10:12:15: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Overthink (talk | contribs)
m fixed major to minor
"Just minor triad" isn't less precise
Line 1: Line 1:
{{Infobox Chord|ColorName=gu or g}}
{{Infobox Chord|ColorName=gu or g}}


'''10:12:15''' is the utonal [[minor triad]], also known as the '''classical minor triad, classical minor triad,''' or more generally - albeit less precisely - as the '''just minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.  
'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.  


== Rotations around the octave ==
== Rotations around the octave ==
Line 39: Line 39:
Common tetrads based on this triad (5-limit except where noted):
Common tetrads based on this triad (5-limit except where noted):


* [[4:5:6]] - chord inversion
* [[4:5:6]] chord inversion
* [[10:12:15:18]] adds [[9/5]]
* [[10:12:15:18]] adds [[9/5]]
* [[30:36:45:50]] adds [[5/3]]
* [[30:36:45:50]] adds [[5/3]]
* [[60:70:84:105]] - adds 8/7 (7-limit)
* [[60:70:84:105]] adds 8/7 (7-limit)


[[Category:Minor triads|#@]] <!-- 2-digit first number -->
[[Category:Minor triads|#@]] <!-- 2-digit first number -->

Revision as of 11:15, 11 November 2025

Chord information
Harmonics 10:12:15
Subharmonics 1/(6:5:4)
Intervals from root 1/16/53/2
Cents from root 316¢702¢
Step intervals 6/5, 5/4
Step cents 316¢, 386¢
Color name gu or g
Prime limit 5
Genus 35 (15)
Intervallic odd limit 5
Otonal odd limit 15
Utonal odd limit 5
Consistent edos (d ≥ 2) 3edo*, 12edo*, 15edo*, 19edo**, …

10:12:15 is a utonal minor triad, known as the just minor triad, classical minor triad, or Ptolemaic minor triad. It is a common chord that appears as a counterpart to the widespread otonal major triad of 4:5:6, the major third swapped with a minor third.

Rotations around the octave

10:12:15 "Root position"
12:15:20 "1st inversion"
15:20:24 "2nd inversion"

Voicings and rotations around two octaves

Voicing
Rotation
Root '3 '15 '3'15
On 3 12:15:40 6:10:15 6:15:20 12:15:20
On 5 10:12:15 10:15:24 5:6:15 5:12:15
On 15 15:40:48 15:24:40 15:20:24 15:20:48

Related chords

Common tetrads based on this triad (5-limit except where noted):