10:12:15: Difference between revisions

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{{Infobox Chord|ColorName=gu or g}}
{{Infobox Chord|ColorName=gu or g}}


'''10:12:15''' is the just [[minor triad]], also known as the '''Ptolemaic minor triad'''.  
'''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 major 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 ==
[[File:SculpEufaDem10-12-15-onD.mp3|none|thumb|10:12:15 "Root position"]]
[[File:SculpEufaDem12-15-20-onD.mp3|none|thumb|12:15:20 "1st inversion"]]
[[File:SculpEufaDem15-20-24-onD.mp3|none|thumb|15:20:24 "2nd inversion"]]
== Voicings and rotations around two octaves ==
{| class="wikitable sortable" style="text-align:center;"
|+
! style="width:90px;" {{diagonal split header|Rotation|Voicing}}
! style="width:90px;" | Root
! style="width:90px;" | '3
! style="width:90px;" | '15
! style="width:90px;" | '''<nowiki/>'''<nowiki/>'3'15
|-
! style="width:90px;" | On 3
| style="width:90px;" data-sort-value="012-015-040" | 12:15:40
| style="width:90px;" data-sort-value="006-010-015" | 6:10:15
| style="width:90px;" data-sort-value="006-015-020" | 6:15:20
| style="width:90px;" data-sort-value="012-015-020" | ''12:15:20''
|-
! style="width:90px;" | On 5
| style="width:90px;" data-sort-value="010-012-015" | ''10:12:15''
| style="width:90px;" data-sort-value="010-015-024" | 10:15:24
| style="width:90px;" data-sort-value="005-006-015" | 5:6:15
| style="width:90px;" data-sort-value="005-012-015" | 5:12:15
|-
! style="width:90px;" | On 15
| style="width:90px;" data-sort-value="015-040-048" | 15:40:48
| style="width:90px;" data-sort-value="015-024-040" | 15:24:40
| style="width:90px;" data-sort-value="015-020-024" | ''15:20:24''
| style="width:90px;" data-sort-value="015-020-048" | 15:20:48
|}
== Related chords ==
Common tetrads based on this triad (5-limit except where noted):
Common tetrads based on this triad (5-limit except where noted):


* [[10:12:15:18]] adds 9/5
* [[4:5:6]] - chord inversion
* [[30:36:45:50]] adds 5/3
* [[10:12:15:18]] adds [[9/5]]
* [[70:84:105:120]] (12:10:8:7) adds 12/7 (7-limit)
* [[30:36:45:50]] adds [[5/3]]
 
* [[60:70:84:105]] - adds 8/7 (7-limit)
{{todo|inline=1|expand}}


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

Revision as of 18:59, 10 November 2025

Chord information
Harmonics 10:12:15
Subharmonics 1/(6:5:4)
Intervals from root 1/1–6/5–3/2
Cents from root 0¢–316¢–702¢
Step intervals 6/5, 5/4
Step cents 316¢, 386¢
Color name gu or g
Prime limit 5
Genus 3⋅5 (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 the utonal minor triad, also known as the classical minor triad, classical minor triad, or more generally - albeit less precisely - as the just major 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):

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