128:160:192:225: Difference between revisions

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{{Infobox Chord|Name=Neapolitan,German sixth}}
{{Infobox Chord|ColorName=yo layoyo-6 or y,Lyy6}}
'''128:160:192:225''', an inversion of the ''Neapolitan''[https://en.wikipedia.org/wiki/Neapolitan_chord] or ''German sixth''[https://en.wikipedia.org/wiki/Augmented_sixth_chord#German_sixth] chord, is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]].
'''128:160:192:225''', a [[German sixth chord]], is found rooted at the ♭II ({{Frac|16|15}}) and ♭VI ({{Frac|8|5}}) of the [[duodene]].


Although [[225/128]] is often considered an augmented sixth rather than a minor seventh, in [[Meantone_family#Septimal_meantone|septimal meantone]] it is tuned identically to the [[7/4|harmonic seventh]], so the chord employing it may be considered a kind of [[dominant seventh chord]].
[[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]] and [[marvel]] 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]] ([[12edo]] and its multiples) it is tuned identically to [[36:45:54:64]] and [[20:25:30:36]].


[[Category:Dominant seventh chords]]
If [[128/125]] is tempered out, this chord is tuned identically to both [[256:320:375:450]] and [[20:25:30:36]].
 
[[Category:German sixth chords|###]] <!-- 3-digit first number -->
[[Category:Dominant seventh chords|###]] <!-- 3-digit first number -->

Latest revision as of 06:04, 4 December 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¢
Color name yo layoyo-6 or y,Lyy6
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 German sixth chord, is found rooted at the ♭II (16⁄15) and ♭VI (8⁄5) 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 and marvel 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 (12edo and its multiples) it is tuned identically to 36:45:54:64 and 20:25:30:36.

If 128/125 is tempered out, this chord is tuned identically to both 256:320:375:450 and 20:25:30:36.

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