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:~~Sarzadoce~~|~~Sarzadoce~~]] and made on <tt>~~2012~~-10-~~02 19~~:51:58 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-03-23 14:13:40 UTC</tt>.

: The original revision id was <tt>~~369724086~~</tt>.

: The original revision id was <tt>417299706</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 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. ~~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~~.

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. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO does not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]].

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).

The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 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. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.

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]], implying the existence of an equal-step tetrachord, which is characteristic of Porcupine. 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).

The 164¢ "flat minor whole tone" is a key interval in 22-EDO, in part because it functions as no less than three different consonant ratios in the [[11-limit]]: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22-EDO can sound very different, with a more complex harmonic quality inevitably arising.

22-EDO also supports Orwell temperament, which uses the septimal subminor third as a generator (5 degrees) and forms MOS scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, Orwell can be tuned more accurately in other temperaments, such as [[31edo]], [[53edo]] and [[84edo]]. But 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.

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.

As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo]], in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. In [[Sagittal]], 11 can be notated as every other note of 22.

===Rank Two Temperaments===

Line 107:

Line 115:

||= 9801/9800 ||< | -3 4 -2 -2 2 > ||> 0.18 ||= Kalisma ||= Gauss' Comma ||= ||

||= 91/90 ||< | -1 -2 -1 1 0 1 > ||> 19.13 ||= Superleap ||= ||= ||

~~===A Superpythagorean System===~~

The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent [[3-limit]] fifth, thus making 22edo a "super-pythagorean" system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the [[7-limit]] ; the [[subminor third]] comes close to [[7_6|7/6]] and the [[supermajor third]] to [[9_7|9/7]]. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and [[8_7|8/7]], and the m2 falling close to a quarter-tone.

===How to Notate 22edo in Sagittal===

Line 118:

Line 123:

The division of the apotome into three syntonic commas also indicates 22's tempering out of the [[250_243|porcupine comma]] (which is equivalent to three syntonic commas minus a Pythagorean apotome).

~~===11edo===~~

~~As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo]], in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 can be notated as every other note of 22.~~

==External links==

Line 133:

Line 134:

----

=~~Compositions~~=

=Music=

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

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

** Sagittal score of Tibia, [[file:xenharmonic/TIBIA.pdf|in F||\]] or [[file:xenharmonic/tibia in g.pdf|in G]]

* [[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095|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://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]]// by [[Joel Grant Taylor]]

* ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]]//// by [[Joel Grant Taylor]]

* //[[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]]

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

* //[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]]// by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.

* ////[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]]//// by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.

* ////[[http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3|The Capture and Release of the Fairy]]//// by [[Chris Vaisvil]] => [[http://chrisvaisvil.com/?p=2494|blog post presentation]]

* //[[http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3|The Capture and Release of the Fairy]]// by [[Chris Vaisvil]] => [[http://chrisvaisvil.com/?p=2494|blog post presentation]]

* [[http://www.youtube.com/watch?v=oNJr1YOOqF8|Yak Butter]] by The Stern Brocot Band, 1L6s MOS, compressed period/generator

* //[[http://www.youtube.com/watch?v=oNJr1YOOqF8|Yak Butter]]// by The Stern Brocot Band, 1L6s MOS, compressed period/generator

[[media type="custom" key="11052222"]]</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>22edo</title></head><body><a href="#Theory">Theory</a> | <a href="#~~Compositions~~">~~Compositions~~</a>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>22edo</title></head><body><a href="#Theory">Theory</a> | <a href="#Music">Music</a>

<hr />

<hr />

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

Line 378:

Line 379:

<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. 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.

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. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO does not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as <a class="wiki_link" href="/34edo">34edo</a>, <a class="wiki_link" href="/41edo">41edo</a> and <a class="wiki_link" href="/53edo">53edo</a>.

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 (LLsLLLs or, <a class="wiki_link" href="/5L%202s">5L 2s</a>), has thirds approximating 9/7 and 7/6, rather than 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. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.

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>, implying the existence of an equal-step tetrachord, which is characteristic of Porcupine. Porcupine is notable for being the 5-limit temperament lowest in <a class="wiki_link" href="/badness">badness</a> 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).

The 164¢ &quot;flat minor whole tone&quot; is a key interval in 22-EDO, in part because it functions as no less than three different consonant ratios in the <a class="wiki_link" href="/11-limit">11-limit</a>: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22-EDO can sound very different, with a more complex harmonic quality inevitably arising.

~~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)~~.

22-EDO also supports Orwell temperament, which uses the septimal subminor third as a generator (5 degrees) and forms MOS scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, Orwell can be tuned more accurately in other temperaments, such as <a class="wiki_link" href="/31edo">31edo</a>, <a class="wiki_link" href="/53edo">53edo</a> and <a class="wiki_link" href="/84edo">84edo</a>. But 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.

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 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.

As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. In <a class="wiki_link" href="/Sagittal">Sagittal</a>, 11 can be notated as every other note of 22.

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

Line 919:

Line 928:

</table>

<h3 id="toc4"><a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"></a>A Superpythagorean System</h3>

~~ ~~

The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent <a class="wiki_link" href="/3-limit">3-limit</a> fifth, thus making 22edo a &quot;super-pythagorean&quot; system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the <a class="wiki_link" href="/7-limit">7-limit</a> ; the <a class="wiki_link" href="/subminor%20third">subminor third</a> comes close to <a class="wiki_link" href="/7_6">7/6</a> and the <a class="wiki_link" href="/supermajor%20third">supermajor third</a> to <a class="wiki_link" href="/9_7">9/7</a>. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and <a class="wiki_link" href="/8_7">8/7</a>, and the m2 falling close to a quarter-tone.

<h3 id="~~toc5~~"><a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"></a>How to Notate 22edo in Sagittal</h3>

<h3 id="toc4"><a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"></a>How to Notate 22edo in Sagittal</h3>

When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:

<img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" />

<img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" />

This notation is consistent with Sagittal's notation of 5-limit JI harmony: &quot;major&quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.

The division of the apotome into three syntonic commas also indicates 22's tempering out of the <a class="wiki_link" href="/250_243">porcupine comma</a> (which is equivalent to three syntonic commas minus a Pythagorean apotome).

<h3 id="toc6"><a name="Theory-Properties of 22 equal temperament-11edo"></a>11edo</h3>

<h2 id="toc5"><a name="Theory-External links"></a>External links</h2>

~~ ~~

As 22 is divisible by 11, a 22edo instrument can play any music in <a class="wiki_link" href="/11edo">11edo</a>, in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 ~~can be notated as every other note of 22. ~~

~~ ~~

~~<h2 id="~~toc7"><a name="Theory-External links"></a>External links</h2>

<a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''</a>

<h2 id="~~toc8~~"><a name="Theory-References"></a>References</h2>

<h2 id="toc6"><a name="Theory-References"></a>References</h2>

Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]

Line 945:

Line 947:

<hr />

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

<h1 id="toc7"><a name="Music"></a>Music</h1>

<ul><li><em~~><a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow">Tibia</a~~></em~~> by <a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a><ul><li>Sagittal score of Tibia, <a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');">in F||\</a> or <a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');">in G</a></li></ul></li><li><a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow">Glassic</a> by Paul Erlich and <a class="wiki_link" href="/Ara%20Sarkissian">Ara Sarkissian</a></li><li><em~~><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/decatonic-swing.mp3" rel="nofollow">Decatonic Swing</a~~></em~~> by Paul Erlich and Ara Sarkissian (jazz)</li><li~~><em~~><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a><~~/em> by <a class~~="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a></li><li><em~~><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~~></em~~> by * <a class="wiki_link" href="/IgliashonJones">Igliashon Jones</a> (synth with electric guitar)</li><li><em~~><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~~></em~~> by Iglashion Jones (progressive metal)</li><li><~~em><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~~></em~~> 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> <em~~><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3" rel="nofollow">play</a~~></em~~> 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> <em~~><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> <em~~><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3" rel="nofollow">play</a~~></em~~> 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> <em~~><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3" rel="nofollow">play</a~~></em~~> by Andrew Heathwaite (orwell-9).</li><li><a class="wiki_link_ext" href="http://soundclick.com/share?songid=8839060" rel="nofollow">being a</a> <~~em><a~~ class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3" rel="nofollow">play</a~~></em~~> 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> <em~~><a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3" rel="nofollow">play</a~~></em~~> by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).</li><li><em~~><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><~~/span> by <a~~ class="wiki_link" href="/Randy%20Winchester">Randy Winchester</a></li><li><em~~><a class="wiki_link_ext" href="http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3" rel="nofollow">Night on Porcupine Mountain</a~~></em~~> Mussorgsky-Smith</li><li><em~~><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=lO5xSjIHyMg" rel="nofollow">Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity</a~~></em~~> - youtube</li><li><~~em><a~~ class="wiki_link_ext" href="http://www.youtube.com/watch?v=WMtp9Wk0tO0" rel="nofollow">Improvisation in 22-equal temperament</a~~></em~~>, 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/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');">Sagittal score of Sunday Pipes</a></li></ul></li><li><em~~><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a~~></em> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow">The Capture and Release of the Fairy</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow">blog post presentation</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow">Yak Butter</a> by The Stern Brocot Band, 1L6s MOS, compressed period/generator</li></ul>

<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><ul><li>Sagittal score of Tibia, <a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');">in F||\</a> or <a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');">in G</a></li></ul></li><li><a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" 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://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow">12-22hexachordal Dirge</a> by <a class="wiki_link" href="/Joel%20Grant%20Taylor">Joel Grant Taylor</a></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/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');">Sagittal score of Sunday Pipes</a></li></ul></li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow">Phobos Light</a> by Chris Vaisvil in Hedgehog[14] <a class="wiki_link" href="/hedgehog14">tuned</a> to 22edo.</li><li><a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow">The Capture and Release of the Fairy</a> by <a class="wiki_link" href="/Chris%20Vaisvil">Chris Vaisvil</a> =&gt; <a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow">blog post presentation</a></li><li><a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow">Yak Butter</a> by The Stern Brocot Band, 1L6s MOS, compressed period/generator</li></ul>

<script type="text/javascript" src="http://mediaplayer.yahoo.com/js">

</script></body></html></pre></div>

@@ 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:Sarzadoce|Sarzadoce]] and made on <tt>2012-10-02 19:51:58 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2013-03-23 14:13:40 UTC</tt>.<br>
-: The original revision id was <tt>369724086</tt>.<br>
+: The original revision id was <tt>417299706</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 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. 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.
+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. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO does not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as [[34edo]], [[41edo]] and [[53edo]].
-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).
+The diatonic scale it produces is instead derived from [[superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L 2s]]), has thirds approximating 9/7 and 7/6, rather than 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. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.
+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]], implying the existence of an equal-step tetrachord, which is characteristic of Porcupine. 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).
+The 164¢ "flat minor whole tone" is a key interval in 22-EDO, in part because it functions as no less than three different consonant ratios in the [[11-limit]]: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22-EDO can sound very different, with a more complex harmonic quality inevitably arising.
+-EDO also supports Orwell temperament, which uses the septimal subminor third as a generator (5 degrees) and forms MOS scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, Orwell can be tuned more accurately in other temperaments, such as [[31edo]], [[53edo]] and [[84edo]]. But 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.
 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.
+As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo]], in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. In [[Sagittal]], 11 can be notated as every other note of 22.
 ===Rank Two Temperaments===
@@ Line 107: / Line 115: @@
 ||= 9801/9800 ||&lt; | -3 4 -2 -2 2 &gt; ||&gt; 0.18 ||= Kalisma ||= Gauss' Comma ||=   ||
 ||= 91/90 ||&lt; | -1 -2 -1 1 0 1 &gt; ||&gt; 19.13 ||= Superleap ||=   ||=   ||
-===A Superpythagorean System===
-The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent [[3-limit]] fifth, thus making 22edo a "super-pythagorean" system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the [[7-limit]] ; the [[subminor third]] comes close to [[7_6|7/6]] and the [[supermajor third]] to [[9_7|9/7]]. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and [[8_7|8/7]], and the m2 falling close to a quarter-tone.
 ===How to Notate 22edo in Sagittal===
@@ Line 118: / Line 123: @@
 The division of the apotome into three syntonic commas also indicates 22's tempering out of the [[250_243|porcupine comma]] (which is equivalent to three syntonic commas minus a Pythagorean apotome).
-===11edo===
-As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo]], in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 can be notated as every other note of 22.
 ==External links==
@@ Line 133: / Line 134: @@
 ----
-=Compositions=
+=Music=
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3|Tibia]]//&lt;/span&gt;&lt;/span&gt; by [[Paul Erlich]]
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3|Tibia]]////&lt;/span&gt;&lt;/span&gt; by [[Paul Erlich]]
 ** Sagittal score of Tibia, [[file:xenharmonic/TIBIA.pdf|in F||\]] or [[file:xenharmonic/tibia in g.pdf|in G]]
 * &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;[[http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095|Glassic]]&lt;/span&gt;&lt;/span&gt; by Paul Erlich and [[Ara Sarkissian]]
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]]//&lt;/span&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://lumma.org/tuning/erlich/decatonic-swing.mp3|Decatonic Swing]]////&lt;/span&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)
-* //[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]]// by [[Joel Grant Taylor]]
+* ////[[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3|12-22hexachordal Dirge]]//// by [[Joel Grant Taylor]]
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&lt;/span&gt; by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&lt;/span&gt; by * [[IgliashonJones|Igliashon Jones]] (synth with electric guitar)
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]]//&lt;/span&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Igs/City%20Of%20The%20Asleep%20-%2022-Numerology.mp3|Numerology]]////&lt;/span&gt;&lt;/span&gt; by Iglashion Jones (progressive metal)
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&lt;/span&gt; by Iglashion Jones (progressive metal)
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&lt;/span&gt; by Iglashion Jones (progressive metal)
-* [[http://chrisvaisvil.com/?p=267|My Crazy Aunt Sophie]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]]//&lt;/span&gt;&lt;/span&gt; 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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://micro.soonlabel.com/22-ET/22edo-piano-my-crazy-aunt-sophie.mp3|play]]////&lt;/span&gt;&lt;/span&gt; by [[Chris Vaisvil]]. Blatantly xenharmonic piano.
-* [[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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]]//&lt;/span&gt;&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=8839058|where words are said to mean]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+wherewordsaresaidtomean.mp3|play]]////&lt;/span&gt;&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]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]]//&lt;/span&gt;&lt;/span&gt; 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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+ivecomewithabucketofroses.mp3|play]]////&lt;/span&gt;&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]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]]//&lt;/span&gt;&lt;/span&gt; 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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+onedropofrain.mp3|play]]////&lt;/span&gt;&lt;/span&gt; by Andrew Heathwaite (orwell-9).
-* [[http://soundclick.com/share?songid=8839060|being a]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]]//&lt;/span&gt;&lt;/span&gt; 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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+beinga.mp3|play]]////&lt;/span&gt;&lt;/span&gt; by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).
-* [[http://soundclick.com/share?songid=8839071|my own house]] &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]]//&lt;/span&gt;&lt;/span&gt; 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;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Heathwaite/andrewheathwaite+myownhouse.mp3|play]]////&lt;/span&gt;&lt;/span&gt; by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]]//&lt;/span&gt;&lt;/span&gt; by [[Randy Winchester]]
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/17%20-%2017.%2022%20octave.mp3|Comets Over Flatland 17]]////&lt;/span&gt;&lt;/span&gt; by [[Randy Winchester]]
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]//&lt;/span&gt;&lt;/span&gt; Mussorgsky-Smith
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://www.archive.org/download/NightOnPorcupineMountain/Genewardsmithmussorgsky-NightOnPorcupineMountain.mp3|Night on Porcupine Mountain]]////&lt;/span&gt;&lt;/span&gt; Mussorgsky-Smith
-* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;//[[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]]//&lt;/span&gt;&lt;/span&gt; - youtube
+* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;////[[http://www.youtube.com/watch?v=lO5xSjIHyMg|Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity]]////&lt;/span&gt;&lt;/span&gt; - youtube
-* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;//[[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]]//&lt;/span&gt;&lt;/span&gt;, Mike Battaglia - youtube
+* &lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;////[[http://www.youtube.com/watch?v=WMtp9Wk0tO0|Improvisation in 22-equal temperament]]////&lt;/span&gt;&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]]
 ** [[file:xenharmonic/sunday3.pdf|Sagittal score of Sunday Pipes]]
-* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;//[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]]//&lt;/span&gt; by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.
+* &lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;////[[http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3|Phobos Light]]////&lt;/span&gt; by Chris Vaisvil in Hedgehog[14] [[hedgehog14|tuned]] to 22edo.
-* ////[[http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3|The Capture and Release of the Fairy]]//// by [[Chris Vaisvil]] =&gt; [[http://chrisvaisvil.com/?p=2494|blog post presentation]]
+* //[[http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3|The Capture and Release of the Fairy]]// by [[Chris Vaisvil]] =&gt; [[http://chrisvaisvil.com/?p=2494|blog post presentation]]
-* [[http://www.youtube.com/watch?v=oNJr1YOOqF8|Yak Butter]] by The Stern Brocot Band, 1L6s MOS, compressed period/generator
+* //[[http://www.youtube.com/watch?v=oNJr1YOOqF8|Yak Butter]]// by The Stern Brocot Band, 1L6s MOS, compressed period/generator
 [[media type="custom" key="11052222"]]</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:21:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;!-- ws:start:WikiTextTocRule:27: --&gt;&lt;!-- ws:end:WikiTextTocRule:27 --&gt;&lt;!-- ws:start:WikiTextTocRule:28: --&gt;&lt;!-- ws:end:WikiTextTocRule:28 --&gt;&lt;!-- ws:start:WikiTextTocRule:29: --&gt;&lt;!-- ws:end:WikiTextTocRule:29 --&gt;&lt;!-- ws:start:WikiTextTocRule:30: --&gt;&lt;!-- ws:end:WikiTextTocRule:30 --&gt;&lt;!-- ws:start:WikiTextTocRule:31: --&gt; | &lt;a href="#Compositions"&gt;Compositions&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:31 --&gt;&lt;!-- ws:start:WikiTextTocRule:32: --&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;22edo&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:17:&amp;lt;img id=&amp;quot;wikitext@@toc@@flat&amp;quot; class=&amp;quot;WikiMedia WikiMediaTocFlat&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/flat?w=100&amp;amp;h=16&amp;quot;/&amp;gt; --&gt;&lt;!-- ws:end:WikiTextTocRule:17 --&gt;&lt;!-- ws:start:WikiTextTocRule:18: --&gt;&lt;a href="#Theory"&gt;Theory&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:18 --&gt;&lt;!-- ws:start:WikiTextTocRule:19: --&gt;&lt;!-- ws:end:WikiTextTocRule:19 --&gt;&lt;!-- ws:start:WikiTextTocRule:20: --&gt;&lt;!-- ws:end:WikiTextTocRule:20 --&gt;&lt;!-- ws:start:WikiTextTocRule:21: --&gt;&lt;!-- ws:end:WikiTextTocRule:21 --&gt;&lt;!-- ws:start:WikiTextTocRule:22: --&gt;&lt;!-- ws:end:WikiTextTocRule:22 --&gt;&lt;!-- ws:start:WikiTextTocRule:23: --&gt;&lt;!-- ws:end:WikiTextTocRule:23 --&gt;&lt;!-- ws:start:WikiTextTocRule:24: --&gt;&lt;!-- ws:end:WikiTextTocRule:24 --&gt;&lt;!-- ws:start:WikiTextTocRule:25: --&gt; | &lt;a href="#Music"&gt;Music&lt;/a&gt;&lt;!-- ws:end:WikiTextTocRule:25 --&gt;&lt;!-- ws:start:WikiTextTocRule:26: --&gt;
-&lt;!-- ws:end:WikiTextTocRule:32 --&gt;&lt;hr /&gt;
+&lt;!-- ws:end:WikiTextTocRule:26 --&gt;&lt;hr /&gt;
 &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;
@@ Line 378: / Line 379: @@
 &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. 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;
+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. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO does not distinguish, such as the two whole tones 9/8 and 10/9. Indeed, these distinctions are exaggerated in comparison to 5-limit JI and many more accurate temperaments such as &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;, &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt; and &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+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 (LLsLLLs or, &lt;a class="wiki_link" href="/5L%202s"&gt;5L 2s&lt;/a&gt;), has thirds approximating 9/7 and 7/6, rather than 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. Superpyth is melodically interesting for having a quasi-equal pentatonic scale (as the large whole tone and subminor third are rather close in size) and a more uneven heptatonic scale, as compared with 12-equal and meantone systems: step patterns 4 4 5 4 5 and 4 4 1 4 4 4 1, respectively.&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;, implying the existence of an equal-step tetrachord, which is characteristic of Porcupine. Porcupine is notable for being the 5-limit temperament lowest in &lt;a class="wiki_link" href="/badness"&gt;badness&lt;/a&gt; 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;
+The 164¢ &amp;quot;flat minor whole tone&amp;quot; is a key interval in 22-EDO, in part because it functions as no less than three different consonant ratios in the &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;: 10/9, 11/10, and 12/11. It is thus extremely ambiguous and flexible. The trade-off is that it is very much in the cracks of the 12-equal piano, and so for most 12-equal listeners, it takes some getting used to. Simple translations of 5-limit music into 22-EDO can sound very different, with a more complex harmonic quality inevitably arising.&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;
+-EDO also supports Orwell temperament, which uses the septimal subminor third as a generator (5 degrees) and forms MOS scales with step patterns 3 2 3 2 3 2 3 2 2 and 1 2 2 1 2 2 1 2 2 1 2 2 2. Harmonically, Orwell can be tuned more accurately in other temperaments, such as &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;, &lt;a class="wiki_link" href="/53edo"&gt;53edo&lt;/a&gt; and &lt;a class="wiki_link" href="/84edo"&gt;84edo&lt;/a&gt;. But 22-equal Orwell has a leg-up on the others melodically, as the large and small steps of Orwell[9] are easier to distinguish in 22.&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 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;
+As 22 is divisible by 11, a 22edo instrument can play any music in &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, in the same way that 12edo can play 6edo (the whole tone scale). 11-equal is interesting for sounding melodically very similar to 12-equal (whole steps, half steps and minor thirds in the familiar 1:2:3 ratio), but harmonically very different, in particular because it lacks perfect fifths/fourths and 5-limit major thirds/minor sixths. In &lt;a class="wiki_link" href="/Sagittal"&gt;Sagittal&lt;/a&gt;, 11 can be notated as every other note of 22.&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-Rank Two Temperaments"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:5 --&gt;Rank Two Temperaments&lt;/h3&gt;
@@ Line 919: / Line 928: @@
 &lt;/table&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Theory-Properties of 22 equal temperament-A Superpythagorean System"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;A Superpythagorean System&lt;/h3&gt;
- &lt;br /&gt;
-The 22edo fifth, measuring approximately 709.1 cents, is wider than the 702-cent &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt; fifth, thus making 22edo a &amp;quot;super-pythagorean&amp;quot; system. As with any superpyth, a chain of fifths produces relatively wide major thirds and narrow minor thirds. In the case of 22edo, the thirds are stretched out to the &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; ; the &lt;a class="wiki_link" href="/subminor%20third"&gt;subminor third&lt;/a&gt; comes close to &lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt; and the &lt;a class="wiki_link" href="/supermajor%20third"&gt;supermajor third&lt;/a&gt; to &lt;a class="wiki_link" href="/9_7"&gt;9/7&lt;/a&gt;. Thus, the resulting diatonic scale, which no longer approximates 5-limit thirds, sounds oddly consonant. The ratio of major 2nd to minor 2nd in this diatonic scale is stretched out to 4:1, with the M2 falling between 9/8 and &lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;, and the m2 falling close to a quarter-tone.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;How to Notate 22edo in Sagittal&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:9:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="Theory-Properties of 22 equal temperament-How to Notate 22edo in Sagittal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:9 --&gt;How to Notate 22edo in Sagittal&lt;/h3&gt;
   &lt;br /&gt;
 When 22edo is treated as generated by a cycle of its fifths, the naturals F C G D A E B represent a chain of those 13\22 fifths; consequently, the whole tone comes out to four degrees and the apotome (pythagorean sharp/flat) comes out to three degrees. Three pairs of sagittal symbols, dividing that apotome into three parts, are all that is necessary, and offer plenty of enharmonic equivalents:&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:801:&amp;lt;img src=&amp;quot;/file/view/22edo.png/269078624/22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:801 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:795:&amp;lt;img src=&amp;quot;/file/view/22edo.png/269078624/22edo.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/22edo.png/269078624/22edo.png" alt="22edo.png" title="22edo.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:795 --&gt;&lt;br /&gt;
 This notation is consistent with Sagittal's notation of 5-limit JI harmony: &amp;quot;major&amp;quot; 3rds and 6ths appear as (super)pythagorean intervals flattened by a syntonic comma.&lt;br /&gt;
 &lt;br /&gt;
 The division of the apotome into three syntonic commas also indicates 22's tempering out of the &lt;a class="wiki_link" href="/250_243"&gt;porcupine comma&lt;/a&gt; (which is equivalent to three syntonic commas minus a Pythagorean apotome).&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="Theory-Properties of 22 equal temperament-11edo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;11edo&lt;/h3&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:11:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:11 --&gt;External links&lt;/h2&gt;
- &lt;br /&gt;
-As 22 is divisible by 11, a 22edo instrument can play any music in &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;, in the same way that 12edo can play 6edo (the whole tone scale). In Sagittal, 11 can be notated as every other note of 22.&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="Theory-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;External links&lt;/h2&gt;
   &lt;br /&gt;
 &lt;a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow"&gt;Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:17:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:17 --&gt;References&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:13:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Theory-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:13 --&gt;References&lt;/h2&gt;
   &lt;br /&gt;
 Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]&lt;br /&gt;
@@ Line 945: / Line 947: @@
 &lt;br /&gt;
 &lt;hr /&gt;
-&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;!-- ws:start:WikiTextHeadingRule:15:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Music"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:15 --&gt;Music&lt;/h1&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt;&lt;/em&gt;&lt;/span&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;ul&gt;&lt;li&gt;Sagittal score of Tibia, &lt;a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');"&gt;in F||\&lt;/a&gt; or &lt;a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');"&gt;in G&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow"&gt;Glassic&lt;/a&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&gt;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow"&gt;12-22hexachordal Dirge&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Joel%20Grant%20Taylor"&gt;Joel Grant Taylor&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&gt;&lt;em&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;/em&gt;&lt;/span&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/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt;&lt;/em&gt;&lt;/span&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow"&gt;The Capture and Release of the Fairy&lt;/a&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt; =&amp;gt; &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow"&gt;blog post presentation&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow"&gt;Yak Butter&lt;/a&gt; by The Stern Brocot Band, 1L6s MOS, compressed period/generator&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://music.columbia.edu/%7Echris/sounds/TIBIA.mp3" rel="nofollow"&gt;Tibia&lt;/a&gt;&lt;/span&gt;&lt;/span&gt; by &lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt;&lt;ul&gt;&lt;li&gt;Sagittal score of Tibia, &lt;a href="http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/TIBIA.pdf/313029038/TIBIA.pdf');"&gt;in F||\&lt;/a&gt; or &lt;a href="http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/tibia%20in%20g.pdf/313029040/tibia%20in%20g.pdf');"&gt;in G&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://www.myspace.com/paulerlich/music/songs/glassic-in-22-tone-equal-temperament-45202095" rel="nofollow"&gt;Glassic&lt;/a&gt;&lt;/span&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&lt;/span&gt; by Paul Erlich and Ara Sarkissian (jazz)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12-22hexachordal%20Dirge.mp3" rel="nofollow"&gt;12-22hexachordal Dirge&lt;/a&gt; by &lt;a class="wiki_link" href="/Joel%20Grant%20Taylor"&gt;Joel Grant Taylor&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover"&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&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;&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;span class="ywp-page-play-pause ywp-page-video ywp-link-hover ywp-page-img-link"&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;&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/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');"&gt;Sagittal score of Sunday Pipes&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;span class="ywp-page-play-pause ywp-page-audio ywp-link-hover ywp-page-img-link"&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120207-phobos-light-hedgehog14.mp3" rel="nofollow"&gt;Phobos Light&lt;/a&gt;&lt;/span&gt; by Chris Vaisvil in Hedgehog[14] &lt;a class="wiki_link" href="/hedgehog14"&gt;tuned&lt;/a&gt; to 22edo.&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/22-ET/20120716_theorbo_22edo.mp3" rel="nofollow"&gt;The Capture and Release of the Fairy&lt;/a&gt;&lt;/em&gt; by &lt;a class="wiki_link" href="/Chris%20Vaisvil"&gt;Chris Vaisvil&lt;/a&gt; =&amp;gt; &lt;a class="wiki_link_ext" href="http://chrisvaisvil.com/?p=2494" rel="nofollow"&gt;blog post presentation&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;em&gt;&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=oNJr1YOOqF8" rel="nofollow"&gt;Yak Butter&lt;/a&gt;&lt;/em&gt; by The Stern Brocot Band, 1L6s MOS, compressed period/generator&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
 &lt;!-- ws:start:WikiTextMediaRule:0:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/custom/11052222?h=0&amp;amp;w=0&amp;quot; class=&amp;quot;WikiMedia WikiMediaCustom&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;custom&amp;amp;quot; key=&amp;amp;quot;11052222&amp;amp;quot;&amp;quot; title=&amp;quot;Custom Media&amp;quot;/&amp;gt; --&gt;&lt;script type="text/javascript" src="http://mediaplayer.yahoo.com/js"&gt;
 &lt;/script&gt;&lt;!-- ws:end:WikiTextMediaRule:0 --&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>