45/32: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Xenwolf (talk | contribs)
+cat
Aura (talk | contribs)
No edit summary
 
(6 intermediate revisions by 6 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = smaller pental tritone, smaller diatonic tritone, ptolemaic augmented fourth
| Ratio = 45/32
| Color name = y4, yo 4th
| Monzo = -5 2 1
| Cents = 590.22372
| Names = smaller pental tritone, <br/>diatonic tritone
| Color name = y4, yo 4th  
| Sound = jid_45_32_pluck_adu_dr220.mp3
| Sound = jid_45_32_pluck_adu_dr220.mp3
}}
}}
'''45/32''' is the '''smaller pental [[tritone]]''' a ''diatonic tritone'' of [[5-limit]] [[just intonation]]. It is separated from its inversion of [[64/45]] by the [[diaschisma]], 2048/2025 (less than 20 cents).


[[Category:Interval]]
'''45/32''' is the '''smaller pental [[tritone]]''', a ''diatonic tritone'' of [[5-limit]] [[just intonation]]- specifically, it is the '''ptolemaic augmented fourth'''. It is a [[syntonic comma]] away from the Pythagorean augmented fourth [[729/512]], which means it is justly tuned in [[1/6 syntonic comma meantone]]. It is separated from its inversion of [[64/45]] by the [[diaschisma]], 2048/2025 (''c''. 19.6 cents).
[[Category:Ratio]]
 
== See also ==
* [[64/45]] – its [[octave complement]]
* [[16/15]] – its [[fifth complement]]
 
[[Category:Tritone]]
[[Category:Tritone]]
[[Category:Overtone]]
[[Category:Meantone]]
 
{{todo|expand}}
[[Category:todo:expand]]

Latest revision as of 19:23, 28 January 2023

Interval information
Ratio 45/32
Factorization 2-5 × 32 × 5
Monzo [-5 2 1
Size in cents 590.2237¢
Names smaller pental tritone,
smaller diatonic tritone,
ptolemaic augmented fourth
Color name y4, yo 4th
FJS name [math]\displaystyle{ \text{A4}^{5} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 10.4919
Weil norm (log2 max(n, d)) 10.9837
Wilson norm (sopfr(nd)) 21

[sound info]
Open this interval in xen-calc

45/32 is the smaller pental tritone, a diatonic tritone of 5-limit just intonation- specifically, it is the ptolemaic augmented fourth. It is a syntonic comma away from the Pythagorean augmented fourth 729/512, which means it is justly tuned in 1/6 syntonic comma meantone. It is separated from its inversion of 64/45 by the diaschisma, 2048/2025 (c. 19.6 cents).

See also