45:54:64:81

From Xenharmonic Wiki
Jump to navigation Jump to search
Chord information
Harmonics 45:54:64:81
Subharmonics 1/(576:480:405:320)
Intervals from root 1/1 – 6/5 – 64/45 – 9/5
Cents from root 0¢ 316¢ 610¢ 1018¢
Step intervals 6/5, 32/27, 81/64
Step cents 316¢, 294¢, 408¢
Color name gu-7 gu-5 or g7(g5)
Prime limit 5
Genus 34 ⋅ 5 (405)
Intervallic odd limit 81
Otonal odd limit 81
Utonal odd limit 405

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).