19edo: Difference between revisions

! #

! Cents

! Approximate Ratios*

! colspan="3" | Interval

! [[Solfege]]

! Dodecatonic Notation

| 0

| 0.00

| [[1/1]]

| Do

| P1

| 1

| 63.16

| [[25/24]], [[28/27]], [[26/25]]

| Di/Ro

| A1, m2

| 2

| 126.32

| [[15/14]], [[16/15]], [[13/12]], [[14/13]]

| Ra

| M2, m3

| 3

| 189.47

| [[9/8]], [[10/9]], [[125/112]]

| M3

| 4

| 252.63

| [[7/6]], [[8/7]], [[15/13]]

| m4, a3

| 5

| 315.79

| [[6/5]]

| Me

| M4, m5

| 6

| 378.95

| [[5/4]], [[16/13]], [[56/45]]

| Mi

| M5

| 442.11

| [[32/25]], [[9/7]], [[13/10]]

| Mo/Fe

| A5, d6

| 8

| [[4/3]], [[75/56]]

| Fa

| 9

| 568.42

| [[25/18]], [[7/5]], [[18/13]]

| Fi

| A6, m7

| 10

| 631.58

| [[36/25]], [[10/7]], [[13/9]]

| Se

| M7, d8

| 11

| 694.74

| [[3/2]], [[112/75]]

| So

| P8

| 12

| 757.89

| [[25/16]], [[14/9]], [[20/13]]

| A8, m9

| 13

| [[8/5]], [[13/8]], [[45/28]]

| Le

| M9, m10

| [[5/3]]

| La

| M10

| 15

| 947.37

| [[7/4]], [[12/7]], [[26/15]]

| Li/Ta

| m11, A10

| 16

| 1010.53

| [[9/5]], [[16/9]], [[224/125]]

| Te

| M11, m12

| 17

| 1073.68

| [[15/8]], [[13/7]], [[28/15]], [[24/13]]

| Ti

| M12

| 18

| 1136.84

| [[48/25]], [[27/14]], [[25/13]]

| A12, d13

| 19

| [[2/1]]

| P13

=== Interval quality and chord names in color notation ===

! Quality

! [[Color name]]

! Monzo Format

! Examples

| diminished

| zo

| (a, b, 0, 1)

| 7/6, 7/4

| rowspan="2" | minor

| fourthward wa

| (a, b), b < -1

| 32/27, 16/9

| gu

| (a, b, -1)

| 6/5, 9/5

| rowspan="2" | major

| yo

| (a, b, 1)

| 5/4, 5/3

| fifthward wa

| (a, b), b > 1

| ru

| (a, b, 0, -1)

| 9/7, 12/7

! [[Kite's color notation|Color of the 3rd]]

! Edosteps

! Notes of C Chord

! Written Name

! Spoken Name

| zo

| 6:7:9

| 0-4-11

| C Ebb G

| C(b3) or C(d3)

| C flat-three or C dim-three

| gu

| 10:12:15

| 0-5-11

| C Eb G

| Cm

| C minor

| yo

| 4:5:6

| 0-6-11

| C E G

| C

| C major or C

| ru

| 14:18:21

| 0-7-11

| C(#3) or C(A3)

| C sharp-three or C aug-three

== JI approximation ==

=== 15-odd-limit interval mappings ===

|+style=white-space:nowrap| 15-odd-limit intervals by direct approximation (even if inconsistent)

! Interval, complement

! Error (abs, [[Cent|¢]])

! Error (rel, [[Relative cent|%]])

| [[6/5]], [[5/3]]

| 0.148

| 0.2

| [[14/13]], [[13/7]]

| 1.982

| 3.1

| [[15/13]], [[26/15]]

| 4.891

| 7.7

| [[18/13]], [[13/9]]

| 8.0

| [[15/14]], [[28/15]]

| 6.873

| 10.9

| [[9/7]], [[14/9]]

| 7.021

| 11.1

| [[10/9]], [[9/5]]

| 7.070

| 11.2

| '''[[4/3]], [[3/2]]'''

| '''7.218'''

| '''11.4'''

| '''[[5/4]], [[8/5]]'''

| '''7.366'''

| '''11.7'''

| [[13/10]], [[20/13]]

| 12.109

| 19.2

| [[13/12]], [[24/13]]

| 12.257

| 19.4

| [[7/5]], [[10/7]]

| 14.091

| 22.3

| [[7/6]], [[12/7]]

| 14.239

| 22.5

| [[9/8]], [[16/9]]

| 14.436

| 22.9

| [[16/15]], [[15/8]]

| 14.585

| 23.1

| '''[[11/8]], [[16/11]]'''

| '''17.103'''

| '''27.1'''

| '''[[16/13]], [[13/8]]'''

| '''19.475'''

| '''30.8'''

| '''[[8/7]], [[7/4]]'''

| '''21.457'''

| '''34.0'''

| [[12/11]], [[11/6]]

| 38.5

| [[11/10]], [[20/11]]

| 24.469

| 38.7

| ''[[14/11]], [[11/7]]''

| ''24.597''

| ''38.9''

| ''[[13/11]], [[22/13]]''

| ''26.580''

| ''42.1''

| ''[[15/11]], [[22/15]]''

| ''31.470''

| ''49.8''

| [[11/9]], [[18/11]]

=== Selected 17-limit intervals ===

== Regular temperament properties ==

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" | [[Mapping]]

! colspan="2" | Tuning Error

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

| 2.3

| {{monzo| -30 19 }}

| [{{val| 19 30 }}]

| 2.28

| 3.61

| 2.3.5

| 81/80, 3125/3072

| [{{val| 19 30 44 }}]

| 1.91

| 3.02

| 49/48, 81/80, 126/125

| [{{val| 19 30 44 53 }}]

| 2.76

| 4.35

| 2.3.5.7.13

| 49/48, 65/64, 81/80, 91/90

| [{{val| 19 30 44 53 70 }}]

| 2.53

| 3.99

=== Uniform maps ===

=== Commas ===

! [[Harmonic limit|Prime<br>Limit]]

! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>

! [[Monzo]]

! [[Cents]]

! [[Color notation/Temperament Names|Color Name]]

! Name

| <abbr title="1162261467/1073741824">(20 digits)</abbr>

| {{monzo| -30 19 }}

| 137.14

|  

|  

| 5

| [[16875/16384]]

| {{monzo| -14 3 4 }}

| 51.12

| Negri comma

| 5

| [[3125/3072]]

| {{monzo| -10 -1 5 }}

| 29.61

| Laquinyo

| Magic comma

| 5

| [[81/80]]

| {{monzo| -4 4 -1 }}

| 21.51

| Gu

| 5

| [[78732/78125]]

| {{monzo| 2 9 -7 }}

| 13.40

| Sepgu

| Sensipent comma

| 5

| [[15625/15552]]

| {{monzo| -6 -5 6 }}

| 8.11

| Tribiyo

| Kleisma

| <abbr title="1224440064/1220703125">(20 digits)</abbr>

| {{monzo| 8 14 -13 }}

| 5.29

| Thegu

| [[Parakleisma]]

| 5

| <abbr title="19073486328125/19042491875328">(28 digits)</abbr>

| {{monzo| -14 -19 19 }}

| 2.82

| [[Enneadeca]]

| 7

| [[1029/1000]]

| {{monzo| -3 1 -3 3 }}

| 49.49

| Trizogu

| Keega

| 7

| [[525/512]]

| {{monzo| -9 1 2 1 }}

| 43.41

| Lazoyoyo

| Avicennma

| [[49/48]]

| {{monzo| -4 -1 0 2 }}

| 35.70

| Zozo

| Slendro diesis

| 7

| [[686/675]]

| {{monzo| 1 -3 -2 3 }}

| 27.99

| Trizo-agugu

| Senga

| 7

| [[875/864]]

| {{monzo| -5 -3 3 1 }}

| 21.90

| Zotrigu

| 7

| [[245/243]]

| {{monzo| 0 -5 1 2 }}

| Zozoyo

| Sensamagic

| 7

| [[126/125]]

| {{monzo| 1 2 -3 1 }}

| 13.79

| Zotrigu

| Starling comma

| 7

| [[225/224]]

| {{monzo| -5 2 2 -1 }}

| 7.71

| Ruyoyo

| Marvel comma

| 7

| [[19683/19600]]

| {{monzo| -4 9 -2 -2 }}

| 7.32

| Labirugu

| Cataharry

| 7

| [[10976/10935]]

| {{monzo| 5 -7 -1 3 }}

| 6.48

| Satrizo-agu

| Hemimage

| 7

| [[3136/3125]]

| {{monzo| 6 0 -5 2 }}

| 6.08

| Zozoquingu

| Hemimean

| 7

| <abbr title="703125/702464">(12 digits)</abbr>

| {{monzo| -11 2 7 -3 }}

| Latriru-asepyo

| [[Meter]]

| 7

| [[4375/4374]]

| {{monzo| -1 -7 4 1 }}

| 0.40

| Zoquadyo

| 11

| [[100/99]]

| {{monzo| 2 -2 2 0 -1 }}

| Luyoyo

| Ptolemisma

| [[896/891]]

| {{monzo| 7 -4 0 1 -1 }}

| 9.69

| Saluzo

| Pentacircle

| 11

| [[65536/65219]]

| {{monzo| 16 0 0 -2 -3 }}

| Satrilu-aruru

| Orgonisma

| 11

| [[385/384]]

| {{monzo| -7 -1 1 1 1 }}

| 4.50

| Lozoyo

| Keenanisma

| 11

| [[540/539]]

| {{monzo| 2 3 1 -2 -1 }}

| 3.21

| Lururuyo

| Swetisma

| 13

| [[65/64]]

| {{monzo| -6 0 1 0 0 1 }}

| 26.84

| Thoyo

| Wilsorma

| 13

| [[343/338]]

| {{monzo| -1 0 0 3 0 -2 }}

| Thuthutrizo

| 13

| [[91/90]]

| {{monzo| -1 -2 -1 1 0 1 }}

| 19.13

| Superleap

| 13

| [[676/675]]

| {{monzo| 2 -3 -2 0 0 2 }}

| 2.56

| Bithogu

| Island comma

<references/>

=== Linear temperaments ===

* [[List of 19et rank two temperaments by badness]]

* [[List of 19et rank two temperaments by complexity]]

* [[List of edo-distinct 19et rank two temperaments]]

* [[Syntonic-kleismic equivalence continuum]]

! Degree

! Cents

! MOSes

! Temperaments

| 1

| A1, d2

|  

| [[Unicorn]] / [[rhinocerus]]

| 2

| 126.32

| m2

| [[1L 8s]], [[9L 1s]]

| [[Negri]]

| 3

| 189.47

| M2

| [[1L 5s]], [[6L 1s]], [[6L 7s]]

| [[Deutone]]<br>[[Spell]]

| 252.63

| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]

| [[Godzilla]]

| 5

| 315.79

| m3

| [[3L 1s]], [[4L 3s]], <br>[[4L 7s]], [[4L 11s]]

| [[Cata]] / [[keemun]]

| 6

| 378.95

| M3

| [[3L 1s]], [[3L 4s]], [[3L 7s]], <br>[[3L 10s]], [[3L 13s]]

| [[Magic]] / [[muggles]]

| 7

| 442.11

| A3, d4

| [[3L 2s]], [[3L 5s]], [[8L 3s]]

| [[Sensi]]

| 8

| 505.26

| P4

| [[2L 3s]], [[5L 2s]], [[7L 5s]]

| [[Meantone]] / [[flattone]]

| 9

| A4

| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]

| [[Liese]] / [[pycnic]]<br>[[Triton]]

== Scales ==

=== MOS scales ===

==== Octave-equivalent mosses ====

* [[meantone]] pentatonic, [[2L 3s]] (gen = 11\19): 33535

* [[meantone]] diatonic, [[5L 2s]] (gen = 11\19): 3323332

* [[meantone]] chromatic, [[7L 5s]] (gen = 11\19): 212122121212

* [[semaphore]][5], [[4L 1s]] (gen = 4\19): 44344

* [[semaphore]][9], [[5L 4s]] (gen = 4\19): 313133131

* [[semaphore]][14], [[5L 9s]] (gen = 4\19): 21211211211211

* [[sensi]][5], [[2L 3s]] (gen = 7\19): 52525

* [[sensi]][8], [[3L 5s]] (gen = 7\19): 23223223

* [[sensi]][11], [[8L 3s]] (gen = 7\19): 22122212221

* [[negri]][9], [[1L 8s]] (gen = 2\19): 222232222

* [[negri]][10], [[9L 1s]] (gen = 2\19): 2222212222

* [[kleismic]][7], [[4L 3s]] (gen = 5\19): 1414144

* [[kleismic]][11], [[4L 7s]] (gen = 5\19): 13113113131

* [[kleismic]][15], [[4L 11s]] (gen = 5\19): 121112111211211

* [[magic]][7], [[3L 4s]] (gen = 6\19): 5151511

* [[magic]][10], [[3L 7s]] (gen = 6\19): 4114114111

* [[magic]][13], [[3L 10s]] (gen = 6\19): 3111311131111

* [[magic]][16], [[3L 13s]] (gen = 6\19): 2111121111211111

* [[liese]][17], [[2L 15s]] (gen = 9\19): 2111111111211111111

=== Other scales ===

* Meantone harmonic minor: 3233242

* Meantone melodic minor: 3233332

* Meantone harmonic major: 3323242

* Meantone / [[marvel double harmonic major]]: 2423242 (subset of Negri[9])

* enharmonic pentatonic: 26326, 62362

* enharmonic octave species: 1163116, 6113611, 1613161

* [[Semiquartal]] 3|5 b2: 133131331

* [[Marvel hexatonic]]: 425242 (subset of Negri[9])

* [[Antipental blues]]: 441244

== Instruments ==

== Music ==

== See also ==

* [[19edo modes]]

* [[19edo chords]]

* [[Strictly proper 19edo scales]]

* [[How to tune a 19edo guitar by ear]]

* [[Primer for 19edo]]

* [[Mason Green's New Common Practice Notation]]

* [[Arto and Tendo Theory]]

* [[Lumatone mapping for 19edo]]

=== References ===

* Bucht, Saku and Huovinen, Erkki, ''Perceived consonance of harmonic intervals in 19-tone equal temperament'', CIM04_proceedings.

* Levy, Kenneth J., ''Costeley's Chromatic Chanson'', Annales Musicologues: Moyen-Age et Renaissance, Tome III (1955), pp. 213-261.

== Further reading ==

* [[Darreg, Ivor]]. ''[http://www.tonalsoft.com/sonic-arts/darreg/case.htm A Case for Nineteen]''. 1982.

* Darreg, Ivor. ''[http://www.microstick.net/nineteenarticle.htm Nineteen for the Nineties]''{{dead link}}. (Unknown date of publication).

* Howe, Hubert S., Jr. [http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications]. c. 2004.

* [[Sethares, William A]]. [http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar]. 1991.

* [[Sword, Ron]]. ''[http://www.metatonalmusic.com/books.html Enneadecaphonic Scales for Guitar: A Repository of Scales, Chord-Scales, Notations and Techniques for Nineteen Equal Divisions of the Octave]''. 2010.

* Yasser, Joseph. ''[https://www.worldcat.org/fr/title/726192994 Theory of Evolving Tonality]''. 1932.

== External links ==

* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on the [[Tonalsoft Encyclopedia]]

* [http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Ingrid Pearson, Graham Hair, Dougie McGilvray, Nick Bailey, Amanda Morrison and Richard Parncutt (from n-ISM, the Network for Interdisciplinary Studies in Science, Technology, and Music)

* [http://mtg.redkeylabs.com/index.php?topic=6.0 Forum Discussion with some 19-EDO xenharmonic scales Hanson (Keemun), Liese, Negri, Magic, Semaphore, Sensi played on guitar].

* [[Bostjan Zupancic]]'s [https://sites.google.com/site/bostjanzupancickhereb/home/bostjan/microtones/19edo 19-EDO pages]  

* [https://sites.google.com/view/19edoscales Catalog of all 19edo heptatonic scales]