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 classical [[minor triad]], and can also be referred to as the '''Ptolemaic minor triad'''.  It is found on the iii ({{Frac|5|4}}) and vi ({{Frac|5|3}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), which is perhaps the most common [[5-limit]] diatonic.  Unlike [[27:32:40]], which appears on the ii of the same scale, 10:12:15 is [[utonal]].
'''10:12:15''' is the just [[minor triad]], also known as the '''Ptolemaic minor triad'''.  


However, there are other 5-limit diatonic scales which don't have the Ptolemaic minor triad occurring in all the same places.  For instance, [[User:Aura|Aura]] is known to use a diatonic minor scale in which this chord only occurs on the i and iv scale degrees while using a Pythagorean minor triad (that is, [[54:64:81]]) on the v.  Conversely, in the diatonic major scale that Aura uses, this chord only really appears on the iii.  Compared to its Pythagorean counterpart, the Ptolemaic major triad sounds like it's more consonant.  Because of these properties, the Ptolemaic major triad has earned its status as a bread-and-butter chord in 5-limit harmony.
Common tetrads based on this triad (5-limit except where noted):


There are a number of possible tetrads which can be reasonably built off of this triad, such as [[10:12:15:18]] in the 5-limit, as well as [[70:84:105:120]] in the 7-limit and [[110:132:165:192]] in the 11-limit.
* [[10:12:15:18]] adds 9/5
* [[30:36:45:50]] adds 5/3
* [[70:84:105:120]] (12:10:8:7) adds 12/7 (7-limit)


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

Revision as of 21:00, 29 October 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 just minor triad, also known as the Ptolemaic minor triad.

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

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