17 equal temperament

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Figure 1: 17-ET on the syntonic temperament’s tuning continuum at P5= 705.88 cents, from (Milne et al. 2007).[1]
Easley Blackwood's[2] notation system for 17 equal temperament: intervals are notated similarly to those they approximate and enharmonic equivalents are distinct from those of 12 equal temperament (e.g., E/F). About this sound Play 
Major chord on C in 17 equal temperament: all notes within 37 cents of just intonation (rather than 14 for 12 equal temperament). About this sound Play 17-et , About this sound Play just , or About this sound Play 12-et 

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 (About this sound Play ). Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale.[3] This is presumably Safi al-Din Urmawi's seventeen tone tuning developed in the thirteenth century and the primary theoretical system until the development of the quarter tone scale.

17-ET is the tuning of the syntonic temperament in which the tempered perfect fifth is equal to 705.88 cents, as shown in Figure 1 (look for the label "17-TET"). On an isomorphic keyboard, the fingering of music composed in 17-ET is precisely the same as it is in any other syntonic tuning (such as 12-ET), so long as the notes are spelled properly -- that is, with no assumption of enharmonicity.

I-IV-V-I chord progression in 17 tone equal temperament.[4] About this sound Play  Whereas in 12TET B is 11 steps, in 17-TET B is 16 steps.

Interval size[edit]

interval name size (steps) size (cents) midi just ratio just (cents) midi error
perfect fifth 10 705.88 About this sound Play  3:2 701.96 About this sound Play  +3.93
septimal tritone 8 564.71 About this sound Play  7:5 582.51 About this sound Play  −17.81
tridecimal narrow tritone 8 564.71 About this sound Play  18:13 563.38 +1.32
undecimal super-fourth 8 564.71 About this sound Play  11:8 551.32 About this sound Play  +13.39
perfect fourth 7 494.12 About this sound Play  4:3 498.04 About this sound Play  −3.93
septimal major third 6 423.53 About this sound Play  9:7 435.08 About this sound Play  −11.55
undecimal major third 6 423.53 About this sound Play  14:11 417.51 About this sound Play  +6.02
major third 5 352.94 About this sound Play  5:4 386.31 About this sound Play  −33.37
tridecimal neutral third 5 352.94 About this sound Play  16:13 359.47 About this sound Play  −6.53
undecimal neutral third 5 352.94 About this sound Play  11:9 347.41 About this sound Play  +5.53
minor third 4 282.35 About this sound Play  6:5 315.64 About this sound Play  −33.29
tridecimal minor third 4 282.35 About this sound Play  13:11 289.21 About this sound play  −6.86
septimal minor third 4 282.35 About this sound Play  7:6 266.87 About this sound Play  +15.48
septimal whole tone 3 211.76 About this sound Play  8:7 231.17 About this sound Play  −19.41
whole tone 3 211.76 About this sound Play  9:8 203.91 About this sound Play  +7.85
neutral second, lesser undecimal 2 141.18 About this sound Play  12:11 150.64 About this sound Play  −9.46
greater tridecimal 2/3-tone 2 141.18 About this sound Play  13:12 138.57 +2.60
lesser tridecimal 2/3-tone 2 141.18 About this sound Play  14:13 128.30 +12.88
septimal diatonic semitone 2 141.18 About this sound Play  15:14 119.44 About this sound Play  +21.73
diatonic semitone 2 141.18 About this sound Play  16:15 111.73 About this sound Play  +29.45
septimal chromatic semitone 1 70.59 About this sound Play  21:20 84.47 About this sound Play  −13.88
chromatic semitone 1 70.59 About this sound Play  25:24 70.67 About this sound Play  −0.08

Relation to 34-ET[edit]

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[edit]

Sources[edit]

  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. ^ Blackwood, Easley (Summer, 1991). "Modes and Chord Progressions in Equal Tunings", p.175, Perspectives of New Music, Vol. 29, No. 2, pp. 166-200.
  3. ^ 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.
  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.