245/243: Difference between revisions

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'''245/243''', the '''sensamagic comma''', is a [[7-limit]] [[small comma]] of 14.2 cents. It is the amount by which two septimal major thirds ([[9/7]]) fall short of a classic major sixth ([[5/3]]), or the difference between [[28/27]] and [[36/35]].  
'''245/243''', the '''sensamagic comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring 14.2 [[cent]]s. It is the amount by which two septimal major thirds ([[9/7]]) fall short of a classic major sixth ([[5/3]]), or the difference between [[28/27]] and [[36/35]].  


== Temperaments ==
== Temperaments ==
Tempering it out leads to the [[sensamagic family]] of temperaments, where 5/3 is split into two equal parts, each representing 9/7~[[35/27]], and may be extended to represent higher-limit ratios like [[13/10]], [[22/17]], etc. It enables [[sensamagic chords]] as well.  
Tempering it out alone in the 7-limit leads to the [[sensamagic]] temperament, where 5/3 is split into two equal parts, each representing 9/7~[[35/27]], and may be extended to represent higher-limit ratios like [[13/10]], [[22/17]], etc. It enables [[sensamagic chords]]. See [[sensamagic family]] for the rank-3 temperament family where it is tempered out. See [[sensamagic clan]] for the rank-2 clan where it is tempered out


== See also ==
== See also ==
* [[Sensamagic family]], the rank-3 family where it is tempered out
* [[Small comma]]
* [[Sensamagic clan]], the rank-2 clan where it is tempered out
* [[Sensamagic chords]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]



Revision as of 13:46, 22 October 2022

Interval information
Ratio 245/243
Factorization 3-5 × 5 × 72
Monzo [0 -5 1 2
Size in cents 14.19052¢
Name sensamagic comma
Color name zzy2, zozoyo 2nd
FJS name [math]\displaystyle{ \text{m2}^{5,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 15.8615
Weil norm (log2 max(n, d)) 15.8733
Wilson norm (sopfr(nd)) 34
Open this interval in xen-calc

245/243, the sensamagic comma, is a small 7-limit comma measuring 14.2 cents. It is the amount by which two septimal major thirds (9/7) fall short of a classic major sixth (5/3), or the difference between 28/27 and 36/35.

Temperaments

Tempering it out alone in the 7-limit leads to the sensamagic temperament, where 5/3 is split into two equal parts, each representing 9/7~35/27, and may be extended to represent higher-limit ratios like 13/10, 22/17, etc. It enables sensamagic chords. See sensamagic family for the rank-3 temperament family where it is tempered out. See sensamagic clan for the rank-2 clan where it is tempered out

See also