The Riemann zeta function and tuning: Difference between revisions

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=== ''k''-ary-peak edos ===

{{Idiosyncratic terms|the term "''k''-ary-peak edos" itself, as well as the names for the different types of ''k''-ary-peak edos. ~~Proposed~~ by {{u|Akselai}} and [[Budjarn Lambeth]].}}

{{Idiosyncratic terms|the term "''k''-ary-peak edos" itself, as well as the names for the different types of ''k''-ary-peak edos. Used by {{u|Akselai}} and [[Budjarn Lambeth]].}}

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'''.

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 '''2-ary peak edos''': defined as non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak edo.

~~Named after the Parker square in recreational mathematics, ''Parker edos'' may be defined as non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak edo.~~ This list can be used 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).

This list can be used 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 '''~~tertiary~~-peak edos''': non-zeta-peak edos with a higher zeta peak than any smaller ~~non-~~zeta-peak ~~''or'' Parker edo~~.

We can then remove those secondary peaks again to get '''3-ary peak edos''': non-zeta-peak edos with a higher zeta peak than any smaller edo that is neither a zeta peak nor a 2-ary peak.

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

We can repeat this process as many times as we want, resulting in '''''k''-ary-peak edos'''. The ordinary peak edos are 1-ary peak edos, then there are 2-ary peak edos, 3-ary peak edos, and so on. However keep in mind that the higher ''k'' gets, the less meaningful the peaks will get, especially for smaller edos (less than about 100).

=== Non-record edos ===

@@ Line 564: / Line 564: @@
 === ''k''-ary-peak edos ===
-{{Idiosyncratic terms|the term "''k''-ary-peak edos" itself, as well as the names for the different types of ''k''-ary-peak edos. Proposed by {{u|Akselai}} and [[Budjarn Lambeth]].}}
+{{Idiosyncratic terms|the term "''k''-ary-peak edos" itself, as well as the names for the different types of ''k''-ary-peak edos. Used by {{u|Akselai}} and [[Budjarn Lambeth]].}}
-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'''.
+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 '''2-ary peak edos''': defined as non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak edo.
-Named after the Parker square in recreational mathematics, ''Parker edos'' may be defined as non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak edo. This list can be used 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).
+This list can be used 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 '''tertiary-peak edos''': non-zeta-peak edos with a higher zeta peak than any smaller non-zeta-peak ''or'' Parker edo.
+We can then remove those secondary peaks again to get '''3-ary peak edos''': non-zeta-peak edos with a higher zeta peak than any smaller edo that is neither a zeta peak nor a 2-ary peak.
 <!-- add list here -->
-We can do this as many times as we want, resulting in '''''k''-ary-peak edos'''. The ordinary peak edos are 1-ary (primary)-peak edos, Parker edos are 2-ary (secondary)-peak edos, and so on.
+We can repeat this process as many times as we want, resulting in '''''k''-ary-peak edos'''. The ordinary peak edos are 1-ary peak edos, then there are 2-ary peak edos, 3-ary peak edos, and so on. However keep in mind that the higher ''k'' gets, the less meaningful the peaks will get, especially for smaller edos (less than about 100).
 === Non-record edos ===