65/64: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 65/64~~

~~| Monzo = -6 0 1 0 0 1~~

~~| Cents = 26.841376~~

| Name = wilsorma

| ~~FJS~~ name = P1<~~sup>65</sup~~>

| Color name = 3oy1, thoyo 1sn,<br>Thoyo comma

| ~~Sound~~ =

| Comma = yes

}}

In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].

In [[~~just intonation~~]]~~, '''65/64''', the '''wilsorma''',~~ is a [[~~superparticular~~]] ~~interval of around 26.8¢~~, ~~nearly a quarter of a semitone or eighth of a tone~~. ~~It belongs to~~ the [[13~~-prime~~-limit]], ~~which means that~~ the ~~highest prime in~~ the ~~ratio~~ is 13. ~~65 is~~ 5 ~~times~~ 13, which ~~means~~ that ~~65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[~~5/4]] and [[16/13~~]];~~ [[8/5]] and [[13/8]]~~; [[~~13/12]] ~~and [[~~16/15~~]];~~ [[~~15/8]] and [[24/~~13~~]], [[~~13~~/10]] and [[32/25~~]]; [[~~20/13~~]] ~~and~~ [[25/16]], ~~and~~ of ~~course, infinitely many other pairs~~ of ~~just intervals. It differs from~~ the ~~septimal comma~~ [[~~64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324~~]].

Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.

== Notation ==

This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.

== Temperaments ==

Tempering it out leads to the rank-2 2.5.13 '''wilsormatic''' temperament, which has a generator tuned to abut 370-375 cents that represents both 5/4 and 16/13, or the rank-5 '''wilsormic''' temperament in the 13-limit. However, it is natural to equate [[14/13]] and [[15/14]] with 13/12[[~]]16/15, thus leading to the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament [[negri]], which splits the perfect fourth [[4/3]] into four equal parts, each being one step of the 12::16 segment of the [[harmonic series]].

== See also ==

* [[Gallery of just intervals]]

* [[64/63]]

[[Category:~~13-limit]]~~

[[Category:Commas with unknown etymology]]

~~[[Category:Interval ratio]]~~

~~[[Category:Superparticular]]~~

~~[[Category:Unison]]~~

~~[[Category:Comma]]~~

~~[[Category:Overtone~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 65/64
-| Monzo = -6 0 1 0 0 1
-| Cents = 26.841376
 | Name = wilsorma
-| FJS name = P1<sup>65</sup>
+| Color name = 3oy1, thoyo 1sn,<br>Thoyo comma
-| Sound =
+| Comma = yes
 }}
+In [[13-limit]] [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8{{cent}}, nearly a quarter of a semitone or eighth of a tone. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].
-In [[just intonation]], '''65/64''', the '''wilsorma''', is a [[superparticular]] interval of around 26.8¢, nearly a quarter of a semitone or eighth of a tone. It belongs to the [[13-prime-limit]], which means that the highest prime in the ratio is 13. 65 is 5 times 13, which means that 65/64 can be treated as a harmonic 13th above a harmonic 5th or vice versa. It is the difference between [[5/4]] and [[16/13]]; [[8/5]] and [[13/8]]; [[13/12]] and [[16/15]]; [[15/8]] and [[24/13]], [[13/10]] and [[32/25]]; [[20/13]] and [[25/16]], and of course, infinitely many other pairs of just intervals. It differs from the septimal comma [[64/63]] by [[4096/4095]] and from the syntonic comma [[81/80]] by [[325/324]].
+Tempering it out turns 5/4 and 13/8 into [[octave complement]]s of one another. This is particularly useful in many [[13-limit]] [[magic family]] extensions, as it means they are very simply mapped to plus and minus one generator.
+== Notation ==
+This interval is the 13th-partial chroma (13-limit formal comma) in [[Ben Johnston's notation]], denoted simply with the number "13", while its reciprocal is denoted as "{{invert|13}}" (a turned "13"). If the base note is C, then [[13/8]] is represented by C–Ab13.
+== Temperaments ==
+Tempering it out leads to the rank-2 2.5.13 '''wilsormatic''' temperament, which has a generator tuned to abut 370-375 cents that represents both 5/4 and 16/13, or the rank-5 '''wilsormic''' temperament in the 13-limit. However, it is natural to equate [[14/13]] and [[15/14]] with 13/12[[~]]16/15, thus leading to the [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament [[negri]], which splits the perfect fourth [[4/3]] into four equal parts, each being one step of the 12::16 segment of the [[harmonic series]].
 == See also ==
 * [[Gallery of just intervals]]
 * [[64/63]]
-[[Category:13-limit]]
+[[Category:Commas with unknown etymology]] <!-- Is it named after Erv Wilson? -->
-[[Category:Interval ratio]]
-[[Category:Superparticular]]
-[[Category:Unison]]
-[[Category:Comma]]
-[[Category:Overtone]]