4000/3993: Difference between revisions

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{{Infobox ~~Interval~~

{{Infobox interval

~~| Icon =~~

| Name = wizardharry comma, pine comma

~~| Ratio = 4000/3993~~

| Color name = 1u3y31, triluyo unison, Triluyo comma

~~| Monzo = 5 -1 3 0 -3~~

| Comma = yes

~~| Cents = 3.03231~~

| Name = wizardharry comma

| Color name = Triluyo comma

| ~~FJS name =~~

~~| Sound~~ =

}}

'''4000/3993''', the '''wizardharry comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] comma with a size of roughly 3.03 [[cents]]. It is the amount by which a stack of three [[11/10]] submajor seconds falls short of the [[4/3]] perfect fourth. Tempering it out means the ~~4th~~ is divided into an equal stepped tetrachord~~; however~~, it ~~does~~ this ~~by means equating a stack~~ of three 11/10's with 4/3, ~~rather than~~ that of three [[10/9]]'s as in the [[~~porcupine~~ family]] of ~~temperaments.~~ 11-limit [[~~porcupine~~]] ~~does both as~~ 11/10 and 10/~~9 are equated~~.

'''4000/3993''', the '''wizardharry comma''' or '''pine comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.5.11 subgroup|2.3.5.11-subgroup]]) [[comma]] with a size of roughly 3.03 [[cents]]. It is the amount by which a stack of three [[11/10]] submajor seconds falls short of the [[4/3]] perfect fourth; in other words it is equal to (4/3)/(11/10)3.

In terms of commas, it is the difference between [[100/99]] ({{S|10}}) and [[121/120]] ({{S|11}}), itself having an [[S-expression]] of S10/S11. It is also the difference between [[540/539]] ([[S-expression|S12/S14]]) and [[9801/9800]] ({{S|99}}). It factors into 13-limit commas as ([[1575/1573]])⋅([[2080/2079]]) or ([[625/624]])⋅([[6656/6655]]).

== Temperaments ==

[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes [[12/11]] and [[10/9]] equidistant from 11/10.

On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)

Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression|S9/S11]]) = ([[3/2]])/([[11/9]])2 leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.

Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression|S10/S12]]), a comma with various advantages.

Observing that 4000/3993 = (540/539)/(9801/9800) also shows a natural path, if one is willing to split the octave in half, leading to [[hades]].

There is a massive wealth of possible high-accuracy temperaments that temper out this comma, including [[311edo]].

== Etymology ==

''Wizardharry comma'' was presumably given by [[Gene Ward Smith]] in 2010<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13567 ''Small comma'' (Revision as of 14:08, 1 September 2010 by Wikispaces>genewardsmith)]. </ref>. It combines ''[[wizard]]'' and ''[[harry]]'', two of the temperaments where the comma is tempered out, the latter being named after [[Harry Partch]]. ''Harry'' gave rise to a number of names related to the ''{{w|Harry Potter}}'' books, which might have been an inspiration for this combination.

''Pine comma'' was given by [[User:Godtone|Godtone]] in 2023, for its relevance and importance to the pine ([[7L 1s]]) scale.

== See also ==

* [[Wizardharry clan]]

== Notes ==

~~[[Category:11-limit]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Wizardharry]]

[[Category:Commas named after composers]]

[[Category:Commas named after music theorists]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
-{{Infobox Interval
+{{Infobox interval
-| Icon =
+| Name = wizardharry comma, pine comma
-| Ratio = 4000/3993
+| Color name = 1u<sup>3</sup>y<sup>3</sup>1, triluyo unison,<br>Triluyo comma
-| Monzo = 5 -1 3 0 -3
+| Comma = yes
-| Cents = 3.03231
-| Name = wizardharry comma
-| Color name = Triluyo comma
-| FJS name =
-| Sound =
 }}
-'''4000/3993''', the '''wizardharry comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] comma with a size of roughly 3.03 [[cents]].  It is the amount by which a stack of three [[11/10]] submajor seconds falls short of the [[4/3]] perfect fourth. Tempering it out means the 4th is divided into an equal stepped tetrachord; however, it does this by means equating a stack of three 11/10's with 4/3, rather than that of three [[10/9]]'s as in the [[porcupine family]] of temperaments. 11-limit [[porcupine]] does both as 11/10 and 10/9 are equated.
+'''4000/3993''', the '''wizardharry comma''' or '''pine comma''' is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.5.11 subgroup|2.3.5.11-subgroup]]) [[comma]] with a size of roughly 3.03 [[cents]]. It is the amount by which a stack of three [[11/10]] submajor seconds falls short of the [[4/3]] perfect fourth; in other words it is equal to (4/3)/(11/10)<sup>3</sup>.
+In terms of commas, it is the difference between [[100/99]] ({{S|10}}) and [[121/120]] ({{S|11}}), itself having an [[S-expression]] of S10/S11. It is also the difference between [[540/539]] ([[S-expression|S12/S14]]) and [[9801/9800]] ({{S|99}}). It factors into 13-limit commas as ([[1575/1573]])⋅([[2080/2079]]) or ([[625/624]])⋅([[6656/6655]]).
+== Temperaments ==
+[[Tempering out]] this comma means the fourth is divided into an equal stepped tetrachord, the step of which is a ''trienfourth'' (from 1/3 of a fourth) or ''submajor second'' and because it is an [[ultraparticular]] it makes [[12/11]] and [[10/9]] equidistant from 11/10.
+On the low-accuracy end, this may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 into three 10/9's instead. In fact, 2.3.5.11-subgroup [[porcupine]] equates 10/9 with 11/10 and 12/11 so that the equally-split fourth represents 9:10:11:12, making porcupine as efficient and elegant as it can reasonably be. (As a [[rank-3]] detemperament of porcupine, one way to extend it to include prime 7 is by tempering out [[385/384]], which septimal porcupine also tempers out.)
+Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament. Tempering it out with the trimitone comma [[8019/8000]] ([[S-expression|S9/S10]], so that three [[10/9]]'s are also an [[11/8]]) implies also tempering out the [[semiparticular]] [[243/242]] ([[S-expression|S9/S11]]) = ([[3/2]])/([[11/9]])<sup>2</sup> leading to [[larry]] in the [[gravity family]]. Tempering it out with both the schisma and trimitone comma gives a description of [[65edo]] in the no-7's 11-limit, making it an excellent way to extend schismic to include prime 11.
+Another strategy is to take advantage of the size of 121/120 (S11) so as to equate it with [[144/143]] ({{S|12}}) = ([[16/13]])/(11/9), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering out the marveltwin comma, [[325/324]] ([[S-expression|S10/S12]]), a comma with various advantages.
+Observing that 4000/3993 = (540/539)/(9801/9800) also shows a natural path, if one is willing to split the octave in half, leading to [[hades]].
+There is a massive wealth of possible high-accuracy temperaments that temper out this comma, including [[311edo]].
+== Etymology ==
+''Wizardharry comma'' was presumably given by [[Gene Ward Smith]] in 2010<ref>See [https://en.xen.wiki/index.php?title=Small_comma&oldid=13567 ''Small comma'' (Revision as of 14:08, 1 September 2010 by Wikispaces>genewardsmith)]. </ref>. It combines ''[[wizard]]'' and ''[[harry]]'', two of the temperaments where the comma is tempered out, the latter being named after [[Harry Partch]]. ''Harry'' gave rise to a number of names related to the ''{{w|Harry Potter}}'' books, which might have been an inspiration for this combination.
+''Pine comma'' was given by [[User:Godtone|Godtone]] in 2023, for its relevance and importance to the pine ([[7L 1s]]) scale.
+== See also ==
+* [[Wizardharry clan]]
+== Notes ==
-[[Category:11-limit]]
-[[Category:Unnoticeable comma]]
 [[Category:Wizardharry]]
+[[Category:Commas named after composers]]
+[[Category:Commas named after music theorists]]
+[[Category:Commas named after musical traditions]]