17edo

# 17 tone equal temperament

**17-EDO** divides 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

\*Ratios based on treating 17edo as a 2.3.7.11.13.25 subgroup

Combining ups and downs notation with color notation, qualities can be loosely associated with colors:

# Chord Names

All 17edo chords can be named using ups and downs. Here are the zo, lova and ru triads:

 lova
 ru

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

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).

### Patent val mapping

File:17ed2-001.svg

17ed2-001.svg

# 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

* Otonal 17
* Blues Peruvian 17edo
* 17edo neutral scale
* Scorp
* Screamapillar
* Hydra
* MOS scales of 17edo (horograms)

List of 17edo rank two temperaments by badness

List of edo-distinct 17c rank two temperaments

# Music

## Compositions

* Demanding Two Faces (xen-pop) by Stephen Weigel
* Where were you at the Apocalypse? (xen-pop) by Stephen Weigel
* Prelude by Daniel Wolf
* Heptadecatonic Drops by Georg Hajdu
* Klangmoraste by Georg Hajdu
* Charles Loli 17edo music for guitar heptadecatonic (2001) and armony inductive microtonaly (1993)
* microtonalismo Heptadecatonic Peruvian
* Multiverse by Jacob Barton

## Sound files

* Shanidar Cave is a piece in 17 edo that features an electric 17 edo guitar and what is essentially an electric tanpura which ends up making this a sort of fusion of middle eastern and Indian music in a sense. by Chris Vaisvil
* *Puhlops and Laugua's Big Adventure*   by |Aaron Krister Johnson
* *Adagio for Margo*   by Aaron Krister Johnson
* *Transformation*   by Herman Miller
* *Waltz*   by Christopher Bailey
* *Lostfound*   by Christopher Bailey
* excerpt from *Balladei*   (in 17, 29 and 12) by Christopher Bailey , CD available here .
* *Two-Part Invention in 17ET*  by Aaron Andrew Hunt
* *Overture to A Midsummer Night's Dream* by Rick McGowan
* *Fairy Lullaby from A Midsummer Night's Dream* by Rick McGowan
* *A Calamitous Simultaneity*  by Igliashon Jones (17edo and 22edo)
* *First Impressions*  by Igliashon Jones
* I Insist by Igliashon Jones
* *Etude no1 for 2 Pianos in 17 Equal Temperament* and *Etude no2 for 2 Pianos in 17 Equal Temperament* Jon Lyle Smith
* A number of compositions from seventeen-tone piano project phase I , seventeen-tone piano project phase II, seventeen-tone piano project phase III.
* 17edo - 17edo-tagged compositions on www.archive.org
* sing a blue by Andrew Heathwaite (composed 2008, recorded 2010). This and the other pieces below by Andrew for cümbüş, steel tubes & voice.
* stringfinger it everybean by Andrew Heathwaite (composed 2008, recorded 2010).
* cat feet belly by Andrew Heathwaite (composed 2008, recorded 2010).
* *17 Tone Jam*  by Marmalade Man
* youtube videos tagged with 17edo
* On the Shores of the Dead Sea blog *video of On the Shores of the Dead Sea*   by Chris Vaisvil
* Only in Disneyland 17 blog edo guitar solo *play Only in Disneyland*   by Chris Vaisvil
* 17 Reasons I Hate the Blues blog *play 17 Reasons I Hate the Blues*   by Chris Vaisvil
* Klingon Opera Overture blog *play Klingon Opera Overture*   by Chris Vaisvil
* Seventeen Selfless Notes blog *play Seventeen Selfless Notes*   by Chris Vaisvil
* 17ET Jazz blog *play 17et Jazz*  by Chris Vaisvil (60 x 60 winner)
* 17 Pink Tuxedos blog *play 17 Pink Tuxedos*  by Chris Vaisvil
* Devil in the Deep Blue Sea blog *play Devil in the Deep Blue sea*  blues collaboration between The Two Regs (vocals / lyrics) and Norm Harris (percussion) and Chris Vaisvil (17 note per octave electric guitar and fretless bass).
* Seventeen Years in the Sixties blog *play Seventeen Years in the Sixties*  by Chris Vaisvil
* CT Scan blog *play video CT Scan*  by Chris Vaisvil
* Fish and a Grenade blog *play Fish and a Grenade*  (parental advisory language) by Chris Vaisvil
* Seventeen Unsteady Hands blog *play video of performance of Seventeen Unsteady Hands*  by Chris Vaisvil
* The Pond blog by Chris Vaisvil and *video version of The Pond with Japanese Garden*
* Graveyard blog *play Graveyard*   by Chris Vaisvil
* *For Brass and Voice Choirs in 17 edo*  by Chris Vaisvil more on the composition
* *And I Became One With My Per Fungi*  by Chris Vaisvil => more on composition
* *counterintuitive (17 edo guitar solo)*  by Chris Vaisvil => more on composition
* No Love by Gregory Sanchez
* Micro7 by Ralph Jarzombek
* Flying Into O'Hare by Chris Vaisvil
* Helas, pitié by Alex Ness (in 17edo with stretched octaves)

# Instruments

* **Guitar Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani** [forbidden]

External image: http://sphotos.ak.fbcdn.net/hphotos-ak-snc4/hs883.snc4/71639\_167001659983806\_100000219181856\_601995\_1526184\_n.jpg [dead link]

**WARNING**: MediaWiki doesn't have very good support for external images.

Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.

* **Bass Heptadecatonic from Peruvian - Charles Loli and Antonio Huamani** [forbidden]

External image: http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs382.ash2/66019\_167001006650538\_100000219181856\_601987\_48585\_n.jpg [dead link]

**WARNING**: MediaWiki doesn't have very good support for external images.

Furthermore, since external images can break, we recommend that you replace the above with a local copy of the image.

* 17 note per octave conversion from a "standard" stratocastor copy - conversion by Brad Smith

17P1050829r.JPG