2ed13/10: Difference between revisions

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'''2 equal divisions of 13/10''', when viewed from a regular temperament perspective, is a nonoctave tuning system created by diving the interval of 13/10 into two steps of about 227.1 cents each. It is equivalent to about 5.284edo.

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===Harmonic content===

Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.

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[[File:sqrt13_10_harmonic_contents.jpg|alt=sqrt13_10_harmonic_contents.jpg|sqrt13_10_harmonic_contents.jpg]]

~~=== ===~~

== Music ==

==Music==

~~[http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by Andrew Heathwaite and Michael Gaiuranos~~

~~===Scala file===~~

* [http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by [[Andrew Heathwaite]] and [[Michael Gaiuranos]]

== Scala file ==

<pre>

! sqrt13over10.scl

The square root of 13:10 nonoctave temperament.

2

!

227.106973952238

13/10

</pre>

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+{{Infobox ET}}
 '''2 equal divisions of 13/10''', when viewed from a regular temperament perspective, is a nonoctave tuning system created by diving the interval of 13/10 into two steps of about 227.1 cents each. It is equivalent to about 5.284edo.
@@ Line 10: / Line 11: @@
 ===Harmonic content===
+{{Harmonics in equal|2|13|10}}
 Sqrt 13:10 (the scale) contains no octaves, and also no close approximation of the third harmonic (the perfect fifth). However, it comes very close to certain just intervals involving the numbers 5, 7, 11 and 13: in particular: 8/7, 13/10, 22/13, 11/5, 5/2, 20/7, 13/4, 26/7, 11/2, and 44/7. These near-just intervals can be combined so as to make available a set of 20 harmonic and subharmonic chords.
@@ Line 17: / Line 20: @@
 [[File:sqrt13_10_harmonic_contents.jpg|alt=sqrt13_10_harmonic_contents.jpg|sqrt13_10_harmonic_contents.jpg]]
-=== ===
+== Music ==
-==Music==
-[http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by Andrew Heathwaite and Michael Gaiuranos
-===Scala file===
+* [http://soundcloud.com/andrew_heathwaite/truffles Truffles?] by [[Andrew Heathwaite]] and [[Michael Gaiuranos]]
+== Scala file ==
+<pre>
 ! sqrt13over10.scl
 The square root of 13:10 nonoctave temperament.
 !
 .106973952238
 /10
+</pre>