128:160:192:225

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Revision as of 05:06, 14 August 2024 by Bcmills (talk | contribs) (In the second paragraph, emphasize the connections between this chord and meantone dominant sevenths, to explain its inclusion in the Dominant seventh chords category.)
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Chord information
Harmonics 128:160:192:225
Subharmonics 1/(225:180:150:128)
Intervals from root 1/1 – 5/4 – 3/2 – 225/128
Cents from root 0¢ 386¢ 702¢ 977¢
Step intervals 5/4, 6/5, 75/64
Step cents 386¢, 316¢, 275¢
Prime limit 5
Genus 32 ⋅ 52 (225)
Intervallic odd limit 225
Otonal odd limit 225
Utonal odd limit 225
Consistent edos (d ≥ 2) 22edo*, 31edo*, 53edo*, 65edo*

128:160:192:225, a 5-limit interpretation of an inversion of the Neapolitan or German sixth chord, is found rooted at the ♭II (1615) and ♭VI (85) of the duodene.

225/128 is usually considered an augmented sixth rather than a minor seventh; however, it is often tempered in a way that makes this chord indistinguishable from certain kinds of dominant seventh chord. For example, in septimal meantone it is tuned identically to the much simpler harmonic seventh chord 4:5:6:7, and in meantone tunings that also temper out the Pythagorean comma (such as 12edo and its multiples) it is tuned identically to 36:45:54:64 and 20:25:30:36.