21edo: Difference between revisions

Revision as of 04:01, 14 December 2019

Theory

Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo augmented triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other EDO <26.

In diatonically-related terms, 21-EDO possesses four types of 2nd (subminor, minor, submajor, and supermajor), three types of 3rd (subminor, neutral, and major), a "third-fourth" (an interval that can function as either a supermajor 3rd or a narrow 4th), a wide (or acute) 4th, and a narrow tritone, as well as the octave-inversions of all of these intervals.

In temperament terms, 21-EDO can be treated as a 13-limit temperament, but of harmonics 3, 5, 7, 11, and 13, the only harmonic 21-EDO approximates with anything approaching a near-Just flavor is the 7th harmonic. On the other hand, 21-EDO provides exceptionally accurate tunings of the 15th, 23rd, and 29th harmonics (within 3 cents or less), as well as a very reasonable approximation of the 27th harmonic (around 8 cents sharp). As such, treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament allows for a more accurate rationalization of the tuning, since almost every interval in 21-EDO can be described as a ratio within the 29-odd-limit. 21-EDO also works well on the 2.9/5.11/5.13/5.17/5.35/5 subgroup, which is possibly a more sensible way to treat it.

The patent val for 21edo tempers out 128/125 and 2187/2000 in the 5-limit, and supplies the optimal patent val for the 5-limit laconic temperament tempering out 2187/2000, and also the optimal patent val for 7-limit, 11-limit and 13-limit laconic, spartan and gorgo temperaments. These temperaments lead to some "interesting" mappings, where 10/9 is larger than 9/8, 11/9 is larger than 16/13, and 8/7 maps to the same interval as 10/9, for instance.

Intervals

Degree	Cents	Up/down notation			5L3s Octotonic Notation	D.-R. Interval Types	Approximate Ratios *1	Approximate Ratios *2	Approximate Ratios *3
0	0.00	1	unison	C	C	Unison	1/1	1/1	1/1
1	57.14	^1 vv2	up unison, double-down 2nd	^C vvD	C#	Subminor 2nd	28/27, 30/29	35/34, 36/35	64/63
2	114.29	^^1 v2	double-up unison, down 2nd	^^C vD	Db	Minor 2nd	16/15, 15/14, 29/27	18/17	16/15, 25/24
3	171.43	2	2nd	D	D	Submajor 2nd	10/9, 32/29	10/9,11/10	9/8
4	228.57	^2 vv3	up 2nd, double-down 3rd	^D vvE	D#	Supermajor 2nd	8/7	8/7	8/7, 10/9, 11/10
5	285.71	^^2 v3	double-up 2nd, down 3rd	^^D vE	Eb	Subminor 3rd	27/23, 32/27	13/11, 20/17	6/5, 7/6
6	342.86	3	3rd	E	E	Neutral 3rd	28/23	11/9	16/13
7	400	^3 vv4	up 3rd, double-down 4th	^E vvF	E#/Fb	Major 3rd	29/23	44/35	5/4, 9/7, 11/9, 14/11
8	457.14	^^3 v4	double-up 3rd, down 4th	^^E vF	F	Third-Fourth	30/23	13/10, 17/13, 22/17	13/10
9	514.29	4	4th	F	F#	Acute 4th	161/120, 256/189	35/26	4/3, 18/13
10	571.43	^4 vv5	up 4th, double-down 5th	^F vvG	Gb	Narrow Tritone	32/23	18/13	7/5, 11/8
11	628.57	^^4 v5	double-up 4th, down 5th	^^F vG	G	Wide Tritone	23/16	13/9	10/7, 16/11
12	685.71	5	5th	G	G#	Grave 5th	189/128, 240/161	52/35	3/2, 13/9
13	742.86	^5 vv6	up 5th, double-down 6th	^G vvA	Hb	Fifth-Sixth	23/15	17/11, 20/13, 26/17	20/13
14	800	^^5 v6	double-up 5th, down 6th	^^G vA	H	Minor 6th	46/29	35/22	8/5, 11/7, 14/9, 18/11
15	857.14	6	6th	A	H#/Ab	Neutral 6th	23/14	18/11	13/8
16	914.29	^6 vv7	up 6th, double-down 7th	^A vvB	A	Supermajor 6th	27/16, 46/27	17/10, 22/13	5/3, 12/7
17	971.43	^^6 v7	double-up 6th, down 7th	^^A vB	A#	Subminor 7th	7/4	7/4	7/4, 9/5, 20/11
18	1028.57	7	7th	B	Bb	Supraminor 7th	29/16, 9/5	9/5, 20/11	16/9
19	1085.71	^7 vv8	up 7th, double-down 8ve	^B vvC	B	Major 7th	15/8	17/9	15/8, 48/25
20	1142.86	^^7 v8	double-up 7th, down 8ve	^^B vC	B#/Cb	Supermajor 7th	27/14, 29/15	35/18, 68/35	63/32
21	1200	8	8ve	C	C	Octave	2/1	2/1	2/1

∗1: based on treating 21-EDO as a 2.7.15.23.27.29 subgroup temperament

∗2: based on treating 21-EDO as a 2.9/5.11/5.13/5.17/5.35/5 subgroup temperament

∗3: based on treating 21-EDO as 13-limit laconic temperament

Chord Names

Ups and downs can be used to name 21edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used.

0-6-12 = C E G = C = C or C perfect

0-5-12 = C vE G = C(v3) = C down-three

0-7-12 = C ^E G = C(^3) = C up-three

0-6-11 = C E vG = C(v5) = C down-five

0-7-13 = C ^E ^G = C(^3,^5) = C up-three up-five

0-6-12-18 = C E G B = C7 = C seven

0-6-12-17 = C E G vB = C,v7 = C add down-seven

0-5-12-18 = C vE G B = C7(v3) = C seven down-three

0-5-12-17 = C vE G vB = Cv7 = C down-seven

For a more complete list, see Ups and Downs Notation - Chords and Chord Progressions.

Triadic Harmony

One interesting feature of 21-EDO is the variety of triads it offers. Five of its intervals--228.6¢, 285.7¢, 342.9¢, 400¢, and 457.1¢ can function categorically as "3rds" for those whose ears are accustomed to diatonic interval categories, representing arto, minor, neutral, major, and tendo 3rds respectively (or double-down, down, perfect, up and double-up). One can couple these with 21-EDO's narrow fifth to form five types of triad. In addition to these, there are a few noteworthy "altered" triads that stand out as representations to parts of the overtone series:

Steps	Cents	Ratio	Example in C	Written name	Spoken name
0-5-10	0-286-571	23:27:32	C vE vvG	Cv(vv5)	C down, double-down five
0-4-11	0-229-629	7:8:10	C vvE vG	Cvv(v5)	C double-down, down five
0-6-11	0-343-629	9:11:13	C E vG	C(v5)	C down-five
0-5-13	0-286-743	11:13:17	C vE ^G	Cv(^5)	C down up-five
0-8-13	0-457-743	13:17:20	C vF ^G	Cv4(^5)	C (sus) down-four up-five
0-5-15	0-286-857	11:13:18	C vE A	A(v5)	(inversion of 9:11:13)

Moment-of-Symmetry Scales

Since 21-EDO contains sub-EDOs of 3 and 7, it contains no heptatonic MOS scales (other than 7-EDO) and a wealth of scales that repeat at a 1/3-octave period.

For 7-limit harmony (based on a chord of 0-7-12-17 approximating 4:5:6:7), using 1/3-octave period scales (i.e. those related to augmented temperament) yields the most harmonically-efficient scales. The 9-note 3L6s scale (related to Tcherepnin's scale in 12-TET) is an excellent example.

For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales.

Examples:

Tetrachordal Scales

While 21-EDO lacks any 7-note MOS scales, one can still construct a variety of interesting and useful 7-note scales using tetrachords instead of MOS generators. The 21-EDO fourth is 9 steps, which can be divided into three parts in the following ways:

Step Pattern	Cents	Example	Name*	Ups/downs name
3, 3, 3	(0)-171-343-(514)	C D E F	Equable diatonic	C perfect
4, 3, 2	(0)-229-400-(514)	C ^D ^E F	Soft diatonic	C upperfect up-2
4, 4, 1	(0)-229-457-(514)	C ^D ^^E F	Intense diatonic	C up-2 & 6, double-up-3 & 7
5, 3, 1	(0)-286-457-(514)	C ^^D ^^E F	Archytas chromatic	C double-up-2, 3, 6 and 7
5, 2, 2	(0)-286-400-(514)	C ^D ^E F	Weak chromatic	C double-up 2 & 6, up-3 & 7
6, 2, 1	(0)-343-457-(514)	C ^3D ^^E F	Strong enharmonic	C triple-up 2 & 6, double-up 3 & 7
7, 1, 1	(0)-400-457-(514)	C ^4D ^^E F	Pythagorean enharmonic	C quadruple-up 2 & 6, double-up 3 & 7

∗These names may not be correct in relating to the ancient Greek tetrachordal genera; please change them if you know better!

The steps of these 7 basic patterns can also be permuted/rotated to give a total of 28 tetrachords, which can then be combined in either conjunct or disjunct form to yield a staggering number of scales. Thus 21edo can do reasonably-convincing imitations of the melodic forms of various tetrachordal musical traditions, such as ancient Greek, maqam, and dastgah.

Rank two temperaments

List of 21edo rank two temperaments by badness

Periods per octave	Generator	Temperaments
1	1\21	Escapade
1	2\21	Miracle
1	4\21	Slendric/Gorgo/Gidorah
1	5\21	Subklei
1	8\21	Tridec
1	10\21	Triton
3	1\21
3	2\21	Augmented/August
3	3\21	Oodako
7	1\21	Whitewood

Commas

21 EDO tempers out the following 13-limit commas. (Note: This assumes the val < 21 33 49 59 73 78 |.)

Ratio	Monzo	Cents	Color Name	Name 1	Name 2
2187/2048	\| -11 7 >	113.69	Lawa	Apotome
128/125	\| 7 0 -3 >	41.06	Trigu	Diesis	Augmented Comma
	\| -25 7 6 >	31.57	Lala-tribiyo	Ampersand's Comma
	\| 32 -7 -9 >	9.49	Sasa-tritrigu	Escapade Comma
1029/1000	\| -3 1 -3 3 >	49.49	Trizogu	Keega
36/35	\| 2 2 -1 -1 >	48.77	Rugu	Septimal Quarter Tone
	\| -10 7 8 -7 >	22.41	Lasepru-aquadbiyo	Blackjackisma
1029/1024	\| -10 1 0 3 >	8.43	Latrizo	Gamelisma
225/224	\| -5 2 2 -1 >	7.71	Ruyoyo	Septimal Kleisma	Marvel Comma
16875/16807	\| 0 3 4 -5 >	6.99	Quinru-aquadyo	Mirkwai
2401/2400	\| -5 -1 -2 4 >	0.72	Bizozogu	Breedsma
	\| 47 -7 -7 -7 >	0.34	Trisa-seprugu	Akjaysma	5\7 Octave Comma
99/98	\| -1 2 0 -2 1 >	17.58	Loruru	Mothwellsma
176/175	\| 4 0 -2 -1 1 >	9.86	Lorugugu	Valinorsma
4000/3993	\| 5 -1 3 0 -3 >	3.03	Triluyo	Wizardharry

Books / Literature

Sword, Ron. "Icosihenaphonic Scales for Guitar". IAAA Press. 1st ed: July 2009.

Music

Iridescent Wenge Fugue by Stephen Weigel (accepted to SEAMUS 2018 and Electroacoustic Barn Dance 2018)
WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate), an album of xenharmonic Christmas covers played by Stephen Weigel, many are in 21edo
21-edo Trio for Organ by Claudi Meneghin
21-penny jingle by Claudi Meneghin
Short Clip of 21-edo Acoustic ^{[dead link]} by Ron Sword
Open tuning Drone Improvisation in 21-edo ^{[dead link]} by Ron Sword
Anomalous Readings (MP3) by Andrew Heathwaite
Comets Over Flatland 15 by Randy Winchester
Comets Over Flatland 18 by Randy Winchester
L'esatonale ubriaco (the drunk hexatonal), ALIENAMENTE by Fabrizio Fulvio Fausto Fiale

21edo: Difference between revisions

Revision as of 04:01, 14 December 2019

Contents

Theory

Intervals

Chord Names

Triadic Harmony

Moment-of-Symmetry Scales

Tetrachordal Scales

Rank two temperaments

Commas

Books / Literature

Music

Navigation menu

@@ Line 6: / Line 6: @@
 }}
-==Introduction==
+==Theory==
 Twenty-one equal divisions of the octave provides the sonic fingerprint of the augmented and 7-edo family, while also giving a some higher harmony possibilities and fun intervals like the apotome. The system can be treated as three intertwining 7-edo or "equi-heptatonic" scales, or as seven 3-edo ''augmented'' triads. The 7/4 at 968.826 cents is only off in 21-tone by 2.6 cents, which is better than any other EDO &lt;26.
-==As a temperament==
 In diatonically-related terms, 21-EDO possesses four types of 2nd (subminor, minor, submajor, and supermajor), three types of 3rd (subminor, neutral, and major), a "third-fourth" (an interval that can function as either a supermajor 3rd or a narrow 4th), a wide (or acute) 4th, and a narrow tritone, as well as the octave-inversions of all of these intervals.
@@ Line 17: / Line 16: @@
 The patent val for 21edo tempers out 128/125 and 2187/2000 in the 5-limit, and supplies the optimal patent val for the 5-limit [[Laconic_Family|laconic]] temperament tempering out 2187/2000, and also the optimal patent val for 7-limit, 11-limit and 13-limit laconic, spartan and gorgo temperaments. These temperaments lead to some "interesting" mappings, where 10/9 is larger than 9/8, 11/9 is larger than 16/13, and 8/7 maps to the same interval as 10/9, for instance.
+== Intervals ==
 {| class="wikitable"
 |-
@@ Line 22: / Line 22: @@
 ! | Cents
 ! colspan="3" | [[Ups_and_Downs_Notation|Up/down notation]]
-! | 5L3s Octotonic Notation
+! | 5L3s Octotonic
+Notation
 ! | D.-R. Interval Types
 ! | Approximate Ratios *1
@@ Line 47: / Line 48: @@
 double-down 2nd
-| | C^
+| | ^C
-Dvv
+vvD
 | style="text-align:center;" | C#
 | style="text-align:center;" | Subminor 2nd
@@ Line 64: / Line 65: @@
 down 2nd
-| | C^^
+| | ^^C
-Dv
+vD
 | style="text-align:center;" | Db
 | style="text-align:center;" | Minor 2nd
@@ Line 92: / Line 93: @@
 double-down 3rd
-| | D^
+| | ^D
-Evv
+vvE
 | style="text-align:center;" | D#
 | style="text-align:center;" | Supermajor 2nd
@@ Line 109: / Line 110: @@
 down 3rd
-| | D^^
+| | ^^D
-Ev
+vE
 | style="text-align:center;" | Eb
 | style="text-align:center;" | Subminor 3rd
@@ Line 137: / Line 138: @@
 double-down 4th
-| | E^
+| | ^E
-Fvv
+vvF
 | style="text-align:center;" | E#/Fb
 | style="text-align:center;" | Major 3rd
@@ Line 154: / Line 155: @@
 down 4th
-| | E^^
+| | ^^E
-Fv
+vF
 | style="text-align:center;" | F
 | style="text-align:center;" | Third-Fourth
@@ Line 182: / Line 183: @@
 double-down 5th
-| | F^
+| | ^F
-Gvv
+vvG
 | style="text-align:center;" | Gb
 | style="text-align:center;" | Narrow Tritone
@@ Line 199: / Line 200: @@
 down 5th
-| | F^^
+| | ^^F
-Gv
+vG
 | style="text-align:center;" | G
 | style="text-align:center;" | Wide Tritone
@@ Line 227: / Line 228: @@
 double-down 6th
-| | G^
+| | ^G
-Avv
+vvA
 | style="text-align:center;" | Hb
 | style="text-align:center;" | Fifth-Sixth
@@ Line 244: / Line 245: @@
 down 6th
-| | G^^
+| | ^^G
-Av
+vA
 | style="text-align:center;" | H
 | style="text-align:center;" | Minor 6th
@@ Line 272: / Line 273: @@
 double-down 7th
-| | A^
+| | ^A
-Bvv
+vvB
 | style="text-align:center;" | A
 | style="text-align:center;" | Supermajor 6th
@@ Line 289: / Line 290: @@
 down 7th
-| | A^^
+| | ^^A
-Bv
+vB
 | style="text-align:center;" | A#
 | style="text-align:center;" | Subminor 7th
@@ Line 317: / Line 318: @@
 double-down 8ve
-| | B^
+| | ^B
-Cvv
+vvC
 | style="text-align:center;" | B
 | style="text-align:center;" | Major 7th
@@ Line 334: / Line 335: @@
 down 8ve
-| | B^^
+| | ^^B
-Cv
+vC
 | style="text-align:center;" | B#/Cb
 | style="text-align:center;" | Supermajor 7th
@@ Line 367: / Line 368: @@
 -6-12 = C E G = C = C or C perfect
--5-12 = C Ev G = C(v3) = C down-three
+-5-12 = C vE G = C(v3) = C down-three
--7-12 = C E^ G = C(^3) = C up-three
+-7-12 = C ^E G = C(^3) = C up-three
--6-11 = C E Gv = C(v5) = C down-five
+-6-11 = C E vG = C(v5) = C down-five
--7-13 = C E^ G^ = C(^3,^5) = C up-three up-five
+-7-13 = C ^E ^G = C(^3,^5) = C up-three up-five
 -6-12-18 = C E G B = C7 = C seven
--6-12-17 = C E G Bv = C(v7) = C down-seven
+-6-12-17 = C E G vB = C,v7 = C add down-seven
--5-12-18 = C Ev G B = C7(v3) = C seven down-three
+-5-12-18 = C vE G B = C7(v3) = C seven down-three
--5-12-17 = C Ev G Bv = C.v7 = C dot down seven
+-5-12-17 = C vE G vB = Cv7 = C down-seven
-For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
+For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
 ==Triadic Harmony==
@@ Line 401: / Line 402: @@
 | style="text-align:center;" | 0-286-571
 | style="text-align:center;" | 23:27:32
-| | C Ev Gvv
+| | C vE vvG
-| | C.v(vv5)
+| | Cv(vv5)
-| | C dot down, double-down five
+| | C down, double-down five
 |-
 | style="text-align:center;" | 0-4-11
 | style="text-align:center;" | 0-229-629
 | style="text-align:center;" | 7:8:10
-| | C Evv Gv
+| | C vvE vG
-| | C.vv(v5)
+| | Cvv(v5)
-| | C dot double-down, down five
+| | C double-down, down five
 |-
 | style="text-align:center;" | 0-6-11
 | style="text-align:center;" | 0-343-629
 | style="text-align:center;" | 9:11:13
-| | C E Gv
+| | C E vG
 | | C(v5)
 | | C down-five
@@ Line 422: / Line 423: @@
 | style="text-align:center;" | 0-286-743
 | style="text-align:center;" | 11:13:17
-| | C Ev G^
+| | C vE ^G
-| | C.v(^5)
+| | Cv(^5)
-| | C dot down up-five
+| | C down up-five
 |-
 | style="text-align:center;" | 0-8-13
 | style="text-align:center;" | 0-457-743
 | style="text-align:center;" | 13:17:20
-| | C Fv G^
+| | C vF ^G
-| | C.v4(^5)
+| | Cv4(^5)
 | | C (sus) down-four up-five
 |-
@@ Line 436: / Line 437: @@
 | style="text-align:center;" | 0-286-857
 | style="text-align:center;" | 11:13:18
-| | C Ev A
+| | C vE A
 | | A(v5)
 | | (inversion of 9:11:13)
@@ Line 473: / Line 474: @@
 | style="text-align:center;" | 4, 3, 2
 | style="text-align:center;" | (0)-229-400-(514)
-| | C D^ E^ F
+| | C ^D ^E F
 | style="text-align:center;" | Soft diatonic
 | | C upperfect up-2
@@ Line 479: / Line 480: @@
 | style="text-align:center;" | 4, 4, 1
 | style="text-align:center;" | (0)-229-457-(514)
-| | C D^ E^^ F
+| | C ^D ^^E F
 | style="text-align:center;" | Intense diatonic
 | | C up-2 &amp; 6, double-up-3 &amp; 7
@@ Line 485: / Line 486: @@
 | style="text-align:center;" | 5, 3, 1
 | style="text-align:center;" | (0)-286-457-(514)
-| | C D^^ E^^ F
+| | C ^^D ^^E F
 | style="text-align:center;" | Archytas chromatic
 | | C double-up-2, 3, 6 and 7
@@ Line 491: / Line 492: @@
 | style="text-align:center;" | 5, 2, 2
 | style="text-align:center;" | (0)-286-400-(514)
-| | C D^^ E^ F
+| | C ^D ^E F
 | style="text-align:center;" | Weak chromatic
 | | C double-up 2 &amp; 6, up-3 &amp; 7
@@ Line 497: / Line 498: @@
 | style="text-align:center;" | 6, 2, 1
 | style="text-align:center;" | (0)-343-457-(514)
-| | C D^<span style="font-size: 90%; vertical-align: super;">3</span> E^^ F
+| | C ^<span style="font-size: 90%; vertical-align: super;">3</span>D ^^E F
 | style="text-align:center;" | Strong enharmonic
 | | C triple-up 2 &amp; 6, double-up 3 &amp; 7
@@ Line 503: / Line 504: @@
 | style="text-align:center;" | 7, 1, 1
 | style="text-align:center;" | (0)-400-457-(514)
-| | C D^<span style="font-size: 90%; vertical-align: super;">4</span> E^^ F
+| | C ^<span style="font-size: 90%; vertical-align: super;">4</span>D ^^E F
 | style="text-align:center;" | Pythagorean enharmonic
 | | C quadruple-up 2 &amp; 6, double-up 3 &amp; 7
@@ Line 562: / Line 563: @@
 ==Commas==
-EDO tempers out the following 13-limit commas. (Note: This assumes the val &lt; 21 33 49 59 73 78 |.)
+EDO tempers out the following 13-limit [[commas]]. (Note: This assumes the val &lt; 21 33 49 59 73 78 |.)
 {| class="wikitable"
 |-
-! | Comma
+! | [[Ratio]]
-! | Monzo
+! | [[Monzo]]
-! | Value (Cents)
+! | [[Cents]]
+![[Color notation/Temperament Names|Color Name]]
 ! | Name 1
 ! | Name 2
@@ Line 575: / Line 577: @@
 | |<nowiki> | -11 7 </nowiki>&gt;
 | style="text-align:right;" | 113.69
+| style="text-align:center;" |Lawa
 | style="text-align:center;" | Apotome
 | style="text-align:center;" |
@@ Line 581: / Line 584: @@
 | |<nowiki> | 7 0 -3 </nowiki>&gt;
 | style="text-align:right;" | 41.06
+| style="text-align:center;" |Trigu
 | style="text-align:center;" | Diesis
 | style="text-align:center;" | Augmented Comma
@@ Line 587: / Line 591: @@
 | |<nowiki> | -25 7 6 </nowiki>&gt;
 | style="text-align:right;" | 31.57
+| style="text-align:center;" |Lala-tribiyo
 | style="text-align:center;" | Ampersand's Comma
 | |
@@ Line 593: / Line 598: @@
 | |<nowiki> | 32 -7 -9 </nowiki>&gt;
 | style="text-align:right;" | 9.49
+| style="text-align:center;" |Sasa-tritrigu
 | style="text-align:center;" | Escapade Comma
 | |
@@ Line 599: / Line 605: @@
 | |<nowiki> | -3 1 -3 3 </nowiki>&gt;
 | style="text-align:right;" | 49.49
+| style="text-align:center;" |Trizogu
 | style="text-align:center;" | Keega
 | style="text-align:center;" |
@@ Line 605: / Line 612: @@
 | |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
 | style="text-align:right;" | 48.77
+| style="text-align:center;" |Rugu
 | style="text-align:center;" | Septimal Quarter Tone
 | |
@@ Line 611: / Line 619: @@
 | |<nowiki> | -10 7 8 -7 </nowiki>&gt;
 | style="text-align:right;" | 22.41
+| style="text-align:center;" |Lasepru-aquadbiyo
 | style="text-align:center;" | Blackjackisma
 | style="text-align:center;" |
@@ Line 617: / Line 626: @@
 | |<nowiki> | -10 1 0 3 </nowiki>&gt;
 | style="text-align:right;" | 8.43
+| style="text-align:center;" |Latrizo
 | style="text-align:center;" | Gamelisma
 | style="text-align:center;" |
@@ Line 623: / Line 633: @@
 | |<nowiki> | -5 2 2 -1 </nowiki>&gt;
 | style="text-align:right;" | 7.71
+| style="text-align:center;" |Ruyoyo
 | style="text-align:center;" | Septimal Kleisma
 | style="text-align:center;" | Marvel Comma
@@ Line 629: / Line 640: @@
 | |<nowiki> | 0 3 4 -5 </nowiki>&gt;
 | style="text-align:right;" | 6.99
+| style="text-align:center;" |Quinru-aquadyo
 | style="text-align:center;" | Mirkwai
 | style="text-align:center;" |
@@ Line 635: / Line 647: @@
 | |<nowiki> | -5 -1 -2 4 </nowiki>&gt;
 | style="text-align:right;" | 0.72
+| style="text-align:center;" |Bizozogu
 | style="text-align:center;" | Breedsma
 | style="text-align:center;" |
@@ Line 641: / Line 654: @@
 | |<nowiki> | 47 -7 -7 -7 </nowiki>&gt;
 | style="text-align:right;" | 0.34
+| style="text-align:center;" |Trisa-seprugu
 | style="text-align:center;" | Akjaysma
 | style="text-align:center;" | 5\7 Octave Comma
@@ Line 647: / Line 661: @@
 | |<nowiki> | -1 2 0 -2 1 </nowiki>&gt;
 | style="text-align:right;" | 17.58
+| style="text-align:center;" |Loruru
 | style="text-align:center;" | Mothwellsma
 | style="text-align:center;" |
@@ Line 653: / Line 668: @@
 | |<nowiki> | 4 0 -2 -1 1 </nowiki>&gt;
 | style="text-align:right;" | 9.86
+| style="text-align:center;" |Lorugugu
 | style="text-align:center;" | Valinorsma
 | style="text-align:center;" |
@@ Line 659: / Line 675: @@
 | |<nowiki> | 5 -1 3 0 -3 </nowiki>&gt;
 | style="text-align:right;" | 3.03
+| style="text-align:center;" |Triluyo
 | style="text-align:center;" | Wizardharry
 | style="text-align:center;" |

21edo: Difference between revisions

Revision as of 04:01, 14 December 2019

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