4:5:6: Difference between revisions

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'''4:5:6''' is the classical [[major triad]], ~~and can~~ also ~~be referred to~~ as the '''Ptolemaic major triad'''. It ~~is found on~~ the ~~I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale (~~[[~~Zarlino~~]]), ~~which is perhaps the most common [[5~~-limit~~]] diatonic~~.

'''4:5:6''' is the classical [[major triad]], also known as the '''Ptolemaic major triad'''. It has the lowest [[odd limit]] of all the JI triads, odd-limit 5.

~~However, there are other 5-limit diatonic scales which don't have the Ptolemaic major triad occurring in all the same places. For instance, [[User:Aura|Aura]]~~ is ~~known to use a diatonic major scale in which this chord only occurs~~ on the I and V scale ~~degrees while using a Pythagorean major triad~~ (~~that is,~~ [[~~64:81:96~~]]) on the IV. Conversely, in the diatonic minor scale that Aura uses, this chord only really appears on the bVI. Compared to its Pythagorean counterpart, the Ptolemaic major triad sounds like it's more easily tonicized, a fact which Aura exploits in order to help stabilize Ionian mode in fixed pitch diatonic scales. Because of these properties, the Ptolemaic major triad has earned its status as a bread-and-butter chord in 5-limit ~~harmony~~.

It is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), a very common [[5-limit]] diatonic.

~~There are a number of possible~~ tetrads ~~which can be reasonably built off of~~ this triad~~, such as~~ [[36:45:54:64]] ~~and~~ [[20:25:30:36]] ~~in the~~ 5~~-limit, as well as~~ [[4:5:6:7]] ~~in the~~ 7-limit ~~and~~ [[32:40:48:55]] ~~in the~~ 11-limit.

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

* [[12:15:18:20]] adds 5/3

* [[8:10:12:15]] adds 15/8

* [[36:45:54:64]] adds 16/9

* [[20:25:30:36]] adds 9/5

* [[4:5:6:7]] adds 7/4 (7-limit)

* [[12:15:18:22]] adds 11/6 (11-limit)

[[Category:Major triads|#]]

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 {{Infobox Chord|ColorName=yo or y}}
-'''4:5:6''' is the classical [[major triad]], and can also be referred to as the '''Ptolemaic major triad'''. It is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), which is perhaps the most common [[5-limit]] diatonic.
+'''4:5:6''' is the classical [[major triad]], also known as the '''Ptolemaic major triad'''. It has the lowest [[odd limit]] of all the JI triads, odd-limit 5.
-However, there are other 5-limit diatonic scales which don't have the Ptolemaic major triad occurring in all the same places.  For instance, [[User:Aura|Aura]] is known to use a diatonic major scale in which this chord only occurs on the I and V scale degrees while using a Pythagorean major triad (that is, [[64:81:96]]) on the IV.  Conversely, in the diatonic minor scale that Aura uses, this chord only really appears on the bVI.  Compared to its Pythagorean counterpart, the Ptolemaic major triad sounds like it's more easily tonicized, a fact which Aura exploits in order to help stabilize Ionian mode in fixed pitch diatonic scales.  Because of these properties, the Ptolemaic major triad has earned its status as a bread-and-butter chord in 5-limit harmony.
+It is found on the I ({{Frac|1|1}}), IV ({{Frac|4|3}}), and V ({{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), a very common [[5-limit]] diatonic.
-There are a number of possible tetrads which can be reasonably built off of this triad, such as [[36:45:54:64]] and [[20:25:30:36]] in the 5-limit, as well as [[4:5:6:7]] in the 7-limit and [[32:40:48:55]] in the 11-limit.
+Common tetrads based on this triad (5-limit except where noted):
+* [[12:15:18:20]] adds 5/3
+* [[8:10:12:15]] adds 15/8
+* [[36:45:54:64]] adds 16/9
+* [[20:25:30:36]] adds 9/5
+* [[4:5:6:7]] adds 7/4 (7-limit)
+* [[12:15:18:22]] adds 11/6 (11-limit)
 [[Category:Major triads|#]] <!-- 1-digit first number -->