75edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
75et [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]) in the [[5-limit]], and provides a good tuning for the [[tetracot]] temperament. It tempers out [[225/224]] and [[1728/1715]] in the [[7-limit]], [[support]]ing [[bunya]] and [[orwell]], and providing the [[optimal patent val]] for [[fog]]. | 75et [[tempering out|tempers out]] 20000/19683 ([[tetracot comma]]) and 2109375/2097152 ([[semicomma]]) in the [[5-limit]], and provides a good tuning for the [[tetracot]] temperament. It tempers out [[225/224]] and [[1728/1715]] in the [[7-limit]], [[support]]ing [[bunya]] and [[orwell]], and providing the [[optimal patent val]] for [[fog]]. | ||
In the [[11-limit]], 75e [[val]] {{val| 75 119 174 211 '''260''' }} (corresponding to [[#Riemann zeta function|401zpi]]) 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]]. It tempers out [[325/324]] and [[512/507]] in the [[13-limit]], [[120/119]] and [[256/255]] in the [[17-limit]], and [[190/189]] and 250/247 in the 19-limit. | In the [[11-limit]], 75e [[val]] {{val| 75 119 174 211 '''260''' }} (corresponding to [[#Riemann zeta function|401zpi]]) 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]]. It tempers out [[325/324]] and [[512/507]] in the [[13-limit]], [[120/119]] and [[256/255]] in the [[17-limit]], and [[190/189]] and 250/247 in the 19-limit. It is an excellent tuning for 2.3.5.11.13 [[tetracot]], and its extension [[bunya]] up to the full 19-limit. | ||
Since 75 is part of the {{w|Fibonacci sequence}} beginning with 5 and 12, it closely approximates the [[peppermint]] temperament. The size of its fifth is exactly 704 | Since 75 is part of the {{w|Fibonacci sequence}} beginning with [[5edo|5]] and [[12edo|12]], after [[46edo|46]] and before [[121edo|121]], it closely approximates the [[peppermint]] temperament. The size of its fifth is exactly 704{{c}}, which is very close to the peppermint fifth of 704.096 cents. This makes it suitable for neo-Gothic tunings. It also approximates the [[Carlos Beta]] scale well ({{nowrap|4\75 ≈ 1\Carlos Beta}}), though [[94edo]] does even better. | ||
=== Odd harmonics === | === Odd harmonics === | ||
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| 8.36 | | 8.36 | ||
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== Instruments == | |||
A [[Lumatone mapping for 75edo]] is available. | |||
== Music == | == Music == | ||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/watch?v=5-G2KkYfKLs&list=WL&index=343&pp=gAQBiAQB8AUB ''microtonal improvisation in 75edo''] (2025-06-22) | |||
* [https://www.youtube.com/shorts/QflMtKRmlSI ''microtonal improvisation in 75edo''] (2025-06-24) | |||
* [https://www.youtube.com/watch?v=LsqNqHOfrBU ''Waltz in 75edo''] (2025) [https://www.youtube.com/shorts/sdN-5y3jhDY short clip demonstrating diatonic Lumatone mapping] | |||
* [https://www.youtube.com/shorts/nlurS-3VYkA ''75edo improv''] (2025) | |||
* [https://www.youtube.com/watch?v=GW-afWikisI ''Caprice in 75edo''] (2025) | |||
; [[Claudi Meneghin]] | ; [[Claudi Meneghin]] | ||
* [https://www.youtube.com/watch?v=oL6K6O4FBxc ''Fugue on The Lick''] (2019) | * [https://www.youtube.com/watch?v=oL6K6O4FBxc ''Fugue on The Lick''] (2019) | ||
[[Category:Listen]] | [[Category:Listen]] | ||