Talk:144/125: Difference between revisions

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== Classic diminished third? ==

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(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. --[[User:Xenwolf|Xenwolf]] ([[User talk: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. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:30, 27 September 2020 (UTC)

:: Maybe ''classic'' is a bit misleading in this context. --[[User:Xenwolf|Xenwolf]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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<sup>±3</sup> [[User:Xenwolf/Interval quartet|interval quartet]] of d6, A3, d3, A6 isn't "classic". --[[User:Xenwolf|Xenwolf]] ([[User talk: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 [https://en.wikipedia.org/wiki/Augmented_sixth_chord 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". --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:01, 27 September 2020 (UTC)

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 == Classic diminished third? ==
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   (6/5) / (25/24) &rarr; (6/5) * (24/25) &rarr; (6*24)/(5*25) &rarr; 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. --[[User:Xenwolf|Xenwolf]] ([[User talk: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. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 15:30, 27 September 2020 (UTC)
+:: Maybe ''classic'' is a bit misleading in this context. --[[User:Xenwolf|Xenwolf]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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<sup>&plusmn;3</sup> [[User:Xenwolf/Interval quartet|interval quartet]] of d6, A3, d3, A6 isn't "classic". --[[User:Xenwolf|Xenwolf]] ([[User talk: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 [https://en.wikipedia.org/wiki/Augmented_sixth_chord 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". --[[User:Aura|Aura]] ([[User talk: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. --[[User:Aura|Aura]] ([[User talk: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 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:01, 27 September 2020 (UTC)