4:5:6: Difference between revisions

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 {{Infobox Chord|ColorName=yo or y}}
-'''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.
+'''4:5:6''' is an otonal [[major triad]], known as the '''just major triad''', '''classical major triad''', or '''Ptolemaic major triad'''. It is the most consonant triad, and it is the most common triad in music. In close voicing root position, it is an [[Delta-rational chord #Isoharmonic chord|isoharmonic chord]]. It occurs as a major triad in the [[meantone]] diatonic scale, as the major third formed by stacking four [[3/2|perfect fifths]] octave reduced, [[81/64]], is equated with [[5/4]]. It serves as the fundamental major root chord in classical music, and approximating is key in [[5-limit]] temperaments. This chord is approximated with all intervals having less than 20{{c}} of error in [[edo]]s {{EDOs|12, 15, 19, 22, 24, 26, 27}}, etc.
-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.
+This chord is formed by stacking [[5/4]] and [[6/5]] in that order. Swapping the order of these intervals results in [[10:12:15]], the classical minor triad. The minor triad can also be obtained from 4:5:6 by flattening the third by [[25/24]], the diptolemaic chromatic semitone.
-Common tetrads based on this triad (5-limit except where noted):
+== Audio of close voicings ==
+[[File:SculpEufaDem4-5-6-onD.mp3|none|thumb|4:5:6, Root position]]
+[[File:SculpEufaDem5-6-8-onD.mp3|none|thumb|5:6:8, 1st inversion]][[File:SculpEufaDem3-4-5-onD.mp3|none|thumb|3:4:5, 2nd inversion]]
-* [[12:15:18:20]] adds 5/3
+== Approximation by edos ==
-* [[8:10:12:15]] adds 15/8
+[[7edo]] contains a rough approximation to 4:5:6, which equates the 5/4 and 6/5 steps. The smallest edo to approximate it with acceptable accuracy is [[12edo]], with [[19edo]] being the next edo to improve on it.
-* [[36:45:54:64]] adds 16/9
+{{chord edo approximation}}
-* [[20:25:30:36]] adds 9/5
-* [[4:5:6:7]] adds 7/4 (7-limit)
+== Notable voicings ==
-* [[12:15:18:22]] adds 11/6 (11-limit)
+Voicings are arranged from simple to complex using [[Wilson norm]]. AOV and CAOV stand for [[Odd limit #Proposed extensions|all-odd voicing]] and ''condensed'' AOV respectively. Numbers in '''bold''' denote doubled pitches. This list is only a brief overview, see [[Voicings of 4:5:6]] for a more comprehensive list and audio examples.
+{| class="wikitable"
+! Voices
+! [[EFR]]
+! [[Kite's thoughts on hi-lo notation|Hi-lo name]]
+! Special properties
+|-
+| rowspan="4" |3 voices
+| 1:3:5
+| hi3loR
+| AOV, [[Delta-rational chord #Isoharmonic chord|isoharmonic]]
+|-
+| 2:3:5
+| hi3
+| CAOV
+|-
+| 3:4:5
+| lo5
+| 1st inversion, isoharmonic
+|-
+| 4:5:6
+| basic
+| isoharmonic
+|-
+| rowspan="4" |4 voices
+| 2:3:'''4''':5
+| hi3add8
+| isoharmonic
+|-
+| 2:'''4''':5:6
+| addloR
+|
+|-
+| 3:4:5:'''6'''
+| addlo5
+| isoharmonic
+|-
+| 4:5:6:'''8'''
+| add8
+|
+|}
+== Related chords ==
+Melodic inversion: 1/(6:5:4) = [[10:12:15]].
+Plausible [[chord homonym|homonyms]]: None.
+Lower limit soundalikes: [[64:81:96]] (3-limit)
+Notable extensions (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)
 [[Category:Major triads|#]] <!-- 1-digit first number -->