In units theta = gamma ln2 / 2pi, Odlyzko's first 100,000 zeros avoid prime-power equal temperaments within 0.0012 of Landau's coefficient and ignore composites at 0.0000, with integer-temperament density 0.801 against 0.800 predicted, which is interesting structure and classical in substance.
hunts/zeta_temperament (Record 59 of 98 in chronological sequence)
Guiding Question
In tuning units theta = gamma ln2 / 2pi, do the Riemann zeros avoid the equal temperaments that tune prime-power harmonics, with the deficit Landau's formula predicts, and ignore composite harmonics?
Method & Verification
Mod-1 Fourier coefficients of Odlyzko's first 100,000 zeros were computed at frequencies log2 n for n <= 32 and compared with -Lambda(n)/sqrt(n)/<log(gamma/2pi)>, with the lab's 2000 cached zeros as a second table and composites as the vanishing control.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
No RESULTS.md or HANDBACK at the pin. Headline filled from the case-log verdict INTERESTING STRUCTURE, classical in substance. A 2026-08-22 correction notes that the composite control re-measures zeta.explicit.prime_spectrum, which this repository already exposed. Nothing here bears on RH.
Date Provenance
commit 2b487026c1ace62b644e305a713e2b3347d05622, hunts/zeta_temperament/, author 2026-08-22T20:02:11-05:00