250/243: Difference between revisions

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Eliora (talk | contribs)
added fact about 250/243 being a chromium period and proposed a new name
De-bold the neologism. The original names are pretty established and not subject to changes. Section into "temperaments" and "approximation"
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'''250/243''' is known as the '''porcupine comma''' or the '''maximal diesis'''. Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5).


'''250/243''' is known as the '''porcupine comma,''' '''maximal diesis''' or the '''chromium quartertone'''.
== Temperaments ==
Tempering it out leads to the [[5-limit]] [[porcupine]] temperament. See [[porcupine family]] for the family of rank-2 temperaments where it is tempered out.  


== Theory ==
== Approximation ==
Measuring about 49{{cent}}, it is a [[medium comma]]. It is the amount by which two [[10/9|minor whole tones]] exceed a minor third, that is, (10/9)<sup>2</sup>/(6/5). Tempering it out leads to [[5-limit]] [[Porcupine family|porcupine temperament]].
If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave. Thus [[Eliora]] proposes the name ''chromium quartertone''.  
 
It serves as a period in the [[chromium]] temperament, where it is mapped to 1/24th of the octave.


[[Category:Porcupine]]
[[Category:Porcupine]]
{{todo|improve layout}}

Revision as of 02:24, 6 November 2022

Interval information
Ratio 250/243
Factorization 2 × 3-5 × 53
Monzo [1 -5 3
Size in cents 49.16614¢
Names porcupine comma,
maximal diesis
Color name y31, Triyo comma
FJS name [math]\displaystyle{ \text{A1}^{5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 15.8906
Weil norm (log2 max(n, d)) 15.9316
Wilson norm (sopfr(nd)) 32
Comma size medium
S-expression S102⋅S11
Open this interval in xen-calc

250/243 is known as the porcupine comma or the maximal diesis. Measuring about 49 ¢, it is a medium comma. It is the amount by which two minor whole tones exceed a minor third, that is, (10/9)2/(6/5).

Temperaments

Tempering it out leads to the 5-limit porcupine temperament. See porcupine family for the family of rank-2 temperaments where it is tempered out.

Approximation

If we do not temper out this interval and instead use it as an identity of some sort, it serves as the period in the chromium temperament, where it is mapped to 1/24th of the octave. Thus Eliora proposes the name chromium quartertone.