In music, 17 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 , or 70.6 cents.

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.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. 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 ! justratio ! just(cents) ! audio ! error |- style="text-align:center;" | octave | 17 | 1200 | | 2:1 | 1200 | | 0 |- style="text-align: center;" |Major seventh |16 |1129.41 | |27:14 |1137.04 | | -7.62 |- style="text-align: center;" |Major seventh |16 |1129.41 | |15:8 |1088.27 | | +41.14 |- style="text-align: center;" |Neutral seventh |15 |1058.82 | |11:6 |1049.36 | | +9.46 |- 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;" |major sixth |13 |917.65 | |27:16 |905.87 | | +11.78 |- style="text-align: center;" |neutral sixth |12 |847.06 | |13:8 |840.53 | | +6.53 |- style="text-align: center;" |minor sixth |11 |776.47 | |14:9 |764.92 | | +11.55 |- style="text-align:center;" | perfect fifth | 10 | 705.88 | | 3:2 | 701.96 | | +3.93 |- style="text-align: center;" |augmented fourth (notational) |9 |635.29 | |16:11 |648.68 | | -13.39 |- style="text-align:center;background:#D4D4D4;" | septimal tritone | 8 | 564.71 | | 7:5 | 582.51 | | −17.81 |- style="text-align:center;" | tridecimal narrow tritone | 8 | 564.71 | | 18:13 | 563.38 | | +1.32 |- style="text-align:center;" | undecimal super-fourth | 8 | 564.71 | | 11:8 | 551.32 | | +13.39 |- style="text-align:center;" | perfect fourth | 7 | 494.12 | | 4:3 | 498.04 | | −3.93 |- style="text-align:center;" | septimal major third | 6 | 423.53 | | 9:7 | 435.08 | | −11.55 |- style="text-align:center;" | undecimal major third | 6 | 423.53 | | 14:11 | 417.51 | | +6.02 |- style="text-align:center;background:#D4D4D4;" | major third | 5 | 352.94 | | 5:4 | 386.31 | | −33.37 |- style="text-align:center;" | tridecimal neutral third | 5 | 352.94 | | 16:13 | 359.47 | | −6.53 |- style="text-align:center;" | undecimal neutral third | 5 | 352.94 | | 11:9 | 347.41 | | +5.53 |- style="text-align:center;background:#D4D4D4;" | minor third | 4 | 282.35 | | 6:5 | 315.64 | | −33.29 |- style="text-align:center;" | tridecimal minor third | 4 | 282.35 | | 13:11 | 289.21 | | −6.86 |- style="text-align:center;" | septimal minor third | 4 | 282.35 | | 7:6 | 266.87 | | +15.48 |- style="text-align:center;background:#D4D4D4;" | septimal whole tone | 3 | 211.76 | | 8:7 | 231.17 | | −19.41 |- style="text-align:center;" | greater whole tone | 3 | 211.76 | | 9:8 | 203.91 | | +7.85 |- style="text-align:center;background:#D4D4D4;" | lesser whole tone | 3 | 211.76 | | 10:9 | 182.40 | | +29.36 |- style="text-align:center;" | neutral second, lesser undecimal | 2 | 141.18 | | 12:11 | 150.64 | | −9.46 |- style="text-align:center;" | greater tridecimal | 2 | 141.18 | | 13:12 | 138.57 | | +2.60 |- style="text-align:center;" | lesser tridecimal | 2 | 141.18 | | 14:13 | 128.30 | | +12.88 |- style="text-align:center;background:#D4D4D4;" | septimal diatonic semitone | 2 | 141.18 | | 15:14 | 119.44 | | +21.73 |- style="text-align:center;background:#D4D4D4;" | diatonic semitone | 2 | 141.18 | | 16:15 | 111.73 | | +29.45 |- style="text-align:center;" | septimal chromatic semitone | 1 | 70.59 | | 21:20 | 84.47 | | −13.88 |- style="text-align:center;" | chromatic semitone | 1 | 70.59 | | 25:24 | 70.67 | | −0.08

Relation to 34 EDO is a subset of

References

Sources

External links 17edo on Xenharmonic Wiki "The 17-tone Puzzle — And the Neo-medieval Key that Unlocks It" by George Secor Libro y Programa Tonalismo, heptadecatonic system applications (in Spanish) Georg Hajdu's 1992 ICMC paper on the 17-tone piano project , by Wongi Hwang