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In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represents a frequency ratio of 19√2, or 63.16 cents ( ⓘ ).
Sep 9, 2018 · In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), or 19 ET, is the tempered scale derived by dividing the octave into 19 equal steps (equal frequency ratios). Each step represents a frequency ratio of 19√ 2, or 63.16 cents ( Play (help·info) ). 19 equal temperament keyboard, after Woolhouse (1835). [2]
- Theory
- Notation
- Approximation to Ji
- Regular Temperament Properties
- Scales
- Music
- See Also
- Further Reading
- External Links
History
Interest in this tuning system goes back to the sixteenth century, when composer Guillaume Costeley used it in his chanson Seigneur Dieu ta pitiéof 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 t...
As an approximation of other temperaments
19edo's most salient characteristic is that, having an almost just minor third and perfect fifths and major thirds about seven cents flat, it serves as a good tuning for meantone. It is also suitable for magic/muggles temperament, because five of its major thirds are equivalent to one of its twelfths. For all of these there are more optimal tunings: the fifth of 19edo is flatter than the usual for meantone, and 31edo is more optimal. Similarly, the generating interval of magic temperament is...
As a means of extending harmony
Because 19edo allows for more blended, consonant harmonies than 12edo does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynchsuggests 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 12edo blend much better in 19edo. 19edo's tritones are als...
Standard 12edo notation can be used, whether it is staff notation (with five lines), letter chain-of-fifths notation(with standard accidentals), solfege, or sargam. Note that D# and Eb are two different notes. In 19edo: 1. ups and downs notationis identical to standard notation; 2. mixed sagittal notation is identical to standard notation, but pure...
15-odd-limit interval mappings
The following table shows how 15-odd-limit intervals are represented in 19edo. Prime harmonics are in bold; inconsistent intervals are in italic.
19et is lower in relative error than any previous equal temperaments in the 5-, 7-, 13-, 17-, and 19-limit – both 19 and 19e val achieve this in the case of 13-limit, 19eg val in the 17-limit, and 19egh val in the 19-limit. The next equal temperaments doing better in those subgroups are 34, 31, 27e, 22, and 26, respectively. 19et is prominent in th...
Other scales
1. Meantone harmonic minor: 3 2 3 3 2 4 2 2. Meantone melodic minor: 3 2 3 3 3 3 2 3. Meantone harmonic major: 3 3 2 3 2 4 2 4. chromatic octave species - Meantone / marvel double harmonic major(subset of Negri): 2 4 2 3 2 4 2 5. chromatic octave species (subset of Negri): 2 2 4 3 2 2 4 6. chromatic octave species - Saharaseptatonic (subset of Negri): 4 2 2 3 4 2 2 7. Marvel hexatonic(subset of Negri): 4 2 5 2 4 2 8. enharmonic pentatonic: 2 6 3 2 6 9. enharmonic pentatonic: 6 2 3 6 2 10. enh...
Main article: 19edo/MusicSee also: Category:19edo tracksDarreg, Ivor. A Case for Nineteen. 1982.Darreg, Ivor. Nineteen for the Nineties[dead link]. (Unknown date of publication).Howe, Hubert S., Jr. 19-Tone Theory and Applications. c. 2004.Sethares, William A. Tunings for 19 Tone Equal Tempered Guitar. 1991.19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2 on the Tonalsoft EncyclopediaBostjan Zupancic's 19-EDO pagesIn music, 19 equal temperament, called 19-TET, 19-EDO, or 19-ET, is the scale derived by dividing the octave into 19 equally large steps. Each step represents a frequency ratio of the 19th root of 2, or 63.16 cents. It is the 8th prime edo, following 17edo and coming before 23edo.
19 TET Keyboard. An online interactive and playable 19 tone equal temperament keyboard. Music Pitch Temperament audio. On a standard piano keyboard, one octave is divided into 12 notes made up from 7 white keys (A, B, C, D, E, F and G), and in between some of these, 5 black keys, which can be called either sharps or flats: A# (Bb), C# (Db), D# ...
An equal temperament is a musical temperament or tuning system that approximates just intervals by dividing an octave (or other interval) into steps such that the ratio of the frequencies of any adjacent pair of notes is the same.
From a just intonation point of view, 19 is a sensible equal temperment because it gives greater purity of major and minor thirds (and their inversions the major and minor sixths) than 12 tone equal temperament, yet it does not have an overwhelmingly large number of pitches per octave.
