Glacier comma: Difference between revisions
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Quintic-particular is an idiosyncratic term Tags: Mobile edit Mobile web edit |
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{{Infobox | {{Infobox interval | ||
| Ratio = 373248/371293 | | Ratio = 373248/371293 | ||
| Name = glacier comma | | Name = glacier comma | ||
| Color name = 3u<sup>5</sup>-2, quinthu negative 2nd | | Color name = 3u<sup>5</sup>-2, quinthu negative 2nd | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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]]). | 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 13-limit leads to the [[glacier]] family. | ||
=== 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, 60, 77, 94, 171}} | |||
[[Badness]]: 0.006431 | |||
== See also == | |||
* [[Quinticular comma]] – another example of quintic-particular comma | |||
[[Category:Commas named after composers]] | [[Category:Commas named after composers]] | ||
[[Category:Commas named after music theorists]] | [[Category:Commas named after music theorists]] | ||
Latest revision as of 12:46, 23 May 2025
| Interval information |
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 term] interval, that is, of the form ((n+5)/n) / ((n+3)/(n+2))5 = (S(n+1)×S(n+2)2) / (S(n+3)2×S(n+4)).
Temperaments
Tempering out this comma in the 13-limit leads to the glacier family.
Glacier (2.3.13)
Subgroup: 2.3.13
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: 8, 9, 17, 60, 77, 94, 171
Badness: 0.006431
See also
- Quinticular comma – another example of quintic-particular comma