19edo: Difference between revisions
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Another option would be to use a stretched octave; the [[The_Riemann_Zeta_Function_and_Tuning|zeta function]]-optimal tuning has an octave of roughly 1203 cents. Stringed instruments, in particular the piano, are frequently tuned with stretched octaves anyway due to the inharmonicity inherent in strings, which makes 19edo a promising option for them. Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-just. For instance, if we're using [[93ed30|93ed30]] (a variant of 19edo in which 30:1 is just), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. | Another option would be to use a stretched octave; the [[The_Riemann_Zeta_Function_and_Tuning|zeta function]]-optimal tuning has an octave of roughly 1203 cents. Stringed instruments, in particular the piano, are frequently tuned with stretched octaves anyway due to the inharmonicity inherent in strings, which makes 19edo a promising option for them. Octave stretching also means that an out-of-tune interval can be replaced with a compounded or inverted version of it which is near-just. For instance, if we're using [[93ed30|93ed30]] (a variant of 19edo in which 30:1 is just), then we have near-just minor thirds (6:5), compound major thirds (as 5:1), and compound fifths (as 6:1), giving us versions of everything in the 5-limit tonality diamond. The compound major and minor triads (1:5:6 and 30:6:5) are near-just as well. | ||
=As a means of extending harmony= | ==As a means of extending harmony== | ||
Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynch suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non diatonic chord extensions which tend to clash in 12 EDO blend much better in 19 EDO. | Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynch suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non diatonic chord extensions which tend to clash in 12 EDO blend much better in 19 EDO. | ||
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==Intervals and linear temperaments== | ==Intervals and linear temperaments== | ||
[[List_of_edo-distinct_19et_rank_two_temperaments|List of edo-distinct 19et rank two temperaments]] | * [[List_of_19et_rank_two_temperaments_by_badness|List of 19et rank two temperaments by badness]] | ||
* [[List_of_19et_rank_two_temperaments_by_complexity|List of 19et rank two temperaments by complexity]] | |||
* [[List_of_edo-distinct_19et_rank_two_temperaments|List of edo-distinct 19et rank two temperaments]] | |||
Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate. | Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate. | ||
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*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible. | <nowiki>*</nowiki> based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible. | ||
Using [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors: | Using [[Kite's_color_notation|color notation]], qualities can be loosely associated with colors: | ||
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=Chord Names= | ==Chord Names== | ||
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the blue, green, yellow and red triads: | All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the blue, green, yellow and red triads: | ||
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=Photos= | |||
[[File:Vaisvil-19edo-guitar-IMG00145-1024x768.jpg|512x384px|thumb|none|19 note per octave Ibanez conversion by Brad Smith (Indianapolis)]] | [[File:Vaisvil-19edo-guitar-IMG00145-1024x768.jpg|512x384px|thumb|none|19 note per octave Ibanez conversion by Brad Smith (Indianapolis)]] | ||
=Compositions= | =Compositions= | ||
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[https://soundcloud.com/camtaylor-1/wurly-minors-and-enharmonic-tetrachords-17-out-of-19edo Wurly Minors and Enharmonic Tetrachords] - 17-tone fifths chain in 19EDO by Cam Taylor | [https://soundcloud.com/camtaylor-1/wurly-minors-and-enharmonic-tetrachords-17-out-of-19edo Wurly Minors and Enharmonic Tetrachords] - 17-tone fifths chain in 19EDO by Cam Taylor | ||
=See also= | |||
*[[19edo_Modes|19edo Modes]] | |||
*[[Strictly_proper_19edo_scales|Strictly proper 19edo scales]] | |||
*[[How_to_tune_a_19edo_guitar_by_ear|How to tune a 19edo guitar by ear]] | |||
*[[Chord_progressions_in_19edo-family_scales|Chord progressions in 19edo-family scales]] | |||
==Articles== | |||
*[http://sonic-arts.org/darreg/case.htm A Case For Nineteen] by [[Ivor_Darreg|Ivor Darreg]] [http://www.webcitation.org/5xZzBtDGF Permalink] | |||
*[http://www.microstick.net/nineteenarticle.htm Nineteen for the Nineties] by Ivor Darreg | |||
*[http://qcpages.qc.edu/%7Ehowe/articles/19-Tone%20Theory.html 19-Tone Theory and Applications] by Hubert S. Howe Jr. [http://www.webcitation.org/5xbMKVaqa Permalink] | |||
*[http://sethares.engr.wisc.edu/tet19/guitarchords19.html Tunings for 19 Tone Equal Tempered Guitar] by William A. Sethares [http://www.webcitation.org/5xeCbEPZ0 Permalink] | |||
*[http://www.n-ism.org/Projects/microtonalism.php Microtonalism] by Bailey, Morrison, Pearson and Parncutt [http://www.webcitation.org/5xeDFQDvn Permalink] | |||
*[http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone - Encyclopedia of Microtonal Music Theory] [http://tonalsoft.com/enc/number/19edo.aspx Permalink] | |||
*[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]. | |||
*[http://www.ronsword.com/books.html Enneadecaphonic Scales for Guitar] by [[Ron_Sword|Ron Sword]] | |||
==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. | |||
[[Category:19-tone]] | [[Category:19-tone]] | ||
[[Category:19edo]] | [[Category:19edo]] | ||