Vulture comma: Difference between revisions

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The '''vulture comma''' ([[monzo]]: {{monzo| 24 -21 4 }}, [[ratio]]: 10485760000/10460353203) of 4.200 [[cent]]s, is the amount by which four grave fourth intervals of [[320/243]] exceed [[3/1]], in other words (320/243)<sup>4</sup>/3. It is also the amount by which a stack of four [[syntonic comma]]s falls short of the [[256/243]] Pythagorean Limma, as well as the amount by which a stack of three [[729/640]] Acute Whole Tones fall short of a [[40/27]] Classic Grave Fifth.
The '''vulture comma''' ([[monzo]]: {{monzo| 24 -21 4 }}, [[ratio]]: 10 485 760 000 / 10 460 353 203) of 4.200 [[cent]]s, is the amount by which four grave fourth intervals of [[320/243]] exceed [[3/1]], in other words (320/243)<sup>4</sup>/3. It is also the amount by which a stack of four [[syntonic comma]]s falls short of the [[256/243]] Pythagorean limma, as well as the amount by which a stack of three [[729/640]] acute whole tones fall short of a [[40/27]] classic grave fifth.


== Temperaments ==
== Temperaments ==

Latest revision as of 12:43, 19 February 2025

Interval information
Ratio 10485760000/10460353203
Factorization 224 × 3-21 × 54
Monzo [24 -21 4
Size in cents 4.199837¢
Name vulture comma
Color name ssy42, Sasaquadyo comma
FJS name [math]\displaystyle{ \text{m2}^{5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 66.5719
Weil norm (log2 max(n, d)) 66.5754
Wilson norm (sopfr(nd)) 131
Comma size small
Open this interval in xen-calc

The vulture comma (monzo: [24 -21 4, ratio: 10 485 760 000 / 10 460 353 203) of 4.200 cents, is the amount by which four grave fourth intervals of 320/243 exceed 3/1, in other words (320/243)4/3. It is also the amount by which a stack of four syntonic commas falls short of the 256/243 Pythagorean limma, as well as the amount by which a stack of three 729/640 acute whole tones fall short of a 40/27 classic grave fifth.

Temperaments

Tempering out this comma leads to the vulture family of temperaments.

Etymology

The vulture comma was named by Paul Erlich in 2002[1].

Notes