2500/2499: Difference between revisions

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 {{Infobox Interval
 | Name = sperasma
-| Color name =
+| Color name = 17urry<sup>4</sup>-3, subiruyoyo negative 3rd
 | 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>).
+'''2500/2499''', the '''sperasma''', is an [[unnoticeable comma|unnoticeable]] [[17-limit]] [[superparticular]] [[comma]] with a size of about 0.693 [[cent]]s. Among other things, it is the difference between the small septimal sixth-tone of [[50/49]] and the large septendecimal sixth-tone of [[51/50]]. It also represents the little gap between [[17/12]] and a stack of two [[25/21]]'s.
+== Commatic relations ==
+This comma is the difference between the following superparticular pairs:
+* [[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.
+=== 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 }}
+: mapping generators: ~2, ~3, ~5, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}
+{{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 }}
+[[Badness]] (Sintel): 0.122
+=== 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]]s:
+* [[WE]]: ~2 = 1199.9902{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2274{{c}}, ~7/4 = 968.9230{{c}}, ~11/8 = 551.3474{{c}}, ~13/8 = 840.5571{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9754{{c}}, ~5/4 = 386.2178{{c}}, ~7/4 = 968.9184{{c}}, ~11/8 = 551.3352{{c}}, ~13/8 = 840.5461{{c}}
+{{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 }}
+[[Badness]] (Sintel): 1.13
+== 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 ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
 == References ==
 <references/>
+[[Category:Sperasmic]]
+[[Category:Commas named by translating something into another language]]