144/143: Difference between revisions
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'''144/143''', the '''grossma''', is a [[13-limit]] [[small comma]]. It is the difference between the [[11/9]] and [[16/13]] neutral thirds, | '''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 == | == 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 | 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 == | == See also == | ||
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[[Category:Grossmic]] | [[Category:Grossmic]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 01:23, 20 May 2026
| Interval information |
Thulu comma
reduced
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 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 . The upward version is called 1/143C or 143C up and is represented by .
See also
- Small comma
- List of superparticular intervals
- Grossmisma, the difference by which a stack of seven 144/143s falls short of 21/20