Amity family: Difference between revisions

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=== Overview to extensions ===

The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, 2401/2400 for amicable, and 16875/16807 for familia.

The second comma to extend the 5-limit amity include [[4375/4374]] for septimal amity, [[225/224]] for houborizic, 65625/65536 for paramity, [[126/125]] for accord, [[245/243]] for bamity, [[2430/2401]] for hamity, [[1029/1024]] for gamity, [[10976/10935]] for chromat, [[703125/702464]] for trinity, [[2401/2400]] for amicable, [[2100875/2097152]] for calamity, [[420175/419904]] for witch, and [[16875/16807]] for familia.

Temperaments discussed elsewhere include:

* ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)

* ''[[Witch]]'' → [[Wizmic microtemperaments #Witch]] (+420175/419904)

The rest are considered below.

== Septimal amity ==

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== Amicable ==

The amicable temperament tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.

The amicable temperament (99 & 311) tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.

While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.

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Badness: 0.028267

== Calamity ==

The calamity temperament (46 & 311) tempers out the [[rainy comma]], 2100875/2097152, splitting the interval of two octaves plus an acute minor third into five.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1600000/1594323, 2100875/2097152

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~48/35 = 547.9092

[[Badness]]: 0.198

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 3025/3024, 12005/11979, 131072/130977

Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}

Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9080

Badness: 0.0604

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979

Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}

Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9066

Badness: 0.0336

== Familia ==

The familia temperament (113 & 152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.

The familia temperament (113 & 152) tempers out the [[mirkwai comma]], 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.

[[Subgroup]]: 2.3.5.7

@@ Line 21: / Line 21: @@
 === Overview to extensions ===
-The second comma to extend the 5-limit amity include 4375/4374 for amity, 225/224 for houborizic, 65625/65536 for paramity, 126/125 for accord, 245/243 for bamity, 2430/2401 for hamity, 1029/1024 for gamity, 2401/2400 for amicable, and 16875/16807 for familia.
+The second comma to extend the 5-limit amity include [[4375/4374]] for septimal amity, [[225/224]] for houborizic, 65625/65536 for paramity, [[126/125]] for accord, [[245/243]] for bamity, [[2430/2401]] for hamity, [[1029/1024]] for gamity, [[10976/10935]] for chromat, [[703125/702464]] for trinity, [[2401/2400]] for amicable, [[2100875/2097152]] for calamity, [[420175/419904]] for witch, and [[16875/16807]] for familia.
 Temperaments discussed elsewhere include:
 * ''[[Chromat]]'' → [[Hemimage temperaments #Chromat]] (+10976/10935)
 * ''[[Witch]]'' → [[Wizmic microtemperaments #Witch]] (+420175/419904)
+The rest are considered below.
 == Septimal amity ==
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 == Amicable ==
-The amicable temperament tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.
+The amicable temperament (99 & 311) tempers out the [[amity comma]] and the [[canousma]] in addition to the breedsma, and is closely associated with the canou temperament.
 While it extends well into 2.3.5.7.13/11, there are multiple reasonable places for the prime 11 and 13 in the interval chain. Amical (311 & 410) does this with no compromise of accuracy, but is enormously complex. Amorous (212 & 311) has the new primes placed on the same side of the interval chain so blends smarter with the other harmonics. Pseudoamical (99 & 113) and pseudoamorous (14cf & 99ef) are the corresponding low-complexity interpretations. Floral (198 & 212) shares the semioctave period and the ~21/20 generator with harry, but in a complementary style, including a characteristic flat 11. Finally, humorous (198 & 311) is one of the best extensions out there and it splits the generator in two.
@@ Line 789: / Line 791: @@
 Badness: 0.028267
+== Calamity ==
+The calamity temperament (46 & 311) tempers out the [[rainy comma]], 2100875/2097152, splitting the interval of two octaves plus an acute minor third into five.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 1600000/1594323, 2100875/2097152
+{{Mapping|legend=1| 1 13 32 -15 | 0 -25 -65 39 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~48/35 = 547.9092
+{{Optimal ET sequence|legend=1| 46, 219c, 265, 311 }}
+[[Badness]]: 0.198
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 3025/3024, 12005/11979, 131072/130977
+Mapping: {{mapping| 1 13 32 -15 -18 | 0 -25 -65 39 47 }}
+Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9080
+{{Optimal ET sequence|legend=1| 46, 219c, 265, 311, 979, 1290 }}
+Badness: 0.0604
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 3025/3024, 4096/4095, 12005/11979
+Mapping: {{mapping| 1 13 32 -15 -18 -31 | 0 -25 -65 39 47 76 }}
+Optimal tuning (CTE): ~2 = 1\1, ~48/35 = 547.9066
+{{Optimal ET sequence|legend=1| 46, 265, 311, 668, 979, 1290 }}
+Badness: 0.0336
 == Familia ==
-The familia temperament (113 &amp; 152) tempers out the mirkwai comma, 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.
+The familia temperament (113 &amp; 152) tempers out the [[mirkwai comma]], 16875/16807. It splits the interval of acute minor tenth (~243/100) in five.
 [[Subgroup]]: 2.3.5.7