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 172, or 70.6 cents (play ).

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.[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.

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 just ratio just (cents) midi error
octave 17 1200 2:1 1200 0
minor seventh 14 988.23 16:9 996 -07.77
perfect fifth 10 705.88 Play  3:2 701.96 Play  +03.93
septimal tritone 08 564.71 Play  7:5 582.51 Play  −17.81
tridecimal narrow tritone 08 564.71 Play  18:13 563.38 Play  +01.32
undecimal super-fourth 08 564.71 Play  11:80 551.32 Play  +13.39
perfect fourth 07 494.12 Play  4:3 498.04 Play  03.93
septimal major third 06 423.53 Play  9:7 435.08 Play  −11.55
undecimal major third 06 423.53 Play  14:11 417.51 Play  +06.02
major third 05 352.94 Play  5:4 386.31 Play  −33.37
tridecimal neutral third 05 352.94 Play  16:13 359.47 Play  06.53
undecimal neutral third 05 352.94 Play  11:90 347.41 Play  +05.53
minor third 04 282.35 Play  6:5 315.64 Play  −33.29
tridecimal minor third 04 282.35 Play  13:11 289.21 play  06.86
septimal minor third 04 282.35 Play  7:6 266.87 Play  +15.48
septimal whole tone 03 211.76 Play  8:7 231.17 Play  −19.41
whole tone 03 211.76 Play  9:8 203.91 Play  +07.85
neutral second, lesser undecimal 02 141.18 Play  12:11 150.64 Play  09.46
greater tridecimal 23-tone 02 141.18 Play  13:12 138.57 Play  +02.60
lesser tridecimal 23-tone 02 141.18 Play  14:13 128.30 Play  +12.88
septimal diatonic semitone 02 141.18 Play  15:14 119.44 Play  +21.73
diatonic semitone 02 141.18 Play  16:15 111.73 Play  +29.45
septimal chromatic semitone 01 070.59 Play  21:20 084.47 Play  −13.88
chromatic semitone 01 070.59 Play  25:24 070.67 Play  00.08

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.

References

  1. 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.
  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", p.175, Perspectives of New Music, Vol. 29, No. 2, pp. 166-200.
  4. 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.

the shbobo shtar, based on a Persian tar, has a 17tet fretboard.

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