17 equal temperament

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.

Notation

Easley Blackwood Jr. created a notation system where sharps and flats raised/lowered 2 steps, identical to ups and downs notation for 17-EDO. ((10*7) mod 17 = 2.) 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 compared to just.

]]

:{| class="wikitable sortable" style="vertical-align:center;text-align:center;" |- style="vertical-align:bottom;" ! interval name ! size (steps) ! size (cents) ! audio ! just ratio ! just (cents) ! audio ! error |- style="text-align:center;" | octave | 17 | 1200 | | 2:1 | 1200 | | 0 |- style="text-align:center;" | minor seventh | 14 | 988.23 | | 16:9 | 996.09 | | −7.77 |- style="text-align:center;background:#D4D4D4;" | harmonic seventh | 14 | 988.23 | | 7:4 | 968.83 | | +19.41 |- style="text-align:center;" | perfect fifth | 10 | 705.88 | [[File:10 steps in 17-et on C.mid|120px]] | 3:2 | 701.96 | [[File:Just perfect fifth on C.mid|120px]] | +3.93 |- style="text-align:center;background:#D4D4D4;" | septimal tritone | 8 | 564.71 | [[File:8 steps in 17-et on C.mid|120px]] | 7:5 | 582.51 | [[File:Lesser septimal tritone on C.mid|120px]] | −17.81 |- style="text-align:center;" | tridecimal narrow tritone | 8 | 564.71 | [[File:8 steps in 17-et on C.mid|120px]] | 18:13 | 563.38 | [[File:Tridecimal narrow tritone on C.mid|120px]] | +1.32 |- style="text-align:center;" | undecimal super-fourth | 8 | 564.71 | [[File:8 steps in 17-et on C.mid|120px]] | 11:8 | 551.32 | [[File:Eleventh harmonic on C.mid|120px]] | +13.39 |- style="text-align:center;" | perfect fourth | 7 | 494.12 | [[File:7 steps in 17-et on C.mid|120px]] | 4:3 | 498.04 | [[File:Just perfect fourth on C.mid|120px]] | −3.93 |- style="text-align:center;" | septimal major third | 6 | 423.53 | [[File:6 steps in 17-et on C.mid|120px]] | 9:7 | 435.08 | [[File:Septimal major third on C.mid|120px]] | −11.55 |- style="text-align:center;" | undecimal major third | 6 | 423.53 | [[File:6 steps in 17-et on C.mid|120px]] | 14:11 | 417.51 | [[File:Undecimal major third on C.mid|120px]] | +6.02 |- style="text-align:center;background:#D4D4D4;" | major third | 5 | 352.94 | [[File:5 steps in 17-et on C.mid|120px]] | 5:4 | 386.31 | [[File:Just major third on C.mid|120px]] | −33.37 |- style="text-align:center;" | tridecimal neutral third | 5 | 352.94 | [[File:5 steps in 17-et on C.mid|120px]] | 16:13 | 359.47 | [[File:Tridecimal neutral third on C.mid|120px]] | −6.53 |- style="text-align:center;" | undecimal neutral third | 5 | 352.94 | [[File:5 steps in 17-et on C.mid|120px]] | 11:9 | 347.41 | [[File:Undecimal neutral third on C.mid|120px]] | +5.53 |- style="text-align:center;background:#D4D4D4;" | minor third | 4 | 282.35 | [[File:4 steps in 17-et on C.mid|120px]] | 6:5 | 315.64 | [[File:Just minor third on C.mid|120px]] | −33.29 |- style="text-align:center;" | tridecimal minor third | 4 | 282.35 | [[File:4 steps in 17-et on C.mid|120px]] | 13:11 | 289.21 | [[File:Tridecimal minor third on C.mid|120px]] | −6.86 |- style="text-align:center;" | septimal minor third | 4 | 282.35 | [[File:4 steps in 17-et on C.mid|120px]] | 7:6 | 266.87 | [[File:Septimal minor third on C.mid|120px]] | +15.48 |- style="text-align:center;background:#D4D4D4;" | septimal whole tone | 3 | 211.76 | [[File:3 steps in 17-et on C.mid|120px]] | 8:7 | 231.17 | [[File:Septimal major second on C.mid|120px]] | −19.41 |- style="text-align:center;" | greater whole tone | 3 | 211.76 | [[File:3 steps in 17-et on C.mid|120px]] | 9:8 | 203.91 | [[File:Major tone on C.mid|120px]] | +7.85 |- style="text-align:center;background:#D4D4D4;" | lesser whole tone | 3 | 211.76 | [[File:3 steps in 17-et on C.mid|120px]] | 10:9 | 182.40 | [[File:Minor tone on C.mid|120px]] | +29.36 |- style="text-align:center;" | neutral second, lesser undecimal | 2 | 141.18 | [[File:2 steps in 17-et on C.mid|120px]] | 12:11 | 150.64 | [[File:Lesser undecimal neutral second on C.mid|120px]] | −9.46 |- style="text-align:center;" | greater tridecimal | 2 | 141.18 | [[File:2 steps in 17-et on C.mid|120px]] | 13:12 | 138.57 | [[File:Greater tridecimal two-third tone on C.mid|120px]] | +2.60 |- style="text-align:center;" | lesser tridecimal | 2 | 141.18 | [[File:2 steps in 17-et on C.mid|120px]] | 14:13 | 128.30 | [[File:Lesser tridecimal two-third tone on C.mid|120px]] | +12.88 |- style="text-align:center;background:#D4D4D4;" | septimal diatonic semitone | 2 | 141.18 | [[File:1_step_in_17-et_on_C.mid|120px]] | 15:14 | 119.44 | [[File:Septimal diatonic semitone on C.mid|120px]] | +21.73 |- style="text-align:center;background:#D4D4D4;" | diatonic semitone | 2 | 141.18 | [[File:2 steps in 17-et on C.mid|120px]] | 16:15 | 111.73 | [[File:Just diatonic semitone on C.mid|120px]] | +29.45 |- style="text-align:center;" | septimal chromatic semitone | 1 | 70.59 | [[File:1_step_in_17-et_on_C.mid|120px]] | 21:20 | 84.47 | [[File:Septimal chromatic semitone on C.mid|120px]] | −13.88 |- style="text-align:center;" | chromatic semitone | 1 | 70.59 | [[File:1_step_in_17-et_on_C.mid|120px]] | 25:24 | 70.67 | [[File:Just chromatic semitone on C.mid|120px]] | −0.08 |}

Relation to 34 EDO

is a subset of

References

Sources

• {{cite journal

References

1. [[Alexander John Ellis. 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.
2. Blackwood, Easley. (Summer 1991). "Modes and Chord Progressions in Equal Tunings". [[Perspectives of New Music]].