4000/3993: Difference between revisions

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{{Infobox Interval

| Name = wizardharry comma

| Name = wizardharry comma, pine comma

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

| Comma = yes

}}

'''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.

'''4000/3993''', the '''wizardharry comma''' (from [[wizard]] and [[harry]] (named after [[Harry Partch]])) 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]])3 = S10/S11.

In terms of commas, it is the difference between [[100/99]] and [[121/120]]~~, and~~ between [[540/539]] and [[9801/9800]]. It factors into 13-limit commas as ([[1575/1573]])([[2080/2079]]) or ([[625/624]])([[6656/6655]]).

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]]).

== Temperaments ==

Tempering it out means the fourth is divided into an equal stepped tetrachord, ~~however, it does this by means equating~~ a ~~stack~~ of ~~three~~ 11/10 ~~intervals with~~ 4/3~~, rather than by equating~~ three [[10/9]] ~~whole tones~~ with 4/3 as in the [[~~porcupine family~~]] ~~of temperaments, although 11-limit~~ [[porcupine]] ~~does both~~ as ~~11/10~~ and ~~10/9 are equated~~.

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. It may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 (''much'' less accurately) into three [[10/9]]'s instead. 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 of [[250/243]] = S102 * S11 so through porkypine we make [[porcupine]] as efficient and elegant as it can reasonably be.

Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament.

Tempering it out with 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]])2 = S9/S11.

These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma.

[[Category:Wizardharry]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = wizardharry comma
+| Name = wizardharry comma, pine comma
 | Color name = 1u<sup>3</sup>y<sup>3</sup>1, triluyo unison,<br>Triluyo comma
 | Comma = yes
 }}
-'''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.
+'''4000/3993''', the '''wizardharry comma''' (from [[wizard]] and [[harry]] (named after [[Harry Partch]])) 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.
-In terms of commas, it is the difference between [[100/99]] and [[121/120]], and between [[540/539]] and [[9801/9800]]. It factors into 13-limit commas as ([[1575/1573]])([[2080/2079]]) or ([[625/624]])([[6656/6655]]).
+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]]).
 == Temperaments ==
-Tempering it out means the fourth is divided into an equal stepped tetrachord, however, it does this by means equating a stack of three 11/10 intervals with 4/3, rather than by equating three [[10/9]] whole tones with 4/3 as in the [[porcupine family]] of temperaments, although 11-limit [[porcupine]] does both as 11/10 and 10/9 are equated.
+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. It may be reminiscent of how the [[250/243|porcupine comma]] splits 4/3 (''much'' less accurately) into three [[10/9]]'s instead. 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 of [[250/243]] = S10<sup>2</sup> * S11 so through porkypine we make [[porcupine]] as efficient and elegant as it can reasonably be.
 Tempering it out along with the [[schisma]] results in the rank-2 [[tertiaschis]] temperament.
+Tempering it out with 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.
+These are just a few examples, but there is a massive wealth of possible high-accuracy temperaments that temper out this comma.
 [[Category:Wizardharry]]