2500/2499: Difference between revisions

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The '''sperasma''' is the [[17-limit]] [[superparticular]] [[comma]] with a ratio of '''2500/2499'''.  Its name comes from the Latin verb "spērāre" meaning "to hope" or "to fear" (meaning  "to hope" or "to fear"<ref>[[Wiktionary: spero #Latin]]</ref>).
The '''sperasma''' is the [[17-limit]] [[superparticular]] [[comma]] with a ratio of '''2500/2499'''.   


== Commatic relations ==
== Commatic relations ==
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* [[4375/4374]] and [[5832/5831]]
* [[4375/4374]] and [[5832/5831]]
* [[3025/3024]] and [[14400/14399]]
* [[3025/3024]] and [[14400/14399]]
== Temperaments ==
Tempering out this comma in the 17-limit results in the rank-6 '''sperasmic temperament''', or in the the 2.3.5.7.17 subgroup, the rank-4 '''speric temperament'''.
== Etymology ==
The sperasma was named by [[Aura]] in 2023. It comes from the Latin verb "spērāre" meaning "to hope" or "to fear"<ref>[[Wiktionary: spero #Latin]]</ref>.


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

Revision as of 08:12, 17 February 2023

Interval information
Ratio 2500/2499
Factorization 22 × 3-1 × 54 × 7-2 × 17-1
Monzo [2 -1 4 -2 0 0 -1
Size in cents 0.6926322¢
Name sperasma
FJS name [math]\displaystyle{ \text{ddd}{-3}^{5,5,5,5}_{7,7,17} }[/math]
Special properties square superparticular,
reduced
Tenney norm (log2 nd) 22.5748
Weil norm (log2 max(n, d)) 22.5754
Wilson norm (sopfr(nd)) 58
Comma size unnoticeable
S-expression S50
Open this interval in xen-calc

The sperasma is the 17-limit superparticular comma with a ratio of 2500/2499.

Commatic relations

This comma is the difference between the following superparticular pairs:

Not to mention some nonsuperparticular but useful relations:

It factors into the following superparticular pairs:

Temperaments

Tempering out this comma in the 17-limit results in the rank-6 sperasmic temperament, or in the the 2.3.5.7.17 subgroup, the rank-4 speric temperament.

Etymology

The sperasma was named by Aura in 2023. It comes from the Latin verb "spērāre" meaning "to hope" or "to fear"[1].

See also

References