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{{Infobox Interval
{{Infobox interval
| Name = wizardharry comma, pine comma
| Name = wizardharry comma, pine comma
| Color name = 1u<sup>3</sup>y<sup>3</sup>1, triluyo unison,<br>Triluyo comma
| Color name = 1u<sup>3</sup>y<sup>3</sup>1, triluyo unison,<br>Triluyo comma
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'''4000/3993''', the '''wizardharry comma''' (from [[wizard]] and [[harry]] (named after [[Harry Partch]]), and possibly as a reference to the ''Harry Potter'' books) or '''pine comma''' (for its relevance and importance to [[7L 1s]]) 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, therefore it is equal to ([[4/3|12/9]])/([[11/10]])<sup>3</sup> = S10/S11.  
'''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 trivially the difference between S10 = [[100/99]] and S11 = [[121/120]] or less trivially between S12/S14 = [[540/539]] and S99 = [[9801/9800]]. It factors into 13-limit commas as ([[1575/1573]])([[2080/2079]]) or ([[625/624]])([[6656/6655]]).  
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 ==
== Temperaments ==
Tempering it out 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.
[[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 and it is for these reasons that 2.3.5.11 [[Porcupine_family#2.3.5.11_subgroup_.28porkypine.29|porkypine]] equates 11/10 with the [[superparticular]]s adjacent to it of 12/11 and 10/9, tempering S10 and S11 as the porcupine comma is [[250/243]] = S10<sup>2</sup> * S11 so through porkypine we make [[porcupine]] as efficient and elegant as it can reasonably be.
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 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.


Tempering it out with the trimitone comma S9/S10 = [[8019/8000]] (so that three [[10/9]]'s are also an [[11/8]]) allows us to also temper the [[semiparticular]] [[243/242]] = ([[3/2|12/8]])/([[11/9]])<sup>2</sup> = S9/S11 leading to [[Gravity_family#Larry|Larry]] in the [[Gravity family]].
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.  


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.
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]].


Another strategy is to take advantage of the size of [[121/120|S11]] so as to equate it with [[144/143|S12 = 144/143]] = ([[16/13]])/([[11/9]]), for those seeking to keep the undecimal and tridecimal neutral thirds distinct, thus tempering [[325/324|S10/S12 = S25*S26 = 325/324]], a comma with various advantages. Observing that [[4000/3993|S10/S11]] = ([[540/539|S12/S14]])/([[9801/9800|S33/S35 = S99]]) then shows a natural path, if one is willing to split the octave in half, leading to [[hades]], which extends naturally to the 17-limit by tempering [[289/288|S17]] = ([[17/12]])/([[24/17]]).
There is a massive wealth of possible high-accuracy temperaments that temper out this comma, including [[311edo]].


These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma, including the [[41-limit]] temperament [[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:Wizardharry]]
[[Category:Wizardharry]]
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