The Riemann zeta function and tuning: Difference between revisions

Line 302:

We may define the ''strict zeta edos'' to be the edos that are in all four of the above lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578, 8539, 14348, 58973}}... .

~~===~~ Non-~~record~~ edos ~~===~~

If we want to find the second-best edos ranked by zeta peaks, then given a full list of zeta peaks, we can remove the successively higher peaks to get another sequence of succesively higher peaks, which correspond to edos called '''Parker edos'''.

'''Parker edos'''{{idiosyncratic}}

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 still-okay 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, 1205}}...

We can then remove those secondary peaks again to get '''Grothendieck edos'''.

~~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.~~

'''Grothendieck edos'''{{idiosyncratic}}

Non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak ''or'' Parker edo. Named after the "Grothendieck prime" (the number 57), another reference to the "almost" nature of these edos.

~~'''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 still~~-~~okay accuracy, but with different regular temperament properties~~ (~~e.g. 9 as alternative to 10~~, ~~17 as alternative to 19)~~.

We can do this as many times as we want, resulting in '''''k''-ary peak edos'''{{idiosyncratic}}. The ordinary peak edos are 1-ary (primary) peak edos, Parker edos are 2-ary (secondary) peak edos, and so on.

~~{{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, 1205}}…~~

=== Non-record edos ===

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'''{{idiosyncratic}}

@@ Line 302: / Line 302: @@
 We may define the ''strict zeta edos'' to be the edos that are in all four of the above lists. The list of strict zeta edos begins {{EDOs|2, 5, 7, 12, 19, 31, 53, 270, 1395, 1578, 8539, 14348, 58973}}... .
-=== Non-record edos ===
+If we want to find the second-best edos ranked by zeta peaks, then given a full list of zeta peaks, we can remove the successively higher peaks to get another sequence of succesively higher peaks, which correspond to edos called '''Parker edos'''.
+'''Parker edos'''{{idiosyncratic}}
+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 still-okay 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, 1205}}...
+We can then remove those secondary peaks again to get '''Grothendieck edos'''.
-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.
+'''Grothendieck edos'''{{idiosyncratic}}
+Non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak ''or'' Parker edo. Named after the "Grothendieck prime" (the number 57), another reference to the "almost" nature of these edos.
-'''Parker edos'''{{idiosyncratic}}
+<!-- add list here -->
-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 still-okay accuracy, but with different regular temperament properties (e.g. 9 as alternative to 10, 17 as alternative to 19).
+We can do this as many times as we want, resulting in '''''k''-ary peak edos'''{{idiosyncratic}}. The ordinary peak edos are 1-ary (primary) peak edos, Parker edos are 2-ary (secondary) peak edos, and so on.
-{{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, 1205}}…
+=== Non-record edos ===
+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'''{{idiosyncratic}}