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'''. | 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 == | ||
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== References == | == References == | ||
<references/> | <references/> | ||
[[Category:Commas named by translating something into another language]] | |||