17 equal temperament
In music, 17 tone 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 17√, 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.
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:
Below are some intervals in 17-EDO compared to just.
|interval name||size (steps)||size (cents)||midi||just ratio||just (cents)||midi||error|
|tridecimal narrow tritone||8||564.71||18:13||563.38||+1.32|
|septimal major third||6||423.53||9:7||435.08||−11.55|
|undecimal major third||6||423.53||14:11||417.51||+6.02|
|tridecimal neutral third||5||352.94||16:13||359.47||−6.53|
|undecimal neutral third||5||352.94||11:9||347.41||+5.53|
|tridecimal minor third||4||282.35||13:11||289.21||−6.86|
|septimal minor third||4||282.35||7:6||266.87||+15.48|
|septimal whole tone||3||211.76||8:7||231.17||−19.41|
|neutral second, lesser undecimal||2||141.18||12:11||150.64||−9.46|
|greater tridecimal 2⁄3-tone||2||141.18||13:12||138.57||+2.60|
|lesser tridecimal 2⁄3-tone||2||141.18||14:13||128.30||+12.88|
|septimal diatonic semitone||2||141.18||15:14||119.44||+21.73|
|septimal chromatic semitone||1||70.59||21:20||84.47||−13.88|
Relation to 34-ET
17-ET is where every other step in the 34-ET scale is included, and the others are not accessible. Conversely 34-ET is a subdivision of 17-ET.
- Milne, A., Sethares, W.A. and Plamondon, J.,"Isomorphic Controllers and Dynamic Tuning: Invariant Fingerings Across a Tuning Continuum", Computer Music Journal, Winter 2007, Vol. 31, No. 4, Pages 15-32.
- 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.
- Blackwood, Easley (Summer, 1991). "Modes and Chord Progressions in Equal Tunings", p.175, Perspectives of New Music, Vol. 29, No. 2, pp. 166-200.
- Andrew Milne, William Sethares, and James Plamondon (2007). "Isomorphic Controllers and Dynamic Tuning: Invariant Fingering over a Tuning Continuum", p.29. Computer Music Journal, 31:4, pp.15–32, Winter 2007.
- Secor, George. "The 17-tone Puzzle — And the. Neo-medieval Key That Unlocks It".
- Microtonalismo Heptadecatonic System Applications
- Georg Hajdu's 1992 ICMC paper on the 17-tone piano project
- ProyectoXVII Heptadecatonic System Applications project XVII - Peruvian
- "Crocus" on YouTube, by Wongi Hwang