75edo: Difference between revisions

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== Theory ==

In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tenpers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e val scores lower in [[~~badness]] than the [[patent val~~]], tempers [[100/99]] and [[243/242]], whereas the patent val tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.

In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tenpers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.

It provides the optimal patent val for the [[~~M&N_temperaments|12&51 temperament~~]] in the 7-limit and the [[~~M&N_temperaments~~|31&~~amp;~~44 temperament]] in the 19-limit.

It provides the [[optimal patent val]] for the [[fog]] temperament in the 7-limit and the [[Temperament merging|31 & 44 temperament]] in the 19-limit.

Since 75 is part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament. The size of its fifth is exactly 704c, which is very close to the peppermint fifth of 704.096c. This makes it suitable for neo-Gothic tunings.

=== ~~Prime~~ harmonics ===

=== Odd harmonics ===

@@ Line 9: / Line 9: @@
 == Theory ==
-In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tenpers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e val scores lower in [[badness]] than the [[patent val]], tempers [[100/99]] and [[243/242]], whereas the patent val tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.
+In the 5-limit, 75et tempers out 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]), and provides a good tuning for the [[tetracot]] temperament. In the 7-limit, it tenpers [[225/224]] and [[1728/1715]]. In the 11-limit, 75e [[val]] {{val| 75 119 174 211 '''260''' }} scores lower in [[TE error|error]], and tempers [[100/99]] and [[243/242]], whereas the [[patent val]] {{val| 75 119 174 211 '''259''' }} tempers [[99/98]] and [[121/120]]. In the 13-limit, it tempers [[325/324]] and [[512/507]], 17-limit [[120/119]] and [[256/255]] and 19-limit 190/189 and 250/247.
-It provides the optimal patent val for the [[M&N_temperaments|12&amp;51 temperament]] in the 7-limit and the [[M&N_temperaments|31&amp;44 temperament]] in the 19-limit.
+It provides the [[optimal patent val]] for the [[fog]] temperament in the 7-limit and the [[Temperament merging|31 & 44 temperament]] in the 19-limit.
 Since 75 is part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament. The size of its fifth is exactly 704c, which is very close to the peppermint fifth of 704.096c. This makes it suitable for neo-Gothic tunings.
-=== Prime harmonics ===
+=== Odd harmonics ===
 {{Harmonics in equal|75}}