The Riemann zeta function and tuning: Difference between revisions

Line 540:

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.

==== Local zeta edos ====

==== Local zeta peak edos ====

We may define ''local zeta'' edos as a generalization of the ''zeta peak~~'' and ''zeta peak integer~~'' edos as those that do not necessarily have successively higher zeta peaks but simply have a higher zeta peak than the edos on either side of them. This is a helpful list for finding edos that approximate primes well (but are not necessarily the best at doing so) for their size, or for finding edos in size ranges that lack any record-holding zeta edos (e.g. between 60 and 70 tones).

We may define ''local zeta peak'' edos as a generalization of the ''zeta peak'' edos as those that do not necessarily have successively higher zeta peaks but simply have a higher zeta peak than the edos on either side of them. This is a helpful list for finding edos that approximate primes well (but are not necessarily the best at doing so) for their size, or for finding edos in size ranges that lack any record-holding zeta edos (e.g. between 60 and 70 tones).

{{EDOs| 5, 7, 10, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 56, 58, 60, 63, 65, 68, 72, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 99, }} …

{{EDOs| 5, 7, 10, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 56, 58, 60, 63, 65, 68, 72, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 99,}} …

==== Local zeta peak integer edos ====

Similarly, we may define ''local zeta peak integer'' edos as a generalization of the ''zeta peak integer'' edos as those that have a higher zeta peak than the edos on either side of them ''with pure octaves'':

{{EDOs| 3, 5, 7, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 34, 36, 41, 43, 46, 48, 50, 53, 56, 58, 63, 65, 68, 70, 72, 74, 77, 80, 82, 84, 87, 89, 94, 96, 99,}} …

EDOs not present in the previous list but present here include 3, 26, 70, 74, …

EDOS present in the previous list but not present here include 27, 38, 60, 75, 91, …

==== Local anti-zeta edos ====

@@ Line 540: / Line 540: @@
 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.
-==== Local zeta edos ====
+==== Local zeta peak edos ====
-We may define ''local zeta'' edos as a generalization of the ''zeta peak'' and ''zeta peak integer'' edos as those that do not necessarily have successively higher zeta peaks but simply have a higher zeta peak than the edos on either side of them. This is a helpful list for finding edos that approximate primes well (but are not necessarily the best at doing so) for their size, or for finding edos in size ranges that lack any record-holding zeta edos (e.g. between 60 and 70 tones).
+We may define ''local zeta peak'' edos as a generalization of the ''zeta peak'' edos as those that do not necessarily have successively higher zeta peaks but simply have a higher zeta peak than the edos on either side of them. This is a helpful list for finding edos that approximate primes well (but are not necessarily the best at doing so) for their size, or for finding edos in size ranges that lack any record-holding zeta edos (e.g. between 60 and 70 tones).
-{{EDOs| 5, 7, 10, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 56, 58, 60, 63, 65, 68, 72, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 99, }} …
+{{EDOs| 5, 7, 10, 12, 15, 17, 19, 22, 24, 27, 29, 31, 34, 36, 38, 41, 43, 46, 48, 50, 53, 56, 58, 60, 63, 65, 68, 72, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 99,}} …
+==== Local zeta peak integer edos ====
+Similarly, we may define ''local zeta peak integer'' edos as a generalization of the ''zeta peak integer'' edos as those that have a higher zeta peak than the edos on either side of them ''with pure octaves'':
+{{EDOs| 3, 5, 7, 10, 12, 15, 17, 19, 22, 24, 26, 29, 31, 34, 36, 41, 43, 46, 48, 50, 53, 56, 58, 63, 65, 68, 70, 72, 74, 77, 80, 82, 84, 87, 89, 94, 96, 99,}} …
+EDOs not present in the previous list but present here include 3, 26, 70, 74, …
+EDOS present in the previous list but not present here include 27, 38, 60, 75, 91, …
 ==== Local anti-zeta edos ====