105/104: Difference between revisions

(5 intermediate revisions by 4 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

| Name = animist comma, small tridecimal comma

~~| Ratio = 105/104~~

| Color name = 3uzy1, thuzoyo unison,<br>Thuzoyo comma

~~| Monzo = -3 1 1 1 0 -1~~

| Comma = yes

~~| Cents = 16.56696~~

| Name = animist comma, ~~<br>~~small tridecimal comma

| Color name = 3uzy1, thuzoyo unison

~~| FJS name = A1<sup>5~~,7<~~/sup><sub>13</sub~~>

| ~~Sound~~ =

}}

'''105/104''', the '''animist comma''', is a [[13-limit]] [[small comma]]. It is the difference between [[5/4]] and [[26/21]], and between [[6/5]] and [[63/52]] (and their [[octave complement]]s, i.e. between [[8/5]] and [[21/13]], and between [[5/3]] and [[~~104~~/63]]).

'''105/104''', the '''animist comma''', is a [[13-limit]] [[superparticular]] [[small comma]]. It arises in several places in 13-limit just intonation, most notably as the difference between [[15/8]] and [[13/7]], between [[8/5]] and [[21/13]], between [[8/7]] and [[15/13]], and between [[21/16]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[16/15]] and [[14/13]], between [[5/4]] and [[26/21]], between [[7/4]] and [[26/15]], and between [[32/21]] and [[20/13]]).

Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[196/195]])([[225/224]]).

== Temperaments ==

Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out 196/195 and/or 225/224, equating [[15/14]] with 14/13~16/15. This in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].

== See also ==

* [[List of superparticular intervals]]

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

~~[[Category:Small commas]]~~

~~[[Category:Superparticular]]~~

[[Category:Animist]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = animist comma, small tridecimal comma
-| Ratio = 105/104
+| Color name = 3uzy1, thuzoyo unison,<br>Thuzoyo comma
-| Monzo = -3 1 1 1 0 -1
+| Comma = yes
-| Cents = 16.56696
-| Name = animist comma, <br>small tridecimal comma
-| Color name = 3uzy1, thuzoyo unison
-| FJS name = A1<sup>5,7</sup><sub>13</sub>
-| Sound =
 }}
-'''105/104''', the '''animist comma''', is a [[13-limit]] [[small comma]]. It is the difference between [[5/4]] and [[26/21]], and between [[6/5]] and [[63/52]] (and their [[octave complement]]s, i.e. between [[8/5]] and [[21/13]], and between [[5/3]] and [[104/63]]).
+'''105/104''', the '''animist comma''', is a [[13-limit]] [[superparticular]] [[small comma]]. It arises in several places in 13-limit just intonation, most notably as the difference between [[15/8]] and [[13/7]], between [[8/5]] and [[21/13]], between [[8/7]] and [[15/13]], and between [[21/16]] and [[13/10]] (and their [[octave complement]]s, i.e. between [[16/15]] and [[14/13]], between [[5/4]] and [[26/21]], between [[7/4]] and [[26/15]], and between [[32/21]] and [[20/13]]).
+Being a [[square superparticular|triangle superparticular]], it factors neatly into ([[196/195]])([[225/224]]).
+== Temperaments ==
+Tempering out this comma leads to a form of '''animist temperament'''. An obvious further temperament is to temper out 196/195 and/or 225/224, equating [[15/14]] with 14/13~16/15. This in the 2.3.5.7.13 [[subgroup]] is an [[extension]] of [[marvel]] and a [[restriction]] of [[tripod]].
 == See also ==
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
-[[Category:Small commas]]
-[[Category:Superparticular]]
 [[Category:Animist]]
+[[Category:Commas with unknown etymology]]