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 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.  
'''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]], with the major third replaced by a minor third.  


== Rotations around the octave ==
== Audio of close voicings ==
[[File:SculpEufaDem10-12-15-onD.mp3|none|thumb|10:12:15 "Root position"]]
[[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: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"]]
[[File:SculpEufaDem15-20-24-onD.mp3|none|thumb|15:20:24 2nd inversion]]


== Voicings and rotations around two octaves ==
== Notable voicings ==
{| class="wikitable sortable" style="text-align:center;"
Voicings are identified with [[Kite's thoughts on hi-lo notation|Hi-lo notation]]. AOV  and CAOV stand for (condensed) [[Odd limit#Proposed extensions|all-odd voicing]].
|+
 
! style="width:90px;" {{diagonal split header|Rotation|Voicing}}
3 voices:  
! style="width:90px;" | Root
 
! style="width:90px;" | '3
* 10:12:15 (6:5:4) - close voicing
! style="width:90px;" | '15
* 6:10:15 (5:3:2) - lo3, CAOV
! style="width:90px;" | '''<nowiki/>'''<nowiki/>'3'15
* 3:5:15 (5:3:1) - lo3hi5, AOV
|-
* 12:15:20 (5:4:3) - 1st inversion
! style="width:90px;" | On 3
* 15:20:24 (8:6:5) - 2nd inversion
| style="width:90px;" data-sort-value="012-015-040" | 12:15:40
* 10:15:24 (12:8:5) - hi3
| style="width:90px;" data-sort-value="006-010-015" | 6:10:15
 
| style="width:90px;" data-sort-value="006-015-020" | 6:15:20
4 voices:
| style="width:90px;" data-sort-value="012-015-020" | ''12:15:20''
 
|-
* 10:12:15:20 (6:5:4:3) - add8
! style="width:90px;" | On 5
* 10:15:20:24 (12:8:6:5) - hi3add8
| 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 ==
== Related chords ==
Common tetrads based on this triad (5-limit except where noted):
Melodic inversion: [[4:5:6]]
 
Notable extensions (5-limit except where noted):


* [[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 below root (7-limit)
* [[70:84:105:120]] (12:10:8:7) – adds 12/7 (7-limit)
* [[70:84:105:120]] – adds 12/7 (7-limit); homonym of 60:70:84:105
* [[60:70:84:105]] (7:6:5:4) – a homonym of the previous chord


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

Revision as of 01:51, 19 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 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, with the major third replaced by a minor third.

Audio of close voicings

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

Notable voicings

Voicings are identified with Hi-lo notation. AOV and CAOV stand for (condensed) all-odd voicing.

3 voices:

  • 10:12:15 (6:5:4) - close voicing
  • 6:10:15 (5:3:2) - lo3, CAOV
  • 3:5:15 (5:3:1) - lo3hi5, AOV
  • 12:15:20 (5:4:3) - 1st inversion
  • 15:20:24 (8:6:5) - 2nd inversion
  • 10:15:24 (12:8:5) - hi3

4 voices:

  • 10:12:15:20 (6:5:4:3) - add8
  • 10:15:20:24 (12:8:6:5) - hi3add8

Related chords

Melodic inversion: 4:5:6

Notable extensions (5-limit except where noted):

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