Talk:144/125

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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)
Ah, great this is of help for you 🙂 - what I think is that 144/125 is definitely not the classic diminished third as well as the whole 5±3 interval quartet of d6, A3, d3, A6 isn't "classic". --Xenwolf (talk) 19:51, 27 September 2020 (UTC)
While I concur with your assessment of 144/125 as not being the classic diminished third, I do have to ask how we distinguish the 5-limit versions of the diminished third, the augmented sixth, the augmented third and the diminished sixth from other varieties... Besides which, as the greater Neapolitan scale and its modes are actually proper modes in 12edo, and we still have to contend with augmented sixth chords appearing in classical music and stuff such, I would think that certain 5-limit augmented thirds, diminished thirds, augmented sixths and diminished sixths should still be counted as "classic" as opposed to just "pental". --Aura (talk) 20:32, 27 September 2020 (UTC)
For instance, I labeled 256/225 and 225/128 as "Neapolitan" intervals because of their appearance in Neapolitan scales in a similar fashion to how Diatonic intervals are labeled "Diatonic" because of their appearance in diatonic scales, and since 256/225 and 225/128 are both 5-limit intervals, I would argue that "Neapolitan diminished third" and "Neapolitan augmented sixth" could be expanded to "Classic Neapolitan diminished third" and "Classic Neapolitan augmented sixth" in order to distinguish them from 7-limit versions of Neapolitan intervals, for instance. I mean, 7-limit intervals can sometimes be considered "Diatonic" in a similar vein, can they not? Besides, 256/225 and 225/128, from what I'm seeing, are likely to be the most frequently encountered among diminished thirds and augmented sixths- with 225/128 in particular being likely to have seen at least a historical presence in the aforementioned augmented sixth chords- and the relative ease of deriving both 256/225 and 225/128 from other "classic" intervals really does make them viable candidates for the "classic" label themselves. --Aura (talk) 20:40, 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)