17 equal temperament

Alexander J. Ellis refers to a tuning of seventeen tones based on perfect fourths and fifths as the Arabic scale.Ellis, Alexander J. (1863). "On the Temperament of Musical Instruments with Fixed Tones", Proceedings of the Royal Society of London, vol. 13. (1863–1864), pp. 404–422. 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.{{Citation needed|date=September 2015}}

File:17-tet scale on C.png{{cite journal|last=Blackwood|first=Easley|author-link=Easley Blackwood Jr.|date=Summer 1991|jstor=833437|title=Modes and Chord Progressions in Equal Tunings|journal=Perspectives of New Music|volume=29|number=2|pages=166–200 (175)|doi=10.2307/833437 }} for 17 equal temperament: intervals are notated similarly to those they approximate and enharmonic equivalents are distinct from those of 12 equal temperament (e.g., A{{music|#}}/C{{music|b}}).File:17-tet scale on C.mid]]

Easley Blackwood Jr. created a notation system where sharps and flats raised/lowered 2 steps.

This yields the chromatic scale:

:C, D{{music|flat}}, C{{music|sharp}}, D, E{{music|flat}}, D{{music|sharp}}, E, F, G{{music|flat}}, F{{music|sharp}}, G, A{{music|flat}}, G{{music|sharp}}, A, B{{music|flat}}, A{{music|sharp}}, B, C

Quarter tone sharps and flats can also be used, yielding the following chromatic scale:

:C, C{{music|t}}/D{{music|flat}}, C{{music|sharp}}/D{{music|d}}, D, D{{music|t}}/E{{music|flat}}, D{{music|sharp}}/E{{music|d}}, E, F, F{{music|t}}/G{{music|flat}}, F{{music|sharp}}/G{{music|d}}, G, G{{music|t}}/A{{music|flat}}, G{{music|sharp}}/A{{music|d}}, A, A{{music|t}}/B{{music|flat}}, A{{music|sharp}}/B{{music|d}}, B, C

Below are some intervals in {{nobr|17 {{sc|EDO}}}} compared to just.

File:Major chord on C.png on C in {{nobr|17 {{sc|EDO}} }}: All notes are within 37 cents of just intonation (rather than 14 cents for {{nobr|12 equal temperament}}).

]]

File:Simple I-IV-V-I isomorphic 17-TET.png in {{nobr|17 {{sc|EDO}}}}.{{sfnp|Milne|Sethares|Plamondon|2007|p=29}}

File:Simple_I-IV-V-I_isomorphic_17-TET.mid Whereas in {{nobr|12 {{sc|EDO}},}} B{{music|natural}} is 11 steps, in {{nobr|17 {{sc|EDO}},}} B{{music|natural}} is 16 steps.]]

:

{{nobr|17 {{sc|EDO}}}} is where every other step in the {{nobr|34 equal temperament}} scale is included, and the others are not accessible. Conversely {{nobr|17 {{sc|EDO}}}} is a subset of {{nobr|34 {{sc|EDO}}.}}

{{reflist|25em}}

• {{cite journal

|last1=Milne |first1=Andrew

|last2=Sethares |first2=William |author2-link=William Sethares

|last3=Plamondon |first3=James

|date=Winter 2007

|title=Isomorphic controllers and dynamic tuning: Invariant fingering over a tuning continuum

|journal=Computer Music Journal

|volume=31 |number=4 |pages=15–32

|s2cid=27906745

|doi=10.1162/comj.2007.31.4.15 |doi-access=free

|url=http://www.mitpressjournals.org/doi/pdf/10.1162/comj.2007.31.4.15

|via=mitpressjournals.org

}}

• [http://www.anaphoria.com/Secor17puzzle.pdf "The 17-tone Puzzle — And the Neo-medieval Key that Unlocks It"] by George Secor
• [https://www.tonalismo.com/programa-tonalismo/ Libro y Programa Tonalismo], heptadecatonic system applications (in Spanish)
• [http://www.georghajdu.de/gh/fileadmin/material/articles/17_tones.ICMC.pdf Georg Hajdu's 1992 ICMC paper on the 17-tone piano project]{{cbignore|bot=medic}}
• {{YouTube|otABmneuKV4|"Crocus", 17 equal temperament, 9 tone mode}}, by Wongi Hwang

{{Microtonal music}}

{{Musical tuning}}

{{DEFAULTSORT:17 Equal Temperament}}

Category:Equal temperaments

Category:Microtonality