The Riemann zeta function and tuning: Difference between revisions
m →Non-record edos: Added the Parker edos up to 1000 |
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The following lists of edos are not determined by successively large measured values, they are edos that satisfy some other property relating to zeta peaks instead. | The following lists of edos are not determined by successively large measured values, they are edos that satisfy some other property relating to zeta peaks instead. | ||
'''Parker edos'''{{idiosyncratic}} | |||
Those non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak edo. Named after the Parker square in mathematics. A helpful list for finding an alternative to any given zeta peak edo of similar size and almost-as-good accuracy, but with different regular temperament properties (e.g. 9 as alternative to 10, 17 as alternative to 19). | |||
{{EDOs|6, 8, 9, 14, 15, 17, 24, 34, 46, 58, 65, 77, 87, 111, 140, 183, 243, 301, 311, 460, 472, 525, 571, 581, 814, 836, 882}}… | |||
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'''Anti-zeta edos'''{{idiosyncratic}} | '''Anti-zeta edos'''{{idiosyncratic}} | ||
Edos with a lower zeta peak than the edos on either side of them. | Edos with a lower zeta peak than the edos on either side of them. Helpful for finding edos that force the use of methods other than traditional concordant harmony, or for composers seeking a challenge to inspire creativity. | ||
{{EDOs|6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 52, 54, 57, 59, 61, 64, 66, 69, 71, 73, 76, 78, 81, 83, 86, 88, 90, 92, 95, 97}}… | {{EDOs|6, 8, 11, 13, 16, 18, 20, 23, 25, 28, 30, 33, 35, 37, 40, 42, 44, 47, 49, 52, 54, 57, 59, 61, 64, 66, 69, 71, 73, 76, 78, 81, 83, 86, 88, 90, 92, 95, 97}}… | ||
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{{EDOs| 9, 14, 21, 26, 32, 39, 45, 51, 55, 62, 67, 70, 74, 79, 85, 93, 98}}… | {{EDOs| 9, 14, 21, 26, 32, 39, 45, 51, 55, 62, 67, 70, 74, 79, 85, 93, 98}}… | ||
== Optimal octave stretch == | == Optimal octave stretch == | ||