3/2: Difference between revisions

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| en =

| es =

| ja =

| ja =3/2

| ko =

| ro = 3/2 (ro)

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'''3/2''', the '''just perfect fifth''', is a very [[consonance|consonant]] interval, due to the numerator and denominator of its ratio being very small numbers, with only the [[~~2/1|~~octave]] and the [[3/1|tritave]] having smaller numbers. As such, it is very important in western music and many musical traditions, and approximating it is key in systems like [[12edo]] and other [[edo]]s.

'''3/2''', the '''just perfect fifth''', is a very [[consonance|consonant]] interval, due to the numerator and denominator of its ratio being very small numbers, with only the [[octave]] and the [[3/1|tritave]] having smaller numbers. As such, it is very important in western music and many musical traditions, and approximating it is key in systems like [[12edo]] and other [[edo]]s.

For harmonic [[timbre]]s, the loudest harmonics are usually the second and third ones (2/1 and 3/1). 3/2 is the interval between these two harmonics (which incidentally makes 3/2 [[superparticular]]). Thus 3/2 is easy to tune by ear, and it is easy to hear if it is mistuned.

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Because 3/2 is a very simple and concordant interval, it is still recognizable even when heavily tempered. Often it is tempered so that an octave-reduced stack of fourths or fifths approximates some other interval. Some examples:

[[Meantone]] temperament flattens the fifth from just (to around 695–700 cents) such that the major third generated by stacking four fifths is closer to (or even identical to) 5/4. The minor ~~3rd~~ generated by stacking three fourths is closer to 6/5.

[[Meantone]] temperament flattens the fifth from just (to around 695–700 cents) such that the major third generated by stacking four fifths is closer to (or even identical to) 5/4. The minor third generated by stacking three fourths is closer to 6/5.

[[Superpyth]] temperaments ''sharpen'' the fifth from just so that the major third is closer to 9/7 and the minor third is closer to 7/6. Thus the minor seventh 16/9 approximates 7/4 instead of 9/5.

* One may choose to prioritize the accurate tuning of either the thirds or the harmonic seventh, leading to a ~710{{c}} tuning when prioritizing the thirds, or a ~715{{c}} tuning when prioritizing 7/4.

[[Schismic]] temperament adjusts the fifth such that the ''diminished fourth'' generated by stacking eight fourths approximates 5/4. As this is already a close approximation, the tuning of the fifth can be varied around its just tuning, but is most accurately flattened by a tiny amount. Thus a triad with 5/4 is written as {{nowrap|{{dash|C, F♭, G}}}} (unless the notation has accidentals for [[81/80]], e.g. {{nowrap|{{dash|C, vE, G}}}}).

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== As a dyad ==

{{Infobox Chord

'''2:3''' is a 3-limit [[dyad]], known as the '''five chord''' (as in C5 not V), or ~~as the '~~''power chord'''. ~~This dyad~~ is indispensable in certain musical genres such as [[African music #Equiheptatonic tunings|mbira music]] and late medieval music. In the latter, when voiced as ~~hi5add8~~, it's known as the '''trine''', a very common closing chord.

| 2:3

| ColorName=5

| debug=1

}}

'''2:3''' is a 3-limit [[dyad]], known as the ''five chord'' (as in C5 not V) or ''power chord''. It is used to create an open, stable, and powerful sound in contemporary western music. It is also indispensable in certain musical genres such as [[African music #Equiheptatonic tunings|mbira music]] and late medieval music. In the latter, when voiced as '''1:2:3''', it is known as the ''trine'', a very common closing chord.

=== Notable voicings ===

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 | en =
 | es =
-| ja =
+| ja =3/2
 | ko =
 | ro = 3/2 (ro)
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 {{Wikipedia|Perfect fifth}}
-'''3/2''', the '''just perfect fifth''', is a very [[consonance|consonant]] interval, due to the numerator and denominator of its ratio being very small numbers, with only the [[2/1|octave]] and the [[3/1|tritave]] having smaller numbers. As such, it is very important in western music and many musical traditions, and approximating it is key in systems like [[12edo]] and other [[edo]]s.
+'''3/2''', the '''just perfect fifth''', is a very [[consonance|consonant]] interval, due to the numerator and denominator of its ratio being very small numbers, with only the [[octave]] and the [[3/1|tritave]] having smaller numbers. As such, it is very important in western music and many musical traditions, and approximating it is key in systems like [[12edo]] and other [[edo]]s.
 For harmonic [[timbre]]s, the loudest harmonics are usually the second and third ones (2/1 and 3/1). 3/2 is the interval between these two harmonics (which incidentally makes 3/2 [[superparticular]]). Thus 3/2 is easy to tune by ear, and it is easy to hear if it is mistuned.
@@ Line 28: / Line 28: @@
 Because 3/2 is a very simple and concordant interval, it is still recognizable even when heavily tempered. Often it is tempered so that an octave-reduced stack of fourths or fifths approximates some other interval. Some examples:
-[[Meantone]] temperament flattens the fifth from just (to around 695–700 cents) such that the major third generated by stacking four fifths is closer to (or even identical to) 5/4. The minor 3rd generated by stacking three fourths is closer to 6/5.
+[[Meantone]] temperament flattens the fifth from just (to around 695–700 cents) such that the major third generated by stacking four fifths is closer to (or even identical to) 5/4. The minor third generated by stacking three fourths is closer to 6/5.
 [[Superpyth]] temperaments ''sharpen'' the fifth from just so that the major third is closer to 9/7 and the minor third is closer to 7/6. Thus the minor seventh 16/9 approximates 7/4 instead of 9/5.
-* One may choose to prioritize the accurate tuning of either the thirds or the harmonic seventh, leading to a ~710{{c}} tuning when prioritizing the thirds, or a ~715{{c}} tuning when prioritizing 7/4.
 [[Schismic]] temperament adjusts the fifth such that the ''diminished fourth'' generated by stacking eight fourths approximates 5/4. As this is already a close approximation, the tuning of the fifth can be varied around its just tuning, but is most accurately flattened by a tiny amount. Thus a triad with 5/4 is written as {{nowrap|{{dash|C, F♭, G}}}} (unless the notation has accidentals for [[81/80]], e.g. {{nowrap|{{dash|C, vE, G}}}}).
@@ Line 265: / Line 263: @@
 == As a dyad ==
-{{Infobox Chord|2:3|ColorName=5|debug=1}}
+{{Infobox Chord
-'''2:3''' is a 3-limit [[dyad]], known as the '''five chord''' (as in C5 not V), or as the '''power chord'''. This dyad is indispensable in certain musical genres such as [[African music #Equiheptatonic tunings|mbira music]] and late medieval music. In the latter, when voiced as hi5add8, it's known as the '''trine''', a very common closing chord.
+| 2:3
+| ColorName=5
+| debug=1
+}}
+'''2:3''' is a 3-limit [[dyad]], known as the ''five chord'' (as in C5 not V) or ''power chord''. It is used to create an open, stable, and powerful sound in contemporary western music. It is also indispensable in certain musical genres such as [[African music #Equiheptatonic tunings|mbira music]] and late medieval music. In the latter, when voiced as '''1:2:3''', it is known as the ''trine'', a very common closing chord.
 === Notable voicings ===