Revision as of 03:34, 23 September 2018

Theory

In music, 22 equal temperament, called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the octave into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 cents. Because it distinguishes 10/9 and 9/8, it's good for 5-limit.

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

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

22-et can also be treated as adding harmonics 3 and 5 to 11-EDO's 2.7.9.11.15.17 subgroup, making it a (rather accurate) 2.3.5.7.11.17 subgroup temperament. Let us also mind it's approximation of the 31st harmonic is within half a cent, which is fairly accurate. It also approximates some intervals involving the 29th harmonic well, especially 29/24, which is also matched within half a cent. This leaves us with 2.3.5.7.11.17.29.31.

22-et is very close to an extended "quarter-comma superpyth", a tuning analogous to quarter-comma meantone except that it tempers out the septimal comma 64:63 instead of the syntonic comma 81:80. Because of this it has nearly pure septimal major thirds (9:7).

Intervalic Naming Systems

The intervals of 22 EDO may be thought of as a system arising from both Superpyth and Porcupine temperament therefore, it makes sense to categorize each on as major and minor of each temperament. s indicates superpyth, p indicates Porcupine, because p now represents procupine and not perfect, P in perfect intervals is no longer used in this system. Instead the number is used without P and is read as either just the number or "Natural". Example: P5 becomes 5 or N5 = Perfect fifth becomes Natural fifth.

Intervals by degree (Superpyth/Porcupine)

Degree	Name and Abbreviation	Cents	Approximate Ratios*
0	Natural Unison, 1	0	1/1
1	s-minor second, sm2	54.55	33/32, 34/33, 32/31
2	p-diminished second, pd2	109.09	18/17, 17/16, 16/15, 15/14
3	p-minor second, pm2	163.64	11/10, 10/9, 32/29
4	(s/p) Major second, M2	218.18	9/8, 8/7, 17/15
5	s-minor third, sm3	272.73	7/6, 20/17
6	p-minor third, pm3	327.27	6/5, 17/14, 11/9, 29/24
7	p-Major third, pM3	381.82	5/4
8	s-Major third, sM3	436.36	9/7, 14/11, 22/17
9	Natural Fourth, 4, N4	490.91	4/3
10	p-Major Fourth, pM4 s-dim fifth	545.45	11/8, 15/11
11	Augmented Fourth, A4, Half-Octave, HO	600	7/5, 10/7, 17/12, 24/17
12	p-minor Fifth, pm5 s-aug fourth	654.55	16/11, 22/15
13	Natural Fifth, 5, N5	709.09	3/2
14	s-minor sixth, sm6	763.64	11/7, 14/9, 17/11
15	p-minor sixth, pm6	818.18	8/5
16	p-Major sixth, pM6	872.73	5/3, 18/11, 28/17
17	s-Major sixth, sM6	927.27	12/7, 17/10
18	(s/p) minor seventh, m7	981.82	7/4, 16/9, 30/17
19	p-Major seventh, pM7	1036.36	20/11, 9/5, 29/16
20	p-Augmented Seventh	1090.91	15/8, 32/17, 17/9, 28/15
21	s-Major Seventh, sM7	1145.45	33/17, 64/33, 31/16
22	Octave, 8	1200	2/1

22edo intervals can also be notated using ups and downs. This notation allows for easy chord naming. The keyboard runs D * * * E F * * * G * * * A * * * B C * * * D. The natural notes represent the conventional chain of 5ths FCGDAEB.

Another possible notation uses the porcupine generator to generate the notation as well. The 2nd and 7th are perfect, and the 4th and 5th are imperfect like the 3rd and 6th. This is the only way to use a heptatonic notation without additional accidentals. The keyboard runs D * * E * * F * * G * * * A * * B * * C * * D. The natural notes represent a chain of 2nds ABCDEFG.

Yet another notation is pentatonic. The degrees are unison, subthird, fourthoid, fifthoid, subseventh and octoid. This is the only way to use a chain-of-fifths notation without additional accidentals. The keyboard runs D * * * * F * * * G * * * A * * * * C * * * D. The natural notes represent a chain of 5ths FCGDA.

Intervals by degree (Ups and Downs, Porcupine and Pentatonic)

Degree	Size (Cents)	Ups and downs			Porcupine			Pentatonic
0	0	perfect unison	P1	D	perfect unison	P1	D	perfect unison	P1	D
1	55	minor 2nd	m2	Eb	aug unison	A1	D#	aug unison	A1	D#
2	109	upminor 2nd	^m2	Eb^	dim 2nd	d2	Eb	double-aug unison, double-dim sub3rd	AA1, dds3	Dx, Fb3
3	164	downmajor 2nd	vM2	Ev	perfect 2nd	P2	E	dim sub3rd	ds3	Fbb
4	218	major 2nd	M2	E	aug 2nd	A2	E#	minor sub3rd	ms3	Fb
5	273	minor 3rd	m3	F	dim 3rd	d3	Fb	major sub3rd	Ms3	F
6	327	upminor 3rd	^m3	F^	minor 3rd	m3	F	aug sub3rd	As3	F#
7	382	downmajor 3rd	vM3	F#v	major 3rd	M3	F#	double-aug sub3rd, double-dim 4thoid	AAs3, dd4d	Fx, Gbb
8	436	major 3rd	M3	F	aug 3rd, dim 4th	A3, d4	Fx, Gb	dim 4thoid	d4d	Gb
9	491	perfect fourth	P4	G	minor 4th	m4	G	perfect 4thoid	P4d	G
10	545	up-4th, dim 5th	^4, d5	G^, Ab	major 4th	M4	G#	aug 4thoid	A4d	G#
11	600	downaug 4th, updim 5th	vA4, ^d5	G#v, Ab^	aug 4th, dim 5th	A4, d5	Gx, Abb	double-aug 4thoid, double-dim 5thoid	AA4d, dd5d	Gx, Abb
12	655	aug 4th, down-5th	A4, v5	G#, Av	minor 5th	m5	Ab	dim 5thoid	d5d	Ab
13	709	perfect 5th	P5	A	major 5th	M5	A	perfect 5thoid	P5d	A
14	764	minor 6th	m6	Bb	aug 5th, dim 6th	A5, d6	A#, Bbb	aug 5thoid	A5d	A#
15	818	upminor 6th	^m6	Bb^	minor 6th	m6	Bb	double-aug 5thoid, double-dim sub7th	AA5d, dds7	Ax, Cb3
16	873	downmajor 6th	vM6	Bv	major 6th	M6	B	dim sub7th	ds7	Cbb
17	927	major 6th	M6	B	aug 6th	A6	B#	minor sub7th	ms7	Cb
18	982	minor 7th	m7	C	dim 7th	d7	Cb	major sub7th	Ms7	C
19	1036	upminor 7th	^m7	C^	perfect 7th	P7	C	aug sub7th	As7	C#
20	1091	downmajor 7th	vM7	C#v	aug 7th	A7	C#	double-aug sub7th, double-dim octave	AAs7, dd8	Cx, Dbb
21	1145	major 7th	M7	C#	dim 8ve	d8	Db	dim octave	d8	Db
22	1200	perfect octave	P8	D	perfect octave	P8	D	perfect octave	P8	D

Combining ups and downs notation with color notation, qualities can be loosely associated with colors:

quality	color	monzo format	examples
minor	zo	{a, b, 0, 1}	7/6, 7/4
"	fourthward wa	{a, b}, b < -1	32/27, 16/9
upminor	gu	{a, b, -1}	6/5, 9/5
downmajor	yo	{a, b, 1}	5/4, 5/3
major	fifthward wa	{a, b}, b > 1	9/8, 27/16
"	ru	{a, b, 0, -1}	9/7, 12/7

Chord Names

All 22edo chords can be named using ups and downs notation. Here are the zo, gu, yo and ru triads:

color of the 3rd	JI chord	notes as edosteps	notes of C chord	written name	spoken name
zo	6:7:9	0-5-13	C Eb G	Cm	C minor
gu	10:12:15	0-6-13	C Eb^ G	C.^m	C upminor
yo	4:5:6	0-7-13	C Ev G	C.v	C downmajor or C dot down
ru	14:18:27	0-8-13	C E G	C	C major or C

For C.v, the period is needed because "Cv", spoken as "C down", is either a note, or a major chord Cv Ev Gv.

The period isn't needed in Cm because there's no ups or downs immediately after the note name.

0-8-13-18 = C E G Bb = C7 = "C seven"

0-7-13-18 = C Ev G Bb = C7(v3) = "C seven, down third"

0-8-13-21 = C E G B = CM7 = "C major seven"

0-7-13-20 = C Ev G Bv = C.vM7 = "C downmajor seven" (the down symbol applies to both the 3rd and the 7th)

0-3-13 = C Dv G = C(v2)

0-4-13 = C D G = C2

0-9-13 = C F G = C4

0-10-13 = C F^ G = C(^4)

0-5-10 = C Eb Gb = Cdim

0-5-11 = C Eb Gb^ = Cdim(^5)

0-5-12 = C Eb Gv = Cm(v5)

0-5-10-15 = C Eb Gb Bbb = Cdim7

0-5-11-14 = C Eb Gb^ Bbbv = Cdim7(^5,v7)

0-6-11-15 = C Eb^ Gb^ Bbb = Cdim7(^3,^5)

0-6-11-16 = C Eb^ Gb^ Bbb^ = C.^dim7(^5) (the up symbol applies to both the 3rd and the 7th)

0-5-13-17 = C Eb G A = Cm6

Sometimes doubled ups/downs are unavoidable:

0-6-12-15 = C Eb^ Gv Avv = Cm6(^3,v5,vv6), or C Eb^ Gb^^ Bbb = Cdim7(^3,^^5)

0-8-13-17 = C E G A = C6

0-8-13-16 = C E G Av = C(v6)

0-7-13-17 = C Ev G A = C6(v3)

0-7-13-16 = C Ev G Av = C.v6 (the down symbol applies to both the 3rd and the 6th)

0-5-13-18 = C Eb G Bb = Cm7

0-6-13-19 = C Eb^ G Bb^ = C.^m7

0-8-13-21 = C E G B = CM7

0-7-13-20 = C Ev G Bv = C.vM7

0-5-13-16 = C Eb G Av = Cm(v6)

0-8-13-19 = C E G Bb^ = C(^7)

0-7-13-18-26 = C Ev G Bb D = C9(v3)

0-7-13-18-26-32 = C Ev G Bb D F^ = C9(v3,^11)

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.

Selected just intervals by error

The following table shows how some prominent just intervals are represented in 22edo (ordered by absolute error).

Best direct mapping, even if inconsistent

Interval, complement	Error (abs., in cents)
9/7, 14/9	1.280
11/10, 20/11	1.368
16/15, 15/8	2.640
5/4, 8/5	4.496
7/6, 12/7	5.856
11/8, 16/11	5.863
4/3, 3/2	7.136
15/11, 22/15	8.504
15/14, 28/15	10.352
6/5, 5/3	11.631
8/7, 7/4	12.992
12/11, 11/6	12.999
9/8, 16/9	14.272
13/11, 22/13	16.482
7/5, 10/7	17.488
13/10, 20/13	17.850
18/13, 13/9	17.928
10/9, 9/5	18.767
14/11, 11/7	18.856
14/13, 13/7	19.207
11/9, 18/11	20.135
16/13, 13/8	22.346
15/13, 26/15	24.986
13/12, 24/13	25.064

Patent val mapping

Interval, complement	Error (abs., in cents)
9/7, 14/9	1.280
11/10, 20/11	1.368
16/15, 15/8	2.640
5/4, 8/5	4.496
7/6, 12/7	5.856
11/8, 16/11	5.863
4/3, 3/2	7.136
15/11, 22/15	8.504
15/14, 28/15	10.352
6/5, 5/3	11.631
8/7, 7/4	12.992
12/11, 11/6	12.999
9/8, 16/9	14.272
13/11, 22/13	16.482
7/5, 10/7	17.488
13/10, 20/13	17.850
10/9, 9/5	18.767
14/11, 11/7	18.856
11/9, 18/11	20.135
16/13, 13/8	22.346
15/13, 26/15	24.986
13/12, 24/13	29.482
14/13, 13/7	35.338
18/13, 13/9	36.618

22ed2-001e.svg

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 meantone temperament. This means that 22 distinguishes a number of Pythagorean and 5-limit intervals that 12-EDO, 19-EDO, 31-EDO, ... do 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.

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, two of which is a slightly sharp 6/5, and three of which is a slightly flat 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 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. 22edo does not contain a neutral third but both the 5-limit thirds have a "neutral-like" quality since they are tempered closer together rather than farther apart as in 12edo.

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, which is a major third above a major whole tone representing 9/8, is equated to its inverted form, 64/45. That the magic comma is tempered out means that 22-et is a 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, (the jubilee comma), and 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. Similarly, 22edo is melodically similar to 24edo as both contain quarter-tones and minor, neutral, and major seconds; but 22edo offers much better all-around harmonies than 24. In Sagittal, 11 can be notated as every other note of 22.

Rank Two Temperaments

List of 22et rank two temperaments by badness

List of 22et rank two temperaments by complexity

List of edo-distinct 22et rank two temperaments

Periods per octave	Period	Generator	Temperaments
1	22\22	1\22	Sensa/chromo/ceratitid
1	22\22	3\22	Porcupine
1	22\22	5\22	Orson/orwell/blair
1	22\22	7\22	Magic/telepathy
1	22\22	9\22	Superpyth/suprapyth
2	11\22	1\22	Shrutar/hemipaj/comic
2	11\22	2\22	Srutal/pajara/pajarous
2	11\22	3\22	Hedgehog/echidna
2	11\22	4\22	Astrology/wizard/antikythera
2	11\22	5\22	Doublewide/fleetwood
11	2\22	1\22	Hendecatonic/undeka

Commas

22 EDO tempers out the following commas. (Note: This assumes the val < 22 35 51 62 76 81 |.)

Rational	Monzo	Size (Cents)	Name 1	Name 2	Name 3
250/243	\| 1 -5 3 >	49.17	Maximal Diesis	Porcupine Comma
3125/3072	\| -10 -1 5 >	29.61	Small Diesis	Magic Comma
2048/2025	\| 11 -4 -2 >	19.55	Diaschisma
2109375/2097152	\| -21 3 7 >	10.06	Semicomma	Fokker Comma
9193891/9143623	\| 32 -7 -9 >	9.49	Escapade Comma
4758837/4757272	\| -53 10 16 >	0.57	Kwazy
50/49	\| 1 0 2 -2 >	34.98	Tritonic Diesis	Jubilisma
64/63	\| 6 -2 0 -1 >	27.26	Septimal Comma	Archytas' Comma	Leipziger Komma
875/864	\| -5 -3 3 1 >	21.90	Keema
2430/2401	\| 1 5 1 -4 >	20.79	Nuwell
245/243	\| 0 -5 1 2 >	14.19	Sensamagic
1728/1715	\| 6 3 -1 -3 >	13.07	Orwellisma	Orwell Comma
225/224	\| -5 2 2 -1 >	7.71	Septimal Kleisma	Marvel Comma
10976/10935	\| 5 -7 -1 3 >	6.48	Hemimage
6144/6125	\| 11 1 -3 -2 >	5.36	Porwell
65625/65536	\| -16 1 5 1 >	2.35	Horwell
420175/419904	\| -6 -8 2 5 >	1.12	Wizma
99/98	\| -1 2 0 -2 1 >	17.58	Mothwellsma
100/99	\| 2 -2 2 0 -1 >	17.40	Ptolemisma
121/120	\| -3 -1 -1 0 2 >	14.37	Biyatisma
125/124	\|-4 0 3 0 ... -1>	13.91	Twizzler
176/175	\| 4 0 -2 -1 1 >	9.86	Valinorsma
896/891	\| 7 -4 0 1 -1 >	9.69	Pentacircle
65536/65219	\| 16 0 0 -2 -3 >	8.39	Orgonisma
385/384	\| -7 -1 1 1 1 >	4.50	Keenanisma
540/539	\| 2 3 1 -2 -1 >	3.21	Swetisma
4000/3993	<\| 5 -1 3 0 -3 >	3.03	Wizardharry
9801/9800	\| -3 4 -2 -2 2 >	0.18	Kalisma	Gauss' Comma
91/90	\| -1 -2 -1 1 0 1 >	19.13	Superleap

How to Notate 22edo in Sagittal

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:

This notation is consistent with Sagittal's notation of 5-limit JI harmony: "major" 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 porcupine comma (which is equivalent to three syntonic commas minus a Pythagorean apotome).

How to notate 22edo with ups and downs

Treating ups and downs as "fused" with sharps and flats, and never appearing separately:

Treating ups and downs as independent of sharps and flats, and sometimes appearing separately:

A D downmajor scale with mandatory accidentals (no key signature), with minimal accidentals (only when needed to override the key signature), and with independent ups and downs.

Paul Erlich's "Tibia" in G, with independent ups and downs:

Tibia in G for the book-1.png

Tibia in G for the book-2.png

The Decatonic System

The decatonic system is an approach of notation based on Paul Erlich's decatonic scales. Unlike typical notation, the decatonic system is based on a scale of 10 tones rather than 7. This approach requires an entire re-learning of chords, intervals, and notation, but it allows 22EDO to be notated using only one pair of accidentals, and gives the opportunity to escape a heptatonic thinking pattern

Decatonic Alphabet

The system is based on two chains of fifths: one represented by Latin letters, the other by Greek. The two chains can be looked at as two juxtaposed pentatonic scales.

Chain 1: C G D A E

Chain 2: γ δ α ε β

The alphabet is, in ascending order: C δ D ε E γ G α A β C

In this alphabet, a chain of fifths is preserved because equivalent Greek letters also represent fifths if they are the same as their Latin counterparts. For example G-D is a fifth, and so is γ-δ.

Internal links

William Lynch's Thoughts on Septimal Harmony and 22 EDO

External links

References

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

Bosanquet, R.H.M. On the Hindoo division of the octave, with additions to the theory of higher orders, Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, Hindu Music from Various Authors, Chowkhamba Sanskrit Series, Varanasi, India, 1965

Music

Stephen Weigel · Dose Of Familiarity/Ode to Microtonality
Couples' Therapy by metaclown
Canon 2 in 1 upon a ground (22edo) by Claudi Meneghin
TIBIA by Paul Erlich
- Sagittal score of Tibia, in F||\ or in G (contains errors in measures 9, 19 and 20)
- Ups and Downs score of Tibia in G page 1 page 2 (no errors)
Glassic by Paul Erlich and Ara Sarkissian
Decatonic Swing by Paul Erlich and Ara Sarkissian (jazz)
12-22hexachordal Dirge by Joel Grant Taylor
Chord sequence in Paul Erlich's 22 EDO decatonic major by Jake Freivald
Porcupine Comma Pump by Jake Freivald
Dragged by a Storm Across the Desert Years by * Igliashon Jones (synth with electric guitar)
Numerology by Iglashion Jones (progressive metal)
Revenge of the inorganic compounds by Iglashion Jones (progressive metal)
My Crazy Aunt Sophie play by Chris Vaisvil. Blatantly xenharmonic piano.
where words are said to mean 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.
I've come with a bucket of roses play by Andrew Heathwaite (orwell-9: 3 2 3 2 3 2 3 2 2).
one drop of rain play by Andrew Heathwaite (orwell-9).
being a play by Andrew Heathwaite (porcupine-8: 3 1 3 3 3 3 3).
my own house play by Andrew Heathwaite (a pelog-flavored subset of orwell-9: 3 2 7 3 7).
Comets Over Flatland 17 by Randy Winchester
Night on Porcupine Mountain Mussorgsky-Smith
Paul Erlich 22-Equal Guitar Improvisation Shredfest Insanity - youtube
Improvisation in 22-equal temperament, Mike Battaglia - youtube
Boxwood Forest, Dream Tone, The Eternal Sleep, Sunday Pipes, Twisted Clowns - MIDI files by Mats Öljare
- Sagittal score of Sunday Pipes
Phobos Light by Chris Vaisvil in Hedgehog[14] tuned to 22edo.
The Capture and Release of the Fairy by Chris Vaisvil => blog post presentation
Yak Butter by The Stern Brocot Band, 1L6s MOS, compressed period/generator
Dirty Drummer, Sevish
Ganymede, Sevish (doesn't sound that xen, but it's in 22-edo)
Ambrosia, Sevish
From the Sky Islands They Came by Chris Vaisvil => blog post presentation
Smoke Filled Bar by Chris Vaisvil => blog presentation
Recurring Mimosa by Redrick Sultan
The Saharan Pump by Chris Vaisvil blog post
Short piece and demonstration (video) by Brendan Byrnes (electric guitar)
22 EDO Guitar Etude by Brendan Byrnes
Llurion by Brendan Byrnes
Imzadi by Omega9
22 edo electric guitar duet by Chris Vaisvil
Mass in 22edo - Sanctus by Gareth Hearne
Mass in 22edo - Agnus Dei by Gareth Hearne
For the Sunset - 22 edo rock ensemble by Chris Vaisvil
tracks of ILEVENS - all their tracks on SoundCloud are tagged with 22edo
Rose, liz, printemps, verdure by Alex Ness (in 22edo with stretched octaves)
Palinkalin Viharo (Flowers in the Mist) by Jake Huryn (Score); uses 11edo machine[6], 22edo orwell[9]

22edo: Difference between revisions