View source for 1ed86.4c

{{Infobox ET|1ed17069/16238}}
{{delete|should be merged with 22edt or 42zpi}}
'''13.888edo''', also known as '''1 equal division of 86.4¢''' ('''1ed86.4c''') or '''arithmetic pitch sequence of 86.4¢''' ('''APS86.4¢'''), is an [[Equal-step tuning|equal-step]] scale generated by dividing [[2/1]] into 13.888 equal parts of about 86.4 [[cents]] each, or every 9th step of [[125edo]].

Because 13.888 is not actually an integer, the scale that results does not actually include [[2/1]], so it is not a ''true'' [[edo]]. Instead it has a [[pseudo-octave]] almost 10 cents sharp, making it a “[[EDO#Non-integer EDO|non-integer edo]]”.

13.888edo has been voted "monthly tuning" multiple times on the [[Monthly Tunings]] Facebook group, owing to its close approximations of many harmonics [[3/1]], [[7/1]], [[9/1]] and [[11/1]].

It is very close to [[Table of zeta-stretched edos|zeta-stretched 14edo]], a.k.a. [[42zpi]], which has a step size of 86.3¢.

==Harmonics==
{{harmonics in cet|86.4|prec=1}}
{{harmonics in cet|86.4|prec=1|start=11}}

[[14edo]], [[22edt]], [[32ed5]], [[39ed7]] for comparison:
{{Harmonics in equal|14|intervals=integer|prec=1|collapsed=1}}
{{Harmonics in equal|22|3|1|intervals=integer|prec=1|collapsed=1}}
{{Harmonics in equal|32|5|1|intervals=integer|prec=1|collapsed=1}}
{{Harmonics in equal|39|7|1|intervals=integer|prec=1|collapsed=1}}

==Scala file==
Tuning file for anything that supports [[Scala]]. Made with [[Scale Workshop]].
<pre>
! 13pt888edo.scl
!
13.888 equal divisions of the octave
 14
!
 86.406
 172.812
 259.218
 345.624
 432.03
 518.436
 604.842
 691.248
 777.654
 864.06
 950.466
 1036.872
 1123.278
 1209.684
</pre>

== Music ==
* ''[https://soundcloud.com/morphosyntax-1/the-butterflys-dream The Butterfly’s Dream]'' - [[Herman Miller]] (2022)

== See also ==
* [[Equal-step tuning]]

[[Category:14-tone scales]]
[[Category:Tempered scales]]
[[Category:Pages with mostly numerical content]]
[[Category:Edonoi]]
[[Category:Pages with Scala files]]