75edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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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. | ||
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 5 and 12, 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}}). | ||
=== Odd harmonics === | === Odd harmonics === | ||