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").
Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale.[1] 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.
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, CQuarter 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
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 | −7.77 | ||||||||||
| perfect fifth | 10 | 705.88 | 3:2 | 701.96 | +3.93 | ||||||||||
| align=center bgcolor="#D4D4D4" | septimal tritone | align=center bgcolor="#D4D4D4" | 8 | align=center bgcolor="#D4D4D4" | 564.71 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 7:5 | align=center bgcolor="#D4D4D4" | 582.51 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | −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 | ||||||||||
| align=center bgcolor="#D4D4D4" | major third | align=center bgcolor="#D4D4D4" | 5 | align=center bgcolor="#D4D4D4" | 352.94 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 5:4 | align=center bgcolor="#D4D4D4" | 386.31 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | −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 | ||||||||||
| align=center bgcolor="#D4D4D4" | minor third | align=center bgcolor="#D4D4D4" | 4 | align=center bgcolor="#D4D4D4" | 282.35 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 6:5 | align=center bgcolor="#D4D4D4" | 315.64 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | −33.29 | ||
| align=center | tridecimal minor third | 4 | 282.35 | 13:11 | 289.21 | −6.86 | |||||||||
| septimal minor third | 4 | 282.35 | 7:6 | 266.87 | +15.48 | ||||||||||
| align=center bgcolor="#D4D4D4" | septimal whole tone | align=center bgcolor="#D4D4D4" | 3 | align=center bgcolor="#D4D4D4" | 211.76 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 8:7 | align=center bgcolor="#D4D4D4" | 231.17 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | −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 -tone | 2 | 141.18 | 13:12 | 138.57 | +2.60 | ||||||||||
| lesser tridecimal -tone | 2 | 141.18 | 14:13 | 128.30 | +12.88 | ||||||||||
| align=center bgcolor="#D4D4D4" | septimal diatonic semitone | align=center bgcolor="#D4D4D4" | 2 | align=center bgcolor="#D4D4D4" | 141.18 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 15:14 | align=center bgcolor="#D4D4D4" | 119.44 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | +21.73 | ||
| align=center bgcolor="#D4D4D4" | diatonic semitone | align=center bgcolor="#D4D4D4" | 2 | align=center bgcolor="#D4D4D4" | 141.18 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | 16:15 | align=center bgcolor="#D4D4D4" | 111.73 | align=center bgcolor="#D4D4D4" | align=center bgcolor="#D4D4D4" | +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 |
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.
Sources