45:54:64:81: Difference between revisions

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{{Infobox Chord}}
{{Infobox Chord}}
'''45:54:64:81''' is a [[half-diminished seventh chord]].
Although it has a relatively high [[odd limit]] for such a chord, this particular tuning of the chord is notable for being both a [[preimage]] of the half-diminished seventh chord in [[meantone]] temperaments (including [[12edo]] and [[quarter-comma meantone]]), and [[tempered together]] with the vastly simpler [[5:6:7:9]] in [[archytas]] temperament (also supported by [[12edo]]).


[[Category:Half-diminished seventh chords|##]]
[[Category:Half-diminished seventh chords|##]]
{{stub}}

Revision as of 02:02, 11 September 2024

Chord information
Harmonics 45:54:64:81
Subharmonics 1/(576:480:405:320)
Intervals from root 1/16/564/459/5
Cents from root 316¢610¢1018¢
Step intervals 6/5, 32/27, 81/64
Step cents 316¢, 294¢, 408¢
Prime limit 5
Genus 345 (405)
Intervallic odd limit 81
Otonal odd limit 81
Utonal odd limit 405
Consistent edos (d ≥ 2) 12edo*, 41edo*, 53edo**, 65edo**

45:54:64:81 is a half-diminished seventh chord.

Although it has a relatively high odd limit for such a chord, this particular tuning of the chord is notable for being both a preimage of the half-diminished seventh chord in meantone temperaments (including 12edo and quarter-comma meantone), and tempered together with the vastly simpler 5:6:7:9 in archytas temperament (also supported by 12edo).