10:12:15: Difference between revisions

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'''10:12:15''' is a [[minor triad]] found on the iii ({{Frac|5|4}}) and vi ({{Frac|5|3}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common [[5-limit]] diatonic.

'''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]].

~~Unlike the~~ other 5-limit minor ([[27:32:40]]), 10:12:15 is [[~~utonal~~]].

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.

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.

[[Category:Minor triads|#@]]

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 {{Infobox Chord|ColorName=gu or g}}
-'''10:12:15''' is a [[minor triad]] found on the iii ({{Frac|5|4}}) and vi ({{Frac|5|3}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common [[5-limit]] diatonic.
+'''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]].
-Unlike the other 5-limit minor ([[27:32:40]]), 10:12:15 is [[utonal]].
+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.
+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.
 [[Category:Minor triads|#@]] <!-- 2-digit first number -->
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