128:160:192:225: Difference between revisions

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[[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]].
[[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]].


[[Category:Dominant seventh chords]]
[[Category:German sixth chords|###]] <!-- 3-digit first number -->
[[Category:Dominant seventh chords|###]] <!-- 3-digit first number -->

Revision as of 04:24, 20 August 2024

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 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.