54:64:81:96: Difference between revisions

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clarify relationship to 5-limit chords (specifically, via meantone)
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'''54:64:81:96''' is a [[minor seventh chord]] found on the ii, iii, and vi of the [[3-limit]] [[5L 2s|diatonic scale]].
'''54:64:81:96''' is a [[minor seventh chord]] found on the ii, iii, and vi of the [[3-limit]] [[5L 2s|diatonic scale]].


It may be considered a 3-limit approximation of both [[10:12:15:18]] and [[27:32:40:48]].
In [[meantone]] this chord is [[tempered together]] with both [[10:12:15:18]] and [[27:32:40:48]].
* Relative to 10:12:15:18, it tempers both the third and seventh by 80/81.
* Relative to 10:12:15:18, it tempers both the third and seventh by 80/81.
* Relative to 27:32:40:48, it tempers the fifth by [[81/80]].
* Relative to 27:32:40:48, it tempers the fifth by [[81/80]].


[[Category:Minor seventh chords|##]]
[[Category:Minor seventh chords|##]]

Revision as of 03:16, 31 August 2024

Chord information
Harmonics 54:64:81:96
Subharmonics 1/(96:81:64:54)
Intervals from root 1/132/273/216/9
Cents from root 294¢702¢996¢
Step intervals 32/27, 81/64, 32/27
Step cents 294¢, 408¢, 294¢
Prime limit 3
Genus 34 (81)
Intervallic odd limit 81
Otonal odd limit 81
Utonal odd limit 81
Consistent edos (d ≥ 2) 12edo**, 17edo*, 24edo*, 29edo*, …

54:64:81:96 is a minor seventh chord found on the ii, iii, and vi of the 3-limit diatonic scale.

In meantone this chord is tempered together with both 10:12:15:18 and 27:32:40:48.

  • Relative to 10:12:15:18, it tempers both the third and seventh by 80/81.
  • Relative to 27:32:40:48, it tempers the fifth by 81/80.