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.

1 Interval size
2 Relation to 34-ET
3 External links
4 Sources

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

Sources

Musical tunings

Measurement

Pitch
Cent
Millioctave
Savart
Interval
Interval ratio
Pitch class
Consonance and dissonance
List of musical intervals (by name or by ratio)
List of intervals in 5-limit just intonation
List of meantone intervals
Microtone

Just intonation

Temperaments

Equal	6-tone 12-tone 15-tone 17-tone 19-tone 22-tone 24-tone 31-tone 34-tone 41-tone 53-tone 72-tone

Linear	Meantone (quarter-comma, septimal) Schismatic Miracle Magic Syntonic

Irregular	Well temperament/Temperament ordinaire (Kirnberger, Werckmeister, Young)

Traditional
non-Western

Chinese musicology
Shí-èr-lǜ
Dastgah
Maqam
- Arabian maqam
- Makam
- Mugham
- Muqam
Octoechos
Pelog
Raga (Carnatic rāga)
Slendro
Tetrachord

Non-octave

833 cents scale
A12 scale
Alpha scale
Beta scale
Gamma scale
Delta scale
Lambda scale (Bohlen-Pierce)

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17 Equal Temperament