Jackpot comma: Difference between revisions

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Another way of looking at it
There's no jackpot temp. Tempering out this comma produces 7et
 
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{{Infobox Interval
{{Infobox Interval
|Ratio = 17249876309/17179869184
| Ratio = 17249876309/17179869184
|Name = jackpot comma
| Name = jackpot comma, 7-29-comma
|Comma = yes
| Comma = yes
}}
}}
Jackpot comma is the difference between a stack of 7 [[29/16]] and 6 [[2/1]] (alternatively, between a stack of 7 [[32/29]] and an octave). Equal divisions that are not multiples of 7 cannot temper it out.
The '''jackpot comma''' ([[monzo]]: 2.29 {{monzo| -34 7 }}, [[ratio]]: 17 249 876 309 / 17 179 869 184), systematically the '''7-29-comma''', is the difference between a stack of seven [[29/16]]'s and six [[2/1|octaves]] (alternatively, between a stack of seven [[32/29]]'s and an octave).  
 
== Temperaments ==
== Temperaments ==
Tempering it out produces the [[jackpot]] temperament, which sets 29th harmonic (octave-reduced) to be represented by 6\7.
[[Tempering out]] this comma splits the octave into 7 equal parts and maps 29/16 to 6\7.  


[[Category:Commas with unknown etymology]]
[[Category:Commas with unknown etymology]]

Latest revision as of 11:36, 29 May 2026

Interval information
Ratio 17249876309/17179869184
Subgroup monzo 2.29 [-34 7
Size in cents 7.040359¢
Names jackpot comma,
7-29-comma
FJS name [math]\displaystyle{ \text{dd1}^{29,29,29,29,29,29,29} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 68.0059
Weil norm (log2 max(n, d)) 68.0117
Wilson norm (sopfr(nd)) 271
Comma size small
Open this interval in xen-calc

The jackpot comma (monzo: 2.29 [-34 7, ratio: 17 249 876 309 / 17 179 869 184), systematically the 7-29-comma, is the difference between a stack of seven 29/16's and six octaves (alternatively, between a stack of seven 32/29's and an octave).

Temperaments

Tempering out this comma splits the octave into 7 equal parts and maps 29/16 to 6\7.