4:5:6: Difference between revisions

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Aura (talk | contribs)
autopatrolled, emailconfirmed
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TallKite (talk | contribs)
autopatrolled, Sysops
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Aura: your additions were too off-topic. This is a page about a chord, not a scale. I suggest moving your personal uses of chords and scales to a personal viewpoints page, e.g. "Aura's thoughts on...". Furthermore, 55/32 is too complex to be a common or reasonable 7th, so I replaced it with11/6.
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{{Infobox Chord|ColorName=yo or y}}
{{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 -->
[[Category:Major triads|#]] <!-- 1-digit first number -->

Revision as of 03:53, 29 October 2025

Chord information
Harmonics 4:5:6
Subharmonics 1/(15:12:10)
Intervals from root 1/1–5/4–3/2
Cents from root 0¢–386¢–702¢
Step intervals 5/4, 6/5
Step cents 386¢, 316¢
Color name yo or y
Prime limit 5
Genus 3⋅5 (15)
Intervallic odd limit 5
Otonal odd limit 5
Utonal odd limit 15
Consistent edos (d ≥ 2) 3edo*, 12edo*, 15edo*, 19edo**, …

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.

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

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

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