Template talk:Harmonics in equal

Fifthspan

(moved from "Module talk:Primes in edo" before its deletion)

I plan to add a fifthspan row in the near future (only to EDOs where it is unique). I tend to making it an option, so there will be a parameter that has to set. --Xenwolf (talk) 12:17, 4 July 2021 (UTC)

21st harmonic in 121edo

From prime harmonics part (it shows odd harmonics somehow) of 121edo#Theory its steps of 21st harmonic is not by adding 3 and 7, was this on purpose?? FilterNashi (talk) 11:51, 24 June 2025 (UTC)

When that table displays composite odd harmonics, it maps them by direct approximation rather than by patent val. In 121edo, the patent val mapping (adding up 3 and 7) is over 50% off for odd 21, and therefore the direct approximation (best) mapping for 21 is different. -- Lériendil (talk) 12:51, 24 June 2025 (UTC)

kinda misleading though. considering there are different temperaments in one single chart. FilterNashi (talk) 13:32, 24 June 2025 (UTC)

From the template's documentation: "By default, edos get primes if they are consistent for the odd harmonics up to 21, otherwise they get odds." And indeed, 121edo is not consistent up to the 21-odd-limit; I edited the subheading on the 121edo page to reflect that. In general, the "harmonics in equal" table does not assume the reader wants to use a regular mapping, and instead shows how well the tuning system is capable of approximating every given harmonic. When the tuning consistent up to the 21-odd-limit, you can calculate the odds up to 21 yourself by stacking the primes, hence you only need the table of primes. Otherwise, the odds table shows you how they don't exactly add up, so you can figure out how you want to work with that feature. --Fredg999 (talk) 15:43, 24 June 2025 (UTC)