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 21/17, or 70.6 cents ( ). Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale.[2] 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. [citation needed]
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
Interval size
interval name | size (steps) | size (cents) | midi | just ratio | just (cents) | midi | error |
---|---|---|---|---|---|---|---|
perfect fifth | 10 | 705.88 | 3:2 | 701.96 | +3.93 | ||
septimal tritone | 8 | 564.71 | 7:5 | 582.51 | −17.81 | ||
tridecimal narrow tritone | 8 | 564.71 | 18:13 | 563.38 | +1.32 | ||
undecimal super-fourth | 8 | 564.71 | 11:8 | 551.32 | +13.39 | ||
perfect fourth | 7 | 494.12 | 4:3 | 498.04 | −3.93 | ||
septimal major third | 6 | 423.53 | 9:7 | 435.08 | −11.55 | ||
undecimal major third | 6 | 423.53 | 14:11 | 417.51 | +6.02 | ||
major third | 5 | 352.94 | 5:4 | 386.31 | −33.37 | ||
tridecimal neutral third | 5 | 352.94 | 16:13 | 359.47 | −6.53 | ||
undecimal neutral third | 5 | 352.94 | 11:9 | 347.41 | +5.53 | ||
minor third | 4 | 282.35 | 6:5 | 315.64 | −33.29 | ||
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 | ||
whole tone | 3 | 211.76 | 9:8 | 203.91 | +7.85 | ||
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 | ||
diatonic semitone | 2 | 141.18 | 16:15 | 111.73 | +29.45 | ||
septimal chromatic semitone | 1 | 70.59 | 21:20 | 84.47 | −13.88 | ||
chromatic semitone | 1 | 70.59 | 25:24 | 70.67 | −0.08 |
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.
External links
- 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
Sources
- ^ 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.