Talk:144/125

Classic diminished third?

I doubt its "class". Does a "classic diminished third" exist at all? To me it seems dubious. Of course, I see that that it can be built by decreasing the classic (5-limit) minor third (6/5) by the classic chromatic semitone (25/24):

(6/5) / (25/24) → (6/5) * (24/25) → (6*24)/(5*25) → 144/125

but: is it this mathematical deduction really of musical relevance? I have the impression that meantone and just intonation got mixed up here. I'd be glad if someone would help me to understand. For instance show me a good example of a diminished third in action. --Xenwolf (talk) 14:33, 27 September 2020 (UTC)

There's not one but more "classic diminished thirds". Try decreasing 6/5 by 135/128 and that yields 256/225. They are identical in meantone, so nobody would distinguish them in classical era. FloraC (talk) 15:30, 27 September 2020 (UTC)

Maybe classic is a bit misleading in this context. --Xenwolf (talk) 15:45, 27 September 2020 (UTC)

I can definitely show you a good example of a 256/225 diminished third in action, however, the best examples of diminished thirds in general seem to show up in Neapolitan modes, and these are tricky to work with even in 12edo, never mind in Just Intonation. Still, while I need to get things straightened on my end, I have to thank the two of you for giving me an idea for how to improve a certain piece I'm writing at the moment- a long song steeped in an approximation of 159edo. --Aura (talk) 18:49, 27 September 2020 (UTC)

As a comma

The idea of tempering out such a big comma confuses me. I read the University temperament article, I heard the piece. Which actually seems to be in a tuning near 21edo. Isn't this just an error in nomenclature? I appreciate any help for better understanding. Thanks --Xenwolf (talk) 16:01, 27 September 2020 (UTC)