19edo: Difference between revisions
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Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work. | Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson [[Seigneur Dieu ta pitié]] of 1558. Costeley understood and desired the circulating aspect of this tuning, which he defined as dividing the just major second into three approximately equal parts. Costeley had other compositions that made use of intervals, such as the diminished third, which have a meaningful context in 19edo, but not in other tuning systems contemporary with the work. | ||
In 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone]], in which the fifth is | In 1577 music theorist Francisco de Salinas proposed [[1/3-comma meantone]], in which the fifth is 694.786 cents; the fifth of 19edo is 694.737, which is only a twentieth of a cent flatter. Salinas suggested tuning nineteen tones to the octave to this tuning, which comes within less than one cent of closing exactly, so that his suggestion is effectively 19edo. | ||
In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]). | In 1835, mathematician and music theorist Wesley Woolhouse proposed it as a more practical alternative to meantone tunings he regarded as better, such as [[50edo|50 equal temperament]] ([http://www.tonalsoft.com/sonic-arts/monzo/woolhouse/essay.htm summary of Woolhouse's essay]). | ||
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Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy. For example, the key of | Key signatures are the same, but with the extra notes and different enharmonic equivalents, some key signatures can get messy. For example, the key of B𝄫 would have double-flats on B and E, and flats on C, D, F, G, and A. Thinking of rewriting this key as A♯ might seem better, but then the key signature would contain double-sharps on C, F, and G, and sharps on A, B, D, and E, which is actually worse. | ||
All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads: | All 19edo chords can be named using conventional methods, expanded to include augmented and diminished 2nd, 3rds, 6ths and 7ths. Here are the zo, gu, yo and ru triads: | ||
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| 6:7:9 | | 6:7:9 | ||
| 0–4–11 | | 0–4–11 | ||
| | | C–E𝄫–G | ||
| Cm( | | Cm(♭3), Cmin(♭3), C(d3) | ||
| C subminor, C minor flat-three, C diminished-three | | C subminor, C minor flat-three, C diminished-three | ||
|- | |- | ||
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| 10:12:15 | | 10:12:15 | ||
| 0–5–11 | | 0–5–11 | ||
| | | C–E♭–G | ||
| Cm, Cmin | | Cm, Cmin | ||
| C minor | | C minor | ||
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| 14:18:21 | | 14:18:21 | ||
| 0–7–11 | | 0–7–11 | ||
| | | C–E♯–G | ||
| C( | | C(E♯3), Cmaj(E♯3), C(A3) | ||
| C supermajor, C major sharp-three, C augmented-three | | C supermajor, C major sharp-three, C augmented-three | ||
|- | |- | ||
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| 4:5:6:7 | | 4:5:6:7 | ||
| 0–6–11–15 | | 0–6–11–15 | ||
| | | C–E–G–B𝄫 | ||
| C(h7), Cadd(d7), Cmaj(add(d7)) | | C(h7), Cadd(d7), Cmaj(add(d7)) | ||
| C harmonic 7, C (major) add dim-seven | | C harmonic 7, C (major) add dim-seven | ||
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| 1/(4:5:6:7)<br />= 1:6/5:3/2:12/7 | | 1/(4:5:6:7)<br />= 1:6/5:3/2:12/7 | ||
| 0–5–11–15 | | 0–5–11–15 | ||
| | | C–E♭–G–AE♯ | ||
| Cm( | | Cm(𦛶), Cm(A6), Cm(add(𦛶)), Cm(add(A6)) | ||
| C minor (add) sharp-six, C minor (add) aug-six | | C minor (add) sharp-six, C minor (add) aug-six | ||
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