Misplaced Pages

In music, 17 equal temperament is the tempered scale derived by dividing the octave into 17 equal steps (equal frequency ratios). Each step represents a frequency ratio of √2, or 70.6 cents.

17-ET is the tuning of the regular diatonic tuning in which the tempered perfect fifth is equal to 705.88 cents, as shown in Figure 1 (look for the label "17-TET").

History and use

Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale. In the thirteenth century, Middle-Eastern musician Safi al-Din Urmawi developed a theoretical system of seventeen tones to describe Arabic and Persian music, although the tones were not equally spaced. This 17-tone system remained the primary theoretical system until the development of the quarter tone scale.

Notation

Easley Blackwood Jr. created a notation system where sharps and flats raised/lowered 2 steps. This yields the chromatic scale:

C, D♭, C♯, D, E♭, D♯, E, F, G♭, F♯, G, A♭, G♯, A, B♭, A♯, B, C

Quarter tone sharps and flats can also be used, yielding the following chromatic scale:

C, C/D♭, C♯/D, D, D/E♭, D♯/E, E, F, F/G♭, F♯/G, G, G/A♭, G♯/A, A, A/B♭, A♯/B, B, C

Interval size

Below are some intervals in 17 EDO compared to just.

interval name	size (steps)	size (cents)	MIDI audio	just ratio	just (cents)	MIDI audio	error
octave	17	1200 00		2:1	1200 00		0
minor seventh	14	988.23		16:9	996.09		−07.77
harmonic seventh	14	988.23		7:4	968.83		+19.41
perfect fifth	10	705.88		3:2	701.96		+03.93
septimal tritone	08	564.71		7:5	582.51		−17.81
tridecimal narrow tritone	08	564.71		18:13	563.38		+01.32
undecimal super-fourth	08	564.71		11:80	551.32		+13.39
perfect fourth	07	494.12		4:3	498.04		−03.93
septimal major third	06	423.53		9:7	435.08		−11.55
undecimal major third	06	423.53		14:11	417.51		+06.02
major third	05	352.94		5:4	386.31		−33.37
tridecimal neutral third	05	352.94		16:13	359.47		−06.53
undecimal neutral third	05	352.94		11:90	347.41		+05.53
minor third	04	282.35		6:5	315.64		−33.29
tridecimal minor third	04	282.35		13:11	289.21		−06.86
septimal minor third	04	282.35		7:6	266.87		+15.48
septimal whole tone	03	211.76		8:7	231.17		−19.41
greater whole tone	03	211.76		9:8	203.91		+07.85
lesser whole tone	03	211.76		10:90	182.40		+29.36
neutral second, lesser undecimal	02	141.18		12:11	150.64		−09.46
greater tridecimal ⁠ 2 / 3 ⁠-tone	02	141.18		13:12	138.57		+02.60
lesser tridecimal ⁠ 2 / 3 ⁠-tone	02	141.18		14:13	128.30		+12.88
septimal diatonic semitone	02	141.18		15:14	119.44		+21.73
diatonic semitone	02	141.18		16:15	111.73		+29.45
septimal chromatic semitone	01	070.59		21:20	084.47		−13.88
chromatic semitone	01	070.59		25:24	070.67		−00.08

Relation to 34 EDO

17 EDO is where every other step in the 34 EDO scale is included, and the others are not accessible. Conversely 17 EDO is a subset of 34 EDO.

References

1. Milne, Sethares & Plamondon 2007, pp. 15–32.
2. Ellis, Alexander J. (1863). "On the Temperament of Musical Instruments with Fixed Tones", Proceedings of the Royal Society of London, vol. 13. (1863–1864), pp. 404–422.
3. Blackwood, Easley (Summer 1991). "Modes and Chord Progressions in Equal Tunings". Perspectives of New Music. 29 (2): 166–200 (175). doi:10.2307/833437. JSTOR 833437.
4. Milne, Sethares & Plamondon (2007), p. 29.

Sources

• Milne, Andrew; Sethares, William; Plamondon, James (Winter 2007). "Isomorphic controllers and dynamic tuning: Invariant fingering over a tuning continuum". Computer Music Journal. 31 (4): 15–32. doi:10.1162/comj.2007.31.4.15. S2CID 27906745 – via mitpressjournals.org.

External links

• "The 17-tone Puzzle — And the Neo-medieval Key that Unlocks It" by George Secor
• Libro y Programa Tonalismo, heptadecatonic system applications (in Spanish)
• Georg Hajdu's 1992 ICMC paper on the 17-tone piano project
• "Crocus", 17 equal temperament, 9 tone mode on YouTube, by Wongi Hwang

v t e Microtonal music
Composers	Richard Barrett Béla Bartók Easley Blackwood Jr. Heinz Bohlen Julián Carrillo Franklin Cox Mildred Couper John Eaton Brian Ferneyhough Michael Finnissy Bjørn Fongaard Alois Hába Christiaan Huygens Charles Ives Ben Johnston György Ligeti Stu Mackenzie Claus-Steffen Mahnkopf Joel Mandelbaum Joe Maneri Roger Redgate John Schneider Sevish Ezra Sims Nicola Vicentino Claude Vivier Elaine Walker Ivan Wyschnegradsky La Monte Young
Inventors	Glenn Branca Wendy Carlos Ivor Darreg Adriaan Fokker Lou Harrison Yuri Landman Harry Partch Tui St. George Tucker Nicola Vicentino
Tunings and scales	Non-octave- repeating scales Alpha scale Beta scale Gamma scale Delta scale Lambda scale (Bohlen–Pierce scale) Equal temperament 15 17 19 22 23 24 31 34 41 53 58 72 96 Just intonation Harry Partch's 43-tone scale Double diatonic
Concepts and techniques	Limit Otonality and Utonality Semitone Sonido 13 Xenharmonicity Tonality diamond
Groups and publications	Boston Microtonal Society Genesis of a Music Huygens-Fokker Foundation
Compositions	Beauty in the Beast quarter tone pieces just pieces Mother Sonata for Microtonal Piano Suite for Microtonal Piano Twelve Microtonal Etudes for Electronic Music Media Flying Microtonal Banana K.G. L.W.
Other topics	Enharmonic keyboard Generalized keyboard Modernism (music)

• Equal temperaments
• Microtonality