In music, 17 tone equal temperament is the tempered scale derived by dividing the octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

 into 17 equal steps (equal frequency ratios). Each step represents a frequency ratio of 2^1/17, or 70.6 cents

Cent (music)

The cent is a logarithmic unit of measure used for musical intervals. Twelve-tone equal temperament divides the octave into 12 semitones of 100 cents each...

 . Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourth

Perfect fourth

In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...

s and fifths

Perfect fifth

In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...

 as the Arabic scale. This is presumably Safi al-Din Urmawi

Safi al-Din Urmawi

Safi al-Din al-Urmawi or Safi al-Din Abd al-Mu'min ibn Yusuf ibn al-Fakhir al-Urmawi was a renowned musician and writer on the theory of music...

's seventeen tone tuning developed in the thirteenth century and the primary theoretical system until the development of the quarter tone scale.

Interval size

interval name	size (steps)	size (cents)	midi	just ratio	just (cents)	midi	error
octave Octave In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...	17	1200		2:1	1200		0
neutral seventh Neutral seventh A neutral seventh is a musical interval wider than a minor seventh but narrower than a major seventh . Four distinct intervals may be termed neutral sevenths:* A septimal neutral seventh has a ratio of 64:35 or about 1045 cents....	15	1058.82		11:6	1049.36		+9.46
minor seventh Minor seventh In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions , and the minor seventh is one of two commonly occurring sevenths. The minor quality specification identifies it as being the smallest of the two: the minor seventh spans ten semitones, the...	14	988.24		16:9	996.09		−7.85
septimal major sixth	13	917.65		12:7	933.13		−15.48
neutral sixth Neutral sixth A neutral sixth is a musical interval wider than a minor sixth but narrower than a major sixth . Three distinct intervals may be termed neutral sixths:...	12	847.06		18:11	852.59		−5.53
septimal minor sixth	11	776.47		14:9	764.92		+11.55
perfect fifth Perfect fifth In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...	10	705.88		3:2	701.96		+3.93
septimal tritone	8	564.71		7:5	582.51		−17.81
undecimal tritone	8	564.71		11:8	551.32		+13.39
perfect fourth Perfect fourth In classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...	7	494.12		4:3	498.04		−3.93
septimal major third Septimal major third In music, the septimal major third , also called the supermajor third and sometimes Bohlen–Pierce third is the musical interval exactly or approximately equal to a just 9:7 ratio of frequencies, or alternately 14:11. It is equal to 435 cents, sharper than a just major third by the septimal...	6	423.53		9:7	435.08		−11.55
major third Major third In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...	5	352.94		5:4	386.31		−33.37
neutral third Neutral third A neutral third is a musical interval wider than a minor third but narrower than a major third . Three distinct intervals may be termed neutral thirds:...	5	352.94		11:9	347.41		+5.53
minor third Minor third In classical music from Western culture, a third is a musical interval encompassing three staff positions , and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major...	4	282.35		6:5	315.64		−33.29
septimal minor third Septimal minor third In music, the septimal minor third , also called the subminor third, is the musical interval exactly or approximately equal to a 7/6 ratio of frequencies. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter than a just minor third of 6/5...	4	282.35		7:6	266.87		+15.48
whole tone	3	211.76		9:8	203.91		+7.85
neutral second Neutral second A neutral second or medium second is a musical interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:... , lesser undecimal	2	141.18		12:11	150.64		−9.46
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 Septimal chromatic semitone In music, a septimal chromatic semitone or minor semitone is the interval 21:20 . It is about 84.47 cents. The septimal chromatic semitone may be derived from the harmonic series as the interval between the twentieth and twenty-first harmonics....	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

• Microtonalismo Heptadecatonic System Applications
• Georg Hajdu's 1992 ICMC paper on the 17-tone piano project
• ProyectoXVII Heptadecatonic System Applications project XVII - Peruvian