2500/2499: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = sperasma
| Name = sperasma
| Color name =
| Color name = 17urry<sup>4</sup>-3, subiruyoyo negative 3rd
| Comma = yes
| Comma = yes
}}
}}
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'''.  Among other things, it equates a stack of two [[25/21]]s with a [[17/12]].
 
== Commatic relations ==
This comma is the difference between the following superparticular pairs:
* [[50/49]] and [[51/50]]
* [[120/119]] and [[126/125]]
* [[375/374]] and [[441/440]]
* [[625/624]] and [[833/832]]
* [[715/714]] and [[1001/1000]]
* [[1225/1224]] and [[2401/2400]]
* [[1275/1274]] and [[2601/2600]]
* [[2080/2079]] and [[12376/12375]]
 
Not to mention some nonsuperparticular but useful relations:
* [[540/539]] and [[1377/1375]]
* [[2025/2023]] and [[1701/1700]]
 
It factors into the following superparticular pairs:
* [[4375/4374]] and [[5832/5831]]
* [[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'''. You may find a list of good equal temperaments that support these temperaments below.
 
=== Sperasmic ===
[[Subgroup]]: 2.3.5.7.11.13.17
 
[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 2 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || -1 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 4 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -2 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}
 
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056, ~11/8, ~13/8
 
{{Optimal ET sequence|legend=1| 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477 }}
 
=== Speric ===
[[Subgroup]]: 2.3.5.7.17
 
{{Mapping|legend=2| 1 0 0 0 2 | 0 1 0 0 -1 | 0 0 1 0 4 | 0 0 0 1 -2 }}
 
: sval mapping generators: ~2, ~3, ~5, ~7
 
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056
 
{{Optimal ET sequence|legend=1| 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648 }}
 
== 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 ==
Line 12: Line 73:
== References ==
== References ==
<references/>
<references/>
[[Category:Commas named by translating something into another language]]

Latest revision as of 02:01, 16 November 2024

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
Color name 17urry4-3, subiruyoyo negative 3rd
FJS name [math]\displaystyle{ \text{ddd}{-3}^{5,5,5,5}_{7,7,17} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 22.5748
Weil height (log2 max(n, d)) 22.5754
Wilson height (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. Among other things, it equates a stack of two 25/21s with a 17/12.

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. You may find a list of good equal temperaments that support these temperaments below.

Sperasmic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨ 1 0 0 0 0 0 2 ],
⟨ 0 1 0 0 0 0 -1 ],
⟨ 0 0 1 0 0 0 4 ],
⟨ 0 0 0 1 0 0 -2 ],
⟨ 0 0 0 0 1 0 0 ],
⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056, ~11/8, ~13/8

Optimal ET sequence: 19, 24d, 27eg, 29g, 31, 41g, 43, 53g, 58g, 60e, 68, 72, 103, 111, 140, 171, 183, 239f, 243e, 270, 311, 354, 414, 422, 494, 581, 764, 935, 1075, 1106, 1178, 1672, 1942, 2113, 2253, 2535, 2805g, 3299d, 3713, 3983g, 4477

Speric

Subgroup: 2.3.5.7.17

Sval mapping: [⟨1 0 0 0 2], ⟨0 1 0 0 -1], ⟨0 0 1 0 4], ⟨0 0 0 1 -2]]

sval mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9677, ~5/4 = 386.2047, ~7/4 - 968.9056

Optimal ET sequence: 19, 27g, 31, 41g, 56, 60, 68, 72, 99, 171, 494, 525, 581, 593, 665, 764, 836, 935, 1771, 1942, 2706, 2877, 4477, 4648

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

  1. ↑ Wiktionary: spero #Latin
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