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.

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 us a diatonic 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. 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.

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 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. 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.

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.

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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.
-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 us a diatonic 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.  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.
+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 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.  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.
 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.