144/143: Difference between revisions

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{{Infobox Interval

~~| Ratio = 144/143~~

~~| Monzo = 4 2 0 0 -1 -1~~

~~| Cents = 12.06440~~

| Name = grossma

| Color name =

| Color name = 3u1u1, thulu 1sn,<br>Thulu comma

~~| FJS name = A1<sub>11~~, 13<~~/sub~~>

| Comma = yes

| ~~Sound~~ =

}}

'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, ~~and~~ between the [[12/11]] and [[13/12]] neutral seconds. [[Teff]] is a temperament of note that targets it.

'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, between the [[12/11]] and [[13/12]] neutral seconds, and between the [[11/8]] and [[18/13]] superfourths/subtritones. Since it separates so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to [[36/35]] in the 2.3.5.7 subgroup ([[7-limit]]), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.

== Temperaments ==

A natural 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].

[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma [[81/80]].

== Sagittal notation ==

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest interval it notates is 143/1 = 11×13 (equiv. 143/128), as for example in C-D{{nbhsp}}{{sagittal | )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal| )~| }}.

== See also ==

* [[Small comma]]

* [[List of superparticular intervals]]

* [[Grossmisma]], the difference by which a stack of seven 144/143s falls short of [[21/20]]

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

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

~~[[Category:Superparticular]]~~

[[Category:Grossmic]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 144/143
-| Monzo = 4 2 0 0 -1 -1
-| Cents = 12.06440
 | Name = grossma
-| Color name =
+| Color name = 3u1u1, thulu 1sn,<br>Thulu comma
-| FJS name = A1<sub>11, 13</sub>
+| Comma = yes
-| Sound =
 }}
-'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, and between the [[12/11]] and [[13/12]] neutral seconds. [[Teff]] is a temperament of note that targets it.
+'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, between the [[12/11]] and [[13/12]] neutral seconds, and between the [[11/8]] and [[18/13]] superfourths/subtritones. Since it separates so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to [[36/35]] in the 2.3.5.7 subgroup ([[7-limit]]), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.
+== Temperaments ==
+A natural 2.3.11.13 temperament that extends it is [[namo]], which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as [[hemififths]] and [[squares]].
+[[Teff]] is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma [[81/80]].
+== Sagittal notation ==
+In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | )~! }} and is called the '''143 comma''', or '''143C''' for short, because the simplest interval it notates is 143/1 = 11×13 (equiv. 143/128), as for example in C-D{{nbhsp}}{{sagittal | )~! }}. The upward version is called '''1/143C''' or '''143C up''' and is represented by {{sagittal| )~| }}.
 == See also ==
 * [[Small comma]]
 * [[List of superparticular intervals]]
+* [[Grossmisma]], the difference by which a stack of seven 144/143s falls short of [[21/20]]
-[[Category:13-limit]]
-[[Category:Small commas]]
-[[Category:Superparticular]]
 [[Category:Grossmic]]
+[[Category:Commas with unknown etymology]]