11358058edo: Difference between revisions

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{{Infobox ET

{{Infobox ET|Consistency=35|Distinct consistency=35~~|Prime factorization=2 × 5679029~~}}

| Prime factorization = 2 × 5679029

| Consistency = 35

| Distinct consistency = 35

}}

Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31~~-prime~~-limit, and is consistent up to the ~~36-~~[[Odd prime sum limit|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[~~EDO|~~edo]], meaning it is very likely a [[The Riemann ~~Zeta~~ function and tuning|zeta peak]] edo.

Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the [[31-limit]], and is [[consistent]] up to the [[Odd prime sum limit|36-OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[edo]], meaning it is very likely a [[The Riemann zeta function and tuning|zeta peak]] edo.

While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.

=== Prime harmonics ===

{{Harmonics in equal

|11358058

{{Harmonics in equal|11358058|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 11358058edo (continued)}}

|columns = 13

}}

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-{{Novelty}}
+{{Mathematical interest}}
+{{Infobox ET
-{{Infobox ET|Consistency=35|Distinct consistency=35|Prime factorization=2 × 5679029}}
+| Prime factorization = 2 × 5679029
+| Consistency = 35
-{{EDO intro}}
+| Distinct consistency = 35
+}}
+{{ED intro}}
-Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the 31-prime-limit, and is consistent up to the 36-[[Odd prime sum limit|OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[EDO|edo]], meaning it is very likely a [[The Riemann Zeta function and tuning|zeta peak]] edo.
+Although its step size is far beyond the human melodic [[just-noticeable difference]], it has been noted for its highly accurate approximation of the [[31-limit]], and is [[consistent]] up to the [[Odd prime sum limit|36-OPSL]], where it has a lower maximum error (i.e. the error of the least accurate approximation of any interval in the limit from JI) than any smaller [[edo]], meaning it is very likely a [[The Riemann zeta function and tuning|zeta peak]] edo.
 While not practical to build an acoustic instrument for, one potential use of this system is in electronic music production, where free modulation between higher-limit JI intervals is desired. Instead of keeping track of the intervals directly, the number of steps to the octave for an interval could simply be added or subtracted from one note to get to the next. However, like all other equal temperaments, the consistency of this tuning is limited, and the sequence of intervals may eventually start to deviate from their true JI counterparts.
 === Prime harmonics ===
-{{Harmonics in equal
+{{Harmonics in equal|11358058|columns=9}}
-|11358058
+{{Harmonics in equal|11358058|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 11358058edo (continued)}}
-|columns = 13
-}}