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## 17 tone equal temperament

## Table of Contents

17-EDOdivides the octave in 17 equal steps, each 70.588 cents in size. It is the seventh prime edo, following 13edo and coming before 19edo.## Theory

An introduction to 17-EDO theory, through the eyes of the SeventeenTonePianoProject: SeventeenTheory.Another introduction into 17-EDO theory: The 17-tone Puzzle by George Secor.

17edo Solfege. 17edo tetrachords. Proyect 17-Perú

17-EDO can plausibly be treated as a 2.3.25.7.11.13.23 subgroup temperament, for which it is quite accurate (though the 7-limit ratios are generally not as well-represented as those of the other integers). Because the 3, 7, 11, and 13 are all sharp, it adapts well to octave shrinking; 27edt (a variant of 17edo in which the octaves are flattened by ~2.5 cents) is a good alternative. Another one is 44ed6.

As a no-fives system, it is best used with timbres in which harmonic multiples of 5 are attenuated or absent. Also, the standard major chord (4:5:6) cannot be used since it includes the fifth harmonic.

Instead, the tonic chords of 17-EDO could be considered to be the tetrad 6:7:8:9 and its utonal inversion, the former of which is a subminor chord with added fourth, and the latter a supermajor chord with added second (resembling the famous mu major chord of Steely Dan fame). These are realized in 17-EDO as 0-4-7-10 and 0-3-6-10, respectively. Both of these have distinct moods, and are stable and consonant, if somewhat more sophisticated than their classic 5-limit counterparts. To this group we could also add the 0-3-7-10 (which is a sus4 with added second, or sus2 with added fourth). These three chords comprise the three ways to divide the 17-EDO perfect fifth into two whole tones and one subminor third. Chromatic alterations of them also exist, for example, the 0-3-7-10 chord may be altered to 0-2-7-10 (which approximates 12:13:16:18) or 0-3-8-10 (which approximates 8:9:11:12). The 0-3-8-10 chord is impressive-sounding, resembling a sus4 but with even more tension; it resolves quite nicely to 0-3-6-10.

## Intervals

Intervals

Ratios*

generated

Minor Second

Neutral Second

Sub Third

Super Second

Neutral Third/

Diminished Fourth

Sub Fourth

Diminished Fifth

diminished 5th

Sub Fifth

down 5th

Minor Sixth

Neutral Sixth/

Diminished Seventh

Sub Seventh

Super Sixth

Neutral Seventh/

Diminished Octave

Sub Octave

## Chord Names

Ups and down notation can be used to name 17edo chords.

0-4-10 = C Eb G = Cm = C minor

0-5-10 = C Ev G = C~ = C mid

0-6-10 = C E G = C = C major

0-4-9 = C Eb Gv = Cm(v5) = C minor down-five

0-5-9 = C Ev G = C~(v5) = C mid down-five

0-6-11 = C E G^ = C(^5) = C up-five

0-4-10-14 = C Eb G Bb = Cm7 = C minor seven

0-5-10-14 = C Ev G Bb = C7(~3) = C seven mid-three

0-6-10-15 = C E G Bv = C(~7) = C mid seven

0-5-10-15 = C Ev G Bv = C.~7 = C dot mid seven

0-4-7-10 = C Eb F G = Cm(11) = C minor add eleven (approximates 6:7:8:9)

0-3-6-10 = C D E G = C(9) = C add nine (approximates 1/(6:7:8:9) = 1/1 - 9/8 - 9/7 - 3/2)

0-3-7-10 = C D F G = C4(9) = C four add nine

0-2-7-10 = C Dv F G = C4(v9) = C four add down-nine (approximates 12:13:16:18)

0-3-8-10 = C D F^ G = C.^4(9) = C up-four add nine (approximates 8:9:11:12)

For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.

## Selected just intervals by error

The following table shows how some prominent just intervals are represented in 17edo (ordered by absolute error).Interval, complementError (abs., in cents)## Commas

17 EDO tempers out the following commas. (Note: This assumes val < 17 27 39 48 59 63 |, cent values rounded to 5 digits.)Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, as stated.

## Scales

List of 17edo rank two temperaments by badness

List of edo-distinct 17c rank two temperaments

## Music

## Compositions

## Sound files

Puhlops and Laugua's Big Adventureby |Aaron Krister JohnsonAdagio for Margoby Aaron Krister JohnsonTransformationby Herman MillerWaltzby Christopher BaileyLostfoundby Christopher BaileyBalladei(in 17, 29 and 12) by Christopher Bailey , CD available here .Two-Part Invention in 17ETby Aaron Andrew HuntOverture to A Midsummer Night's Dreamby Rick McGowanFairy Lullaby from A Midsummer Night's Dreamby Rick McGowanA Calamitous Simultaneityby Igliashon Jones (17edo and 22edo)First Impressionsby Igliashon JonesEtude no1 for 2 Pianos in 17 Equal TemperamentandEtude no2 for 2 Pianos in 17 Equal TemperamentJon Lyle Smith17 Tone Jamby Marmalade Manvideo of On the Shores of the Dead Seaby Chris Vaisvilplay Only in Disneylandby Chris Vaisvilplay 17 Reasons I Hate the Bluesby Chris Vaisvilplay Klingon Opera Overtureby Chris Vaisvilplay Seventeen Selfless Notesby Chris Vaisvilplay 17et Jazzby Chris Vaisvil (60 x 60 winner)play 17 Pink Tuxedosby Chris Vaisvilplay Devil in the Deep Blue seablues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass).play Seventeen Years in the Sixtiesby Chris Vaisvilplay video CT Scanby Chris Vaisvilplay Fish and a Grenade(parental advisory language) by Chris Vaisvilplay video of performance of Seventeen Unsteady Handsby Chris Vaisvilvideo version of The Pond with Japanese Gardenplay Graveyardby Chris VaisvilFor Brass and Voice Choirs in 17 edoby Chris Vaisvil more on the compositionAnd I Became One With My Per Fungiby Chris Vaisvil => more on compositioncounterintuitive (17 edo guitar solo)by Chris Vaisvil => more on composition## Instruments

Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio HuamaniBass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani