22edo: Difference between revisions
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=Theory= | ==Theory== | ||
In music, ''22 equal temperament'', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[Octave|octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent|cent]]s. Because it distinguishes 10/9 and 9/8, it's not meantone. | In music, ''22 equal temperament'', called 22-tet, 22-edo, or 22-et, is the scale derived by dividing the [[Octave|octave]] into 22 equally large steps. Each step represents a frequency ratio of the twenty-second root of 2, or 54.55 [[cent|cent]]s. Because it distinguishes 10/9 and 9/8, it's not meantone. | ||
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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). | 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). | ||
== | ==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. 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|34edo]], [[41edo|41edo]] and [[53edo|53edo]]. | |||
The diatonic scale it produces is instead derived from [[Superpyth|superpyth]] temperament, which despite having the same melodic structure as meantone's diatonic scale (LLsLLLs or, [[5L_2s|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|porcupine]] temperament. The generator for porcupine 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|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|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|31edo]], [[53edo|53edo]] and [[84edo|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|diatonic tritone]] [[45/32|45/32]], which is a major third above a [[major_whole_tone|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|jubilee comma]]), and [[64/63|64/63]], (the [[Septimal_comma|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|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|orwell comma]]; and the [[orwell_tetrad|orwell tetrad]] is also a chord of 22-et. | |||
As 22 is divisible by 11, a 22edo instrument can play any music in [[11edo|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|Sagittal]], 11 can be notated as every other note of 22. | |||
==Notation== | |||
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. | 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)== | ===Intervals by degree (Superpyth/Porcupine)=== | ||
{| class="wikitable" | {| class="wikitable" | ||
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|} | |} | ||
==Intervals by degree (Ups and Downs, Porcupine and Pentatonic)== | ===Intervals by degree (Ups and Downs, Porcupine and Pentatonic)=== | ||
22edo intervals can also be notated using [[Ups_and_Downs_Notation|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. | 22edo intervals can also be notated using [[Ups_and_Downs_Notation|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. | ||
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|- | |- | ||
! | [[Degree|Degree]] | ! | [[Degree|Degree]] | ||
! | | ! | [[cent|Cents]] | ||
! colspan="3" | Ups and downs | ! colspan="3" | [[Ups and Downs Notation|Ups and downs]] | ||
! colspan="3" | Porcupine | ! colspan="3" | Porcupine | ||
! colspan="3" | Pentatonic | ! colspan="3" | Pentatonic | ||
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| style="text-align:center;" | upminor 2nd | | style="text-align:center;" | upminor 2nd | ||
| style="text-align:center;" | ^m2 | | style="text-align:center;" | ^m2 | ||
| style="text-align:center;" | Eb | | style="text-align:center;" | ^Eb | ||
| style="text-align:center;" | dim 2nd | | style="text-align:center;" | dim 2nd | ||
| style="text-align:center;" | d2 | | style="text-align:center;" | d2 | ||
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| style="text-align:center;" | downmajor 2nd | | style="text-align:center;" | downmajor 2nd | ||
| style="text-align:center;" | vM2 | | style="text-align:center;" | vM2 | ||
| style="text-align:center;" | | | style="text-align:center;" | vE | ||
| style="text-align:center;" | perfect 2nd | | style="text-align:center;" | perfect 2nd | ||
| style="text-align:center;" | P2 | | style="text-align:center;" | P2 | ||
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| style="text-align:center;" | upminor 3rd | | style="text-align:center;" | upminor 3rd | ||
| style="text-align:center;" | ^m3 | | style="text-align:center;" | ^m3 | ||
| style="text-align:center;" | F | | style="text-align:center;" | ^F | ||
| style="text-align:center;" | minor 3rd | | style="text-align:center;" | minor 3rd | ||
| style="text-align:center;" | m3 | | style="text-align:center;" | m3 | ||
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| style="text-align:center;" | downmajor 3rd | | style="text-align:center;" | downmajor 3rd | ||
| style="text-align:center;" | vM3 | | style="text-align:center;" | vM3 | ||
| style="text-align:center;" | | | style="text-align:center;" | vF# | ||
| style="text-align:center;" | major 3rd | | style="text-align:center;" | major 3rd | ||
| style="text-align:center;" | M3 | | style="text-align:center;" | M3 | ||
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| style="text-align:center;" | up-4th, dim 5th | | style="text-align:center;" | up-4th, dim 5th | ||
| style="text-align:center;" | ^4, d5 | | style="text-align:center;" | ^4, d5 | ||
| style="text-align:center;" | G | | style="text-align:center;" | ^G, Ab | ||
| style="text-align:center;" | major 4th | | style="text-align:center;" | major 4th | ||
| style="text-align:center;" | M4 | | style="text-align:center;" | M4 | ||
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updim 5th | updim 5th | ||
| style="text-align:center;" | vA4, ^d5 | | style="text-align:center;" | vA4, ^d5 | ||
| style="text-align:center;" | | | style="text-align:center;" | vG#, | ||
Ab | ^Ab | ||
| style="text-align:center;" | aug 4th, | | style="text-align:center;" | aug 4th, | ||
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| style="text-align:center;" | aug 4th, down-5th | | style="text-align:center;" | aug 4th, down-5th | ||
| style="text-align:center;" | A4, v5 | | style="text-align:center;" | A4, v5 | ||
| style="text-align:center;" | G#, | | style="text-align:center;" | G#, vA | ||
| style="text-align:center;" | minor 5th | | style="text-align:center;" | minor 5th | ||
| style="text-align:center;" | m5 | | style="text-align:center;" | m5 | ||
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| style="text-align:center;" | upminor 6th | | style="text-align:center;" | upminor 6th | ||
| style="text-align:center;" | ^m6 | | style="text-align:center;" | ^m6 | ||
| style="text-align:center;" | Bb | | style="text-align:center;" | ^Bb | ||
| style="text-align:center;" | minor 6th | | style="text-align:center;" | minor 6th | ||
| style="text-align:center;" | m6 | | style="text-align:center;" | m6 | ||
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| style="text-align:center;" | downmajor 6th | | style="text-align:center;" | downmajor 6th | ||
| style="text-align:center;" | vM6 | | style="text-align:center;" | vM6 | ||
| style="text-align:center;" | | | style="text-align:center;" | vB | ||
| style="text-align:center;" | major 6th | | style="text-align:center;" | major 6th | ||
| style="text-align:center;" | M6 | | style="text-align:center;" | M6 | ||
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| style="text-align:center;" | upminor 7th | | style="text-align:center;" | upminor 7th | ||
| style="text-align:center;" | ^m7 | | style="text-align:center;" | ^m7 | ||
| style="text-align:center;" | C | | style="text-align:center;" | ^C | ||
| style="text-align:center;" | perfect 7th | | style="text-align:center;" | perfect 7th | ||
| style="text-align:center;" | P7 | | style="text-align:center;" | P7 | ||
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| style="text-align:center;" | downmajor 7th | | style="text-align:center;" | downmajor 7th | ||
| style="text-align:center;" | vM7 | | style="text-align:center;" | vM7 | ||
| style="text-align:center;" | | | style="text-align:center;" | vC# | ||
| style="text-align:center;" | aug 7th | | style="text-align:center;" | aug 7th | ||
| style="text-align:center;" | A7 | | style="text-align:center;" | A7 | ||
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|} | |} | ||
=Chord Names= | ===Decatonic Notation=== | ||
The decatonic notation is 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. 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. | |||
==Chord Names== | |||
See also [[22 EDO Chords|22 EDO Chords]], [[Chords of orwell|Chords of Orwell]]. | See also [[22 EDO Chords|22 EDO Chords]], [[Chords of orwell|Chords of Orwell]]. | ||
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| style="text-align:center;" | 10:12:15 | | style="text-align:center;" | 10:12:15 | ||
| style="text-align:center;" | 0-6-13 | | style="text-align:center;" | 0-6-13 | ||
| style="text-align:center;" | C Eb | | style="text-align:center;" | C ^Eb G | ||
| style="text-align:center;" | C | | style="text-align:center;" | C^m | ||
| style="text-align:center;" | C upminor | | style="text-align:center;" | C upminor | ||
|- | |- | ||
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| style="text-align:center;" | 4:5:6 | | style="text-align:center;" | 4:5:6 | ||
| style="text-align:center;" | 0-7-13 | | style="text-align:center;" | 0-7-13 | ||
| style="text-align:center;" | C | | style="text-align:center;" | C vE G | ||
| style="text-align:center;" | | | style="text-align:center;" | Cv | ||
| style="text-align:center;" | C downmajor or C | | style="text-align:center;" | C downmajor or C down | ||
|- | |- | ||
| style="text-align:center;" | ru | | style="text-align:center;" | ru | ||
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| style="text-align:center;" | C major or C | | style="text-align:center;" | C major or C | ||
|} | |} | ||
An up or down after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). | |||
Alterations are always enclosed in parentheses, additions never are. | |||
0-8-13-18 = C E G Bb = C7 = "C seven" | 0-8-13-18 = C E G Bb = C7 = "C seven" | ||
0-7-13-18 = C | 0-7-13-18 = C vE G Bb = C7(v3) = "C seven, down third" | ||
0-8-13-21 = C E G B = CM7 = "C major seven" | 0-8-13-21 = C E G B = CM7 = "C major seven" | ||
0-7-13-20 = C | 0-7-13-20 = C vE G vB = CvM7 = "C downmajor seven" | ||
0-3-13 = C | 0-3-13 = C vD G = Cv2 or C(v2) = "C down-two" | ||
0-4-13 = C D G = C2 | 0-4-13 = C D G = C2 | ||
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0-9-13 = C F G = C4 | 0-9-13 = C F G = C4 | ||
0-10-13 = C F | 0-10-13 = C ^F G = C^4 or C(^4) | ||
0-5-10 = C Eb Gb = Cdim | 0-5-10 = C Eb Gb = Cdim | ||
0-5-11 = C Eb Gb | 0-5-11 = C Eb ^Gb = Cdim(^5) | ||
0-5-12 = C Eb | 0-5-12 = C Eb vG = Cm(v5) | ||
0-5-10-15 = C Eb Gb Bbb = Cdim7 | 0-5-10-15 = C Eb Gb Bbb = Cdim7 | ||
0-5-11-14 = C Eb Gb | 0-5-11-14 = C Eb ^Gb vBbb = Cdim7(^5,v7) | ||
0-6-11-15 = C Eb^ Gb | 0-6-11-15 = C ^Eb ^Gb Bbb = Cdim7(^3,^5) | ||
0-6-11-16 = C Eb^ Gb^ Bbb | 0-6-11-16 = C ^Eb ^Gb ^Bbb = C^dim7(^5) | ||
0-5-13-17 = C Eb G A = Cm6 | 0-5-13-17 = C Eb G A = Cm6 | ||
0-8-13-17 = C E G A = C6 | 0-8-13-17 = C E G A = C6 | ||
0-8-13-16 = C E G | 0-8-13-16 = C E G vA = C,v6 = C add down-six | ||
0-7-13-17 = C | 0-7-13-17 = C vE G A = C6(v3) | ||
0-7-13-16 = C | 0-7-13-16 = C vE G vA = Cv6 | ||
0-5-13-18 = C Eb G Bb = Cm7 | 0-5-13-18 = C Eb G Bb = Cm7 | ||
0-6-13-19 = C Eb^ | 0-6-13-19 = C ^Eb G ^Bb = C^m7 | ||
0-8-13-21 = C E G B = CM7 | 0-8-13-21 = C E G B = CM7 | ||
0-7-13-20 = C | 0-7-13-20 = C vE G vB = CvM7 | ||
0-5-13-16 = C Eb G vA = Cm,v6 = "C minor add down-6" | |||
0-8-13-19 = C E G ^Bb = C,^7 = "C add up-seven" | |||
0- | 0-7-13-18-26 = C vE G Bb D = C9(v3) | ||
0- | 0-7-13-18-26-32 = C vE G Bb D vF = C9(v3)^11 | ||
Sometimes doubled ups/downs are unavoidable: | |||
0- | 0-6-12-15 = C ^Eb vG vvA = Cm6(^3,v5,vv6), or C ^Eb ^^Gb Bbb = Cdim7(^3,^^5) | ||
For a more complete list, see [[ | For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]]. | ||
== Scales == | == Scales == | ||
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See also: [[22edo_Solfege|22edo Solfege]], [[22edo_tetrachords|22edo Tetrachords]], [[22_EDO_Chords|22 EDO Chords]], [[22edo_Modes|22edo Modes]] | See also: [[22edo_Solfege|22edo Solfege]], [[22edo_tetrachords|22edo Tetrachords]], [[22_EDO_Chords|22 EDO Chords]], [[22edo_Modes|22edo Modes]] | ||
==Rank Two Temperaments== | |||
[[List_of_22et_rank_two_temperaments_by_badness|List of 22et rank two temperaments by badness]] | [[List_of_22et_rank_two_temperaments_by_badness|List of 22et rank two temperaments by badness]] | ||
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|} | |} | ||
==Commas== | |||
22 EDO tempers out the following commas. (Note: This assumes the val < 22 35 51 62 76 81 |.) | 22 EDO tempers out the following [[commas]]. (Note: This assumes the val < 22 35 51 62 76 81 |.) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! | [[Ratio]] | ||
! | Monzo | ! | [[Monzo]] | ||
! | | ! | [[Cents]] | ||
![[Color notation|Color Name]] | |||
! | Name 1 | ! | Name 1 | ||
! | Name 2 | ! | Name 2 | ||
| Line 988: | Line 1,000: | ||
| |<nowiki> | 1 -5 3 </nowiki>> | | |<nowiki> | 1 -5 3 </nowiki>> | ||
| style="text-align:right;" | 49.17 | | style="text-align:right;" | 49.17 | ||
| style="text-align:center;" |Triyo | |||
| style="text-align:center;" | Maximal Diesis | | style="text-align:center;" | Maximal Diesis | ||
| style="text-align:center;" | Porcupine Comma | | style="text-align:center;" | Porcupine Comma | ||
| Line 995: | Line 1,008: | ||
| |<nowiki> | -10 -1 5 </nowiki>> | | |<nowiki> | -10 -1 5 </nowiki>> | ||
| style="text-align:right;" | 29.61 | | style="text-align:right;" | 29.61 | ||
| style="text-align:center;" |Laquinyo | |||
| style="text-align:center;" | Small Diesis | | style="text-align:center;" | Small Diesis | ||
| style="text-align:center;" | Magic Comma | | style="text-align:center;" | Magic Comma | ||
| Line 1,002: | Line 1,016: | ||
| |<nowiki> | 11 -4 -2 </nowiki>> | | |<nowiki> | 11 -4 -2 </nowiki>> | ||
| style="text-align:right;" | 19.55 | | style="text-align:right;" | 19.55 | ||
| style="text-align:center;" |Sagugu | |||
| style="text-align:center;" | Diaschisma | | style="text-align:center;" | Diaschisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,009: | Line 1,024: | ||
| |<nowiki> | -21 3 7 </nowiki>> | | |<nowiki> | -21 3 7 </nowiki>> | ||
| style="text-align:right;" | 10.06 | | style="text-align:right;" | 10.06 | ||
| style="text-align:center;" |Lasepyo | |||
| style="text-align:center;" | Semicomma | | style="text-align:center;" | Semicomma | ||
| style="text-align:center;" | Fokker Comma | | style="text-align:center;" | Fokker Comma | ||
| Line 1,016: | Line 1,032: | ||
| |<nowiki> | 32 -7 -9 </nowiki>> | | |<nowiki> | 32 -7 -9 </nowiki>> | ||
| style="text-align:right;" | 9.49 | | style="text-align:right;" | 9.49 | ||
| style="text-align:center;" |Sasa-tritrigu | |||
| style="text-align:center;" | Escapade Comma | | style="text-align:center;" | Escapade Comma | ||
| | | | | | ||
| Line 1,023: | Line 1,040: | ||
| |<nowiki> | -53 10 16 </nowiki>> | | |<nowiki> | -53 10 16 </nowiki>> | ||
| style="text-align:right;" | 0.57 | | style="text-align:right;" | 0.57 | ||
| style="text-align:center;" |Quadla-quadquadyo | |||
| style="text-align:center;" | Kwazy | | style="text-align:center;" | Kwazy | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,030: | Line 1,048: | ||
| |<nowiki> | 1 0 2 -2 </nowiki>> | | |<nowiki> | 1 0 2 -2 </nowiki>> | ||
| style="text-align:right;" | 34.98 | | style="text-align:right;" | 34.98 | ||
| style="text-align:center;" |Biruyo | |||
| style="text-align:center;" | Tritonic Diesis | | style="text-align:center;" | Tritonic Diesis | ||
| style="text-align:center;" | Jubilisma | | style="text-align:center;" | Jubilisma | ||
| Line 1,037: | Line 1,056: | ||
| |<nowiki> | 6 -2 0 -1 </nowiki>> | | |<nowiki> | 6 -2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 27.26 | | style="text-align:right;" | 27.26 | ||
| style="text-align:center;" |Ru | |||
| style="text-align:center;" | Septimal Comma | | style="text-align:center;" | Septimal Comma | ||
| style="text-align:center;" | Archytas' Comma | | style="text-align:center;" | Archytas' Comma | ||
| Line 1,044: | Line 1,064: | ||
| |<nowiki> | -5 -3 3 1 </nowiki>> | | |<nowiki> | -5 -3 3 1 </nowiki>> | ||
| style="text-align:right;" | 21.90 | | style="text-align:right;" | 21.90 | ||
| style="text-align:center;" |Zotriyo | |||
| style="text-align:center;" | Keema | | style="text-align:center;" | Keema | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,051: | Line 1,072: | ||
| |<nowiki> | 1 5 1 -4 </nowiki>> | | |<nowiki> | 1 5 1 -4 </nowiki>> | ||
| style="text-align:right;" | 20.79 | | style="text-align:right;" | 20.79 | ||
| style="text-align:center;" |Quadru-ayo | |||
| style="text-align:center;" | Nuwell | | style="text-align:center;" | Nuwell | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,058: | Line 1,080: | ||
| |<nowiki> | 0 -5 1 2 </nowiki>> | | |<nowiki> | 0 -5 1 2 </nowiki>> | ||
| style="text-align:right;" | 14.19 | | style="text-align:right;" | 14.19 | ||
| style="text-align:center;" |Zozoyo | |||
| style="text-align:center;" | Sensamagic | | style="text-align:center;" | Sensamagic | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,065: | Line 1,088: | ||
| |<nowiki> | 6 3 -1 -3 </nowiki>> | | |<nowiki> | 6 3 -1 -3 </nowiki>> | ||
| style="text-align:right;" | 13.07 | | style="text-align:right;" | 13.07 | ||
| style="text-align:center;" |Triru-agu | |||
| style="text-align:center;" | Orwellisma | | style="text-align:center;" | Orwellisma | ||
| style="text-align:center;" | Orwell Comma | | style="text-align:center;" | Orwell Comma | ||
| Line 1,072: | Line 1,096: | ||
| |<nowiki> | -5 2 2 -1 </nowiki>> | | |<nowiki> | -5 2 2 -1 </nowiki>> | ||
| style="text-align:right;" | 7.71 | | style="text-align:right;" | 7.71 | ||
| style="text-align:center;" |Ruyoyo | |||
| style="text-align:center;" | Septimal Kleisma | | style="text-align:center;" | Septimal Kleisma | ||
| style="text-align:center;" | Marvel Comma | | style="text-align:center;" | Marvel Comma | ||
| Line 1,079: | Line 1,104: | ||
| |<nowiki> | 5 -7 -1 3 </nowiki>> | | |<nowiki> | 5 -7 -1 3 </nowiki>> | ||
| style="text-align:right;" | 6.48 | | style="text-align:right;" | 6.48 | ||
| style="text-align:center;" |Trizo-agu | |||
| style="text-align:center;" | Hemimage | | style="text-align:center;" | Hemimage | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,086: | Line 1,112: | ||
| |<nowiki> | 11 1 -3 -2 </nowiki>> | | |<nowiki> | 11 1 -3 -2 </nowiki>> | ||
| style="text-align:right;" | 5.36 | | style="text-align:right;" | 5.36 | ||
| style="text-align:center;" |Saruru-atrigu | |||
| style="text-align:center;" | Porwell | | style="text-align:center;" | Porwell | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,093: | Line 1,120: | ||
| |<nowiki> | -16 1 5 1 </nowiki>> | | |<nowiki> | -16 1 5 1 </nowiki>> | ||
| style="text-align:right;" | 2.35 | | style="text-align:right;" | 2.35 | ||
| style="text-align:center;" |Lazoquinyo | |||
| style="text-align:center;" | Horwell | | style="text-align:center;" | Horwell | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,100: | Line 1,128: | ||
| |<nowiki> | -6 -8 2 5 </nowiki>> | | |<nowiki> | -6 -8 2 5 </nowiki>> | ||
| style="text-align:right;" | 1.12 | | style="text-align:right;" | 1.12 | ||
| style="text-align:center;" |Quinzo-ayoyo | |||
| style="text-align:center;" | Wizma | | style="text-align:center;" | Wizma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,107: | Line 1,136: | ||
| |<nowiki> | -1 2 0 -2 1 </nowiki>> | | |<nowiki> | -1 2 0 -2 1 </nowiki>> | ||
| style="text-align:right;" | 17.58 | | style="text-align:right;" | 17.58 | ||
| style="text-align:center;" |Loruru | |||
| style="text-align:center;" | Mothwellsma | | style="text-align:center;" | Mothwellsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,114: | Line 1,144: | ||
| |<nowiki> | 2 -2 2 0 -1 </nowiki>> | | |<nowiki> | 2 -2 2 0 -1 </nowiki>> | ||
| style="text-align:right;" | 17.40 | | style="text-align:right;" | 17.40 | ||
| style="text-align:center;" |Luyoyo | |||
| style="text-align:center;" | Ptolemisma | | style="text-align:center;" | Ptolemisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,121: | Line 1,152: | ||
| |<nowiki> | -3 -1 -1 0 2 </nowiki>> | | |<nowiki> | -3 -1 -1 0 2 </nowiki>> | ||
| style="text-align:right;" | 14.37 | | style="text-align:right;" | 14.37 | ||
| style="text-align:center;" |Lologu | |||
| style="text-align:center;" | Biyatisma | | style="text-align:center;" | Biyatisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,128: | Line 1,160: | ||
| |<nowiki> |-4 0 3 0 ... -1</nowiki>> | | |<nowiki> |-4 0 3 0 ... -1</nowiki>> | ||
| style="text-align:right;" | 13.91 | | style="text-align:right;" | 13.91 | ||
| style="text-align:center;" |Thirty-wutriyo | |||
| style="text-align:center;" | Twizzler | | style="text-align:center;" | Twizzler | ||
| | | | | | ||
| Line 1,135: | Line 1,168: | ||
| |<nowiki> | 4 0 -2 -1 1 </nowiki>> | | |<nowiki> | 4 0 -2 -1 1 </nowiki>> | ||
| style="text-align:right;" | 9.86 | | style="text-align:right;" | 9.86 | ||
| style="text-align:center;" |Lorugugu | |||
| style="text-align:center;" | Valinorsma | | style="text-align:center;" | Valinorsma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,142: | Line 1,176: | ||
| |<nowiki> | 7 -4 0 1 -1 </nowiki>> | | |<nowiki> | 7 -4 0 1 -1 </nowiki>> | ||
| style="text-align:right;" | 9.69 | | style="text-align:right;" | 9.69 | ||
| style="text-align:center;" |Saluzo | |||
| style="text-align:center;" | Pentacircle | | style="text-align:center;" | Pentacircle | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,149: | Line 1,184: | ||
| |<nowiki> | 16 0 0 -2 -3 </nowiki>> | | |<nowiki> | 16 0 0 -2 -3 </nowiki>> | ||
| style="text-align:right;" | 8.39 | | style="text-align:right;" | 8.39 | ||
| style="text-align:center;" |Satrilu-aruru | |||
| style="text-align:center;" | Orgonisma | | style="text-align:center;" | Orgonisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,156: | Line 1,192: | ||
| |<nowiki> | -7 -1 1 1 1 </nowiki>> | | |<nowiki> | -7 -1 1 1 1 </nowiki>> | ||
| style="text-align:right;" | 4.50 | | style="text-align:right;" | 4.50 | ||
| style="text-align:center;" |Lozoyo | |||
| style="text-align:center;" | Keenanisma | | style="text-align:center;" | Keenanisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,163: | Line 1,200: | ||
| |<nowiki> | 2 3 1 -2 -1 </nowiki>> | | |<nowiki> | 2 3 1 -2 -1 </nowiki>> | ||
| style="text-align:right;" | 3.21 | | style="text-align:right;" | 3.21 | ||
| style="text-align:center;" |Lururuyo | |||
| style="text-align:center;" | Swetisma | | style="text-align:center;" | Swetisma | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,168: | Line 1,206: | ||
|- | |- | ||
| style="text-align:center;" | 4000/3993 | | style="text-align:center;" | 4000/3993 | ||
| | | | | <nowiki>| 5 -1 3 0 -3 </nowiki>> | ||
| style="text-align:right;" | 3.03 | | style="text-align:right;" | 3.03 | ||
| style="text-align:center;" |Triluyo | |||
| style="text-align:center;" | Wizardharry | | style="text-align:center;" | Wizardharry | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| Line 1,177: | Line 1,216: | ||
| |<nowiki> | -3 4 -2 -2 2 </nowiki>> | | |<nowiki> | -3 4 -2 -2 2 </nowiki>> | ||
| style="text-align:right;" | 0.18 | | style="text-align:right;" | 0.18 | ||
| style="text-align:center;" |Bilorugu | |||
| style="text-align:center;" | Kalisma | | style="text-align:center;" | Kalisma | ||
| style="text-align:center;" | Gauss' Comma | | style="text-align:center;" | Gauss' Comma | ||
| Line 1,184: | Line 1,224: | ||
| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | | |<nowiki> | -1 -2 -1 1 0 1 </nowiki>> | ||
| style="text-align:right;" | 19.13 | | style="text-align:right;" | 19.13 | ||
| style="text-align:center;" |Thozogu | |||
| style="text-align:center;" | Superleap | | style="text-align:center;" | Superleap | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
| style="text-align:center;" | | | style="text-align:center;" | | ||
|} | |} | ||
== Staff Notation == | |||
===How to Notate 22edo in Sagittal=== | ===How to Notate 22edo in Sagittal=== | ||
| Line 1,199: | Line 1,242: | ||
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). | 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). | ||
===How to | ===How to Notate 22edo with Ups and Downs=== | ||
Treating [[Ups_and_Downs_Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately: | Treating [[Ups_and_Downs_Notation|ups and downs]] as "fused" with sharps and flats, and never appearing separately: | ||
| Line 1,218: | Line 1,261: | ||
[[File:Tibia_in_G_for_the_book-2.png|alt=Tibia in G for the book-2.png|800x889px|Tibia in G for the book-2.png]] | [[File:Tibia_in_G_for_the_book-2.png|alt=Tibia in G for the book-2.png|800x889px|Tibia in G for the book-2.png]] | ||
==Internal links== | ==Internal links== | ||