Glacier comma: Difference between revisions

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Badness (Sintel)
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The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).
The '''glacier comma''' is a [[13-limit]] comma which is the difference between five small tridecimal neutral seconds of [[13/12]] and a perfect fifth ([[3/2]]). It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n'' + 5)/''n'') / ((''n'' + 3)/(''n'' + 2))<sup>5</sup> = (S(''n'' + 1)⋅S(''n'' + 2)<sup>2</sup>) / (S(''n'' + 3)<sup>2</sup>⋅S(''n'' + 4)).


== Temperaments ==
== Temperaments ==
Tempering out this comma in the 13-limit leads to the [[glacier]] family.
[[Tempering out]] this comma in the 2.3.13 subgroup leads to the [[glacier]] temperament.
 
=== Glacier (2.3.13) ===
[[Subgroup]]: 2.3.13
 
[[Mapping]]: {{mapping|1 1 3|0 5 6}}
 
: Mapping generators: ~2, ~13/12
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~13/12 = 140.3277
 
{{Optimal ET sequence|legend=1|8, 9, 17, 26, 60, 77, 94, 111, 171}}
 
[[Badness]]: 0.383 (Sintel)


== See also ==
== See also ==