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17 Equal Temperament

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17 Equal Temperament



In music, 17 tone equal temperament is 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.

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

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