User talk:UnbihexiumFan/Temperaments

Plausibility of interpretation

In the "243/242+2079/2048-based temperaments" section, you wrote:

While the major third is too sharp to be seen as 5/4, it can be seen as 24/19 or 64/51.

The major third is actually further away from 24/19 than 5/4, so that interpretation probably wouldn't be more plausible. What do you think about this?--Overthink (talk) 19:27, 8 February 2026 (UTC)

You're right. What I meant was that mapping the major third to 24/19 would make it so that the resulting tuning would be "better" than mapping it to 5/4 would be (gives better approximations of intervals like 9/7 and 7/6). The other reasonable approximation for 5/4 is sesquiaugmented second, which is a worse 5/4 than the major third for most EDOs that support it (except for 31edo where they are the same), but using that one gives better 5/3s and 9/5s. Would it be better to say it approximates other intervals better than to say that it is too sharp/flat? UnbihexiumFan (talk) 02:51, 9 February 2026 (UTC)