-9).
-* [[http://soundclick.com/share?songid=8839060|being a]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]] by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).
+* [[http://soundclick.com/share?songid=8839060|being a]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]]&lt;/span&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).
-* [[http://soundclick.com/share?songid=8839071|my own house]] [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]] by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).
+* [[http://soundclick.com/share?songid=8839071|my own house]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]]&lt;/span&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).
-* [[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]] by [[Randy Winchester]]
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]]&lt;/span&gt; by [[Randy Winchester]]
-* [[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]] Mussorgsky-Smith
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]&lt;/span&gt; Mussorgsky-Smith
-* [[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]] - youtube
+* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;[[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]]&lt;/span&gt; - youtube
-* [[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]], Mike Battaglia - youtube
+* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;[[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]]&lt;/span&gt;, Mike Battaglia - youtube
 * Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - [[http://www.angelfire.com/mo/oljare/midicomp.html|MIDI files]]
 ** [[http://xenharmonic.wikispaces.com/file/view/sunday3.pdf|Sagittal score of Sunday Pipes]]
@@ Line 152: / Line 156: @@
 &lt;!-- ws:start:WikiTextHeadingRule:1:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:1 --&gt;Theory&lt;/h1&gt;
   &lt;br /&gt;
-In music, &lt;em&gt;22 equal temperament&lt;/em&gt;, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 22 equally large steps. Each step represents a frequency ratio of twenty-second root of 2, or 54.55 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
+In music, &lt;em&gt;22 equal temperament&lt;/em&gt;, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the &lt;a class="wiki_link" href="/octave"&gt;octave&lt;/a&gt; into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 &lt;a class="wiki_link" href="/cent"&gt;cent&lt;/a&gt;s.&lt;br /&gt;
 &lt;br /&gt;
 The idea of dividing the octave into 22 steps of equal size seems to have originated with nineteenth century music theorist RHM Bosanquet. Inspired by the division of the octave into 22 unequal parts in the &lt;a class="wiki_link" href="/Indian"&gt;music theory of India&lt;/a&gt;, Bosenquet noted that such an equal division was capable of representing 5-limit music with tolerable accuracy. In this he was followed in the twentieth century by theorist José Würschmidt, who noted it as a possible next step after &lt;a class="wiki_link" href="/19edo"&gt;19 equal temperament&lt;/a&gt;, and J. Murray Barbour in his classic survey of tuning history, ''Tuning and Temperament''.&lt;br /&gt;
 &lt;br /&gt;
-The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; music, and while not an integral or gap edo it at least qualifies as a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta peak&lt;/a&gt;. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to do rough justice to the &lt;a class="wiki_link" href="/7-limit"&gt;7-&lt;/a&gt; and &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;s. While &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt; does much better, 22-et at least allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit&lt;a class="wiki_link" href="/consistent"&gt; consistent&lt;/a&gt;ly. Furthermore, 22-et, unlike 12 and &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, is not a &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.&lt;br /&gt;
+The 22-et system is in fact the third equal division, after 12 and 19, which is capable of approximating the &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt; to within a TE error of 4 cents/oct. While not an integral or gap edo it at least qualifies as a &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists"&gt;zeta peak&lt;/a&gt;. Moreover, there is more to it than just the 5-limit; unlike 12 or 19 it is able to approximate the &lt;a class="wiki_link" href="/7-limit"&gt;7-&lt;/a&gt; and &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;s to within 3 cents/oct of error. While &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt; does much better, 22-et still allows the use of these higher-limit harmonies, and in fact 22 is the smallest equal division to represent the 11-limit&lt;a class="wiki_link" href="/consistent"&gt; consistent&lt;/a&gt;ly. Furthermore, 22-et, unlike 12 and &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, is not a &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.&lt;br /&gt;
 &lt;br /&gt;
 -et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament.&lt;br /&gt;
@@ Line 365: / Line 369: @@
 &lt;!-- ws:start:WikiTextHeadingRule:3:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Theory-Properties of 22 equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:3 --&gt;Properties of 22 equal temperament&lt;/h2&gt;
   &lt;br /&gt;
-Possibly the most striking characteristic of 22-et to those not used to it is that it does &lt;strong&gt;not&lt;/strong&gt; &amp;quot;temper out&amp;quot; the syntonic comma of 81/80, and therefore is not a system of &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; temperament. It does, however, temper out the diaschisma, 2048/2025, the magic comma or small diesis, 3125/3072, and the porcupine comma, or maximal diesis, 250/243. In a diaschismic system, such as 12-et or 22-et, the &lt;a class="wiki_link" href="/diatonic%20tritone"&gt;diatonic tritone&lt;/a&gt; &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, which is a major third above a &lt;a class="wiki_link" href="/major%20whole%20tone"&gt;major whole tone&lt;/a&gt; representing &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, is equated to its inverted form, &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;. That the magic comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; system, where five major thirds make up a perfect fifth. That the porcupine comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#porcupine"&gt;porcupine&lt;/a&gt; system, where three &lt;a class="wiki_link" href="/minor%20whole%20tone"&gt;minor whole tone&lt;/a&gt;s (&lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt; tones) give a fourth, and five give a minor sixth.&lt;br /&gt;
+Possibly the most striking characteristic of 22-et to those not used to it is that it does &lt;strong&gt;not&lt;/strong&gt; &amp;quot;temper out&amp;quot; the syntonic comma of 81/80, and therefore is not a system of &lt;a class="wiki_link" href="/Regular%20Temperaments#meantone"&gt;meantone&lt;/a&gt; temperament. The diatonic scale it produces is instead derived from &lt;a class="wiki_link" href="/superpyth"&gt;superpyth&lt;/a&gt; temperament, which despite having the same melodic structure as meantone's diatonic scale has thirds of 9/7 and 7/6, rather than of 5/4 and 6/5. This means that the septimal comma of 64/63 vanishes, rather than the syntonic comma of 81/80, which is one of the core features of 22-EDO.&lt;br /&gt;
+&lt;br /&gt;
+It additionally tempers out the porcupine comma or maximal diesis of 250/243, which means that 22-EDO supports &lt;a class="wiki_link" href="/porcupine"&gt;porcupine&lt;/a&gt; temperament. The generator for porcupine is is a flat minor whole tone of &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, two of which is a slightly sharp &lt;a class="wiki_link" href="/6_5"&gt;6/5&lt;/a&gt;, and three of which is a slightly flat &lt;a class="wiki_link" href="/4_3"&gt;4/3&lt;/a&gt;. Porcupine is notable for being the 5-limit temperament lowest in badness which is &lt;em&gt;not&lt;/em&gt; approximated by the familiar 12-tone equal temperament, and as such represents one excellent point of departure for examining the harmonic properties of 22-EDO. It forms &lt;a class="wiki_link" href="/MOSScales"&gt;MOS&lt;/a&gt;'s of 7 and 8, which in 22-EDO are tuned respectively as 4 3 3 3 3 3 3 and 3 1 3 3 3 3 3 3 (and their respective modes).&lt;br /&gt;
+&lt;br /&gt;
+Other 5-limit commas 22-EDO tempers out include the diaschisma, 2048/2025 and the magic comma or small diesis, 3125/3072. In a diaschismic system, such as 12-et or 22-et, the &lt;a class="wiki_link" href="/diatonic%20tritone"&gt;diatonic tritone&lt;/a&gt; &lt;a class="wiki_link" href="/45_32"&gt;45/32&lt;/a&gt;, which is a major third above a &lt;a class="wiki_link" href="/major%20whole%20tone"&gt;major whole tone&lt;/a&gt; representing &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, is equated to its inverted form, &lt;a class="wiki_link" href="/64_45"&gt;64/45&lt;/a&gt;. That the magic comma is tempered out means that 22-et is a &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; system, where five major thirds make up a perfect fifth.&lt;br /&gt;
 &lt;br /&gt;
-In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, (the &lt;a class="wiki_link" href="/jubilee%20comma"&gt;jubilee comma&lt;/a&gt;), and &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, (the &lt;a class="wiki_link" href="/septimal%20comma"&gt;septimal comma&lt;/a&gt;), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritons of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the &lt;a class="wiki_link" href="/orwell%20comma"&gt;orwell comma&lt;/a&gt;; and the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; is also a chord of 22-et.&lt;br /&gt;
+In the 7-limit 22-et tempers out certain commas also tempered out by 12-et; this relates 12 equal to 22 in a way different from the way in which meantone systems are akin to it. Both &lt;a class="wiki_link" href="/50_49"&gt;50/49&lt;/a&gt;, (the &lt;a class="wiki_link" href="/jubilee%20comma"&gt;jubilee comma&lt;/a&gt;), and &lt;a class="wiki_link" href="/64_63"&gt;64/63&lt;/a&gt;, (the &lt;a class="wiki_link" href="/septimal%20comma"&gt;septimal comma&lt;/a&gt;), are tempered out in both systems. Hence because of 50/49 they both equate the two septimal tritones of 7/5 and 10/7, and because of 64/63 they both do not distinguish between a dominant seventh chord and an otonal tetrad. Hence both also temper out (50/49)/(64/63) = 225/224, the &lt;a class="wiki_link" href="/septimal%20kleisma"&gt;septimal kleisma&lt;/a&gt;, so that the septimal kleisma augmented triad is a chord of 22-et, as it also is of any meantone tuning. A septimal comma not tempered out by 12-et which 22-et does temper out is 1728/1715, the &lt;a class="wiki_link" href="/orwell%20comma"&gt;orwell comma&lt;/a&gt;; and the &lt;a class="wiki_link" href="/orwell%20tetrad"&gt;orwell tetrad&lt;/a&gt; is also a chord of 22-et.&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:5:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Theory-Properties of 22 equal temperament-Linear Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Linear Temperaments&lt;/h3&gt;
@@ Line 911: / Line 919: @@
 &lt;!-- ws:start:WikiTextHeadingRule:19:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:19 --&gt;Compositions&lt;/h1&gt;
   &lt;br /&gt;
-&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&gt; by Paul Erlich and &lt;a class="wiki_link" href="/Ara%20Sarkissian"&gt;Ara Sarkissian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow"&gt;Dragged by a Storm Across the Desert Years&lt;/a&gt; by * &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Jones&lt;/a&gt; (synth with electric guitar)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow"&gt;Numerology&lt;/a&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow"&gt;Revenge of the inorganic compounds&lt;/a&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow"&gt;My Crazy Aunt Sophie&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;. Blatantly xenharmonic piano.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow"&gt;where words are said to mean&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp;amp; the following pieces by Andrew are for 22-tone guitar &amp;amp; voice.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow"&gt;I've come with a bucket of roses&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow"&gt;one drop of rain&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Andrew Heathwaite (orwell-9).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow"&gt;being a&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow"&gt;my own house&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 17&lt;/a&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt; Mussorgsky-Smith&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow"&gt;Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity&lt;/a&gt; - youtube&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow"&gt;Improvisation in 22-equal temperament&lt;/a&gt;, Mike Battaglia - youtube&lt;/li&gt;&lt;li&gt;Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - &lt;a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow"&gt;MIDI files&lt;/a&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/~chris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/music/theory/tctmo/glassic.mp3" rel="nofollow"&gt;Glassic&lt;/a&gt;&lt;/span&gt; by Paul Erlich and &lt;a class="wiki_link" href="/Ara%20Sarkissian"&gt;Ara Sarkissian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow"&gt;Decatonic Swing&lt;/a&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%20Dragged%20By%20a%20Storm%20Across%20the%20Desert%20Years.mp3" rel="nofollow"&gt;Dragged by a Storm Across the Desert Years&lt;/a&gt;&lt;/span&gt; by * &lt;a class="wiki_link" href="/IgliashonJones"&gt;Igliashon Jones&lt;/a&gt; (synth with electric guitar)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3" rel="nofollow"&gt;Numerology&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Revenge%20of%20the%20Inorganic%20Compounds.mp3" rel="nofollow"&gt;Revenge of the inorganic compounds&lt;/a&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=267" rel="nofollow"&gt;My Crazy Aunt Sophie&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt;. Blatantly xenharmonic piano.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839058" rel="nofollow"&gt;where words are said to mean&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt;, a setting of a text by Herbert Brün to a 22-tone row, thrice repeated. This &amp;amp; the following pieces by Andrew are for 22-tone guitar &amp;amp; voice.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101704" rel="nofollow"&gt;I've come with a bucket of roses&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=9101705" rel="nofollow"&gt;one drop of rain&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow"&gt;being a&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839071" rel="nofollow"&gt;my own house&lt;/a&gt; &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow"&gt;play&lt;/a&gt;&lt;/span&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3" rel="nofollow"&gt;Comets Over Flatland 17&lt;/a&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Randy%20Winchester"&gt;Randy Winchester&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow"&gt;Night on Porcupine Mountain&lt;/a&gt;&lt;/span&gt; Mussorgsky-Smith&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow"&gt;Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity&lt;/a&gt;&lt;/span&gt; - youtube&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow"&gt;Improvisation in 22-equal temperament&lt;/a&gt;&lt;/span&gt;, Mike Battaglia - youtube&lt;/li&gt;&lt;li&gt;Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns, Mats Öljare - &lt;a class="wiki_link_ext" href="http://www.angelfire.com/mo/oljare/midicomp.html" rel="nofollow"&gt;MIDI files&lt;/a&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;