5/1: Difference between revisions

(8 intermediate revisions by 6 users not shown)

Line 1:

{{Infobox Interval

~~| Ratio = 5/1~~

| Name = 5th harmonic, pentave, quintuple

~~| Monzo = 0 0 1~~

~~| Cents = 2786.31371~~

| Name = 5th harmonic, ~~ ~~pentave

| Color name = ccy3, cocoyo 3rd

~~| FJS name = M175~~

| Sound = jid_5_1_pluck_adu_dr110.mp3

}}

'''5/1''', the '''5th harmonic''', '''pentave''' or '''quintuple''', is the [[harmonic]] past [[4/1]] and before [[6/1]]. It is two [[octave]]s above [[5/4]], and is the basis of [[5-limit]] harmony, as many 5-limit intervals can be expressed as the difference between this and another harmonic.

~~'''~~5/1~~'''~~ is the ~~5th [[harmonic]], or~~ the ~~'''pentave'''; two octaves above~~ [[5/4|~~5/4~~]].

5/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]].

~~5/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the~~ [[~~81/80|syntonic comma~~]].

== See also ==

* [[Ed5]] – equal divisions of the 5th harmonic

== References ==

~~https:~~//~~oeis.org~~/~~A081464~~

* {{OEIS|A081464}} – Numbers ''k'' such that the fractional part of (3/2)''k'' decreases monotonically to zero

* {{OEIS|A267122}} – Numbers ''n'' such that (3/2)n is closer to an integer than (3/2)m for any 0 < ''m'' < ''n''

~~[[Category:5-limit]]~~

~~[[Category:Harmonics]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 5/1
+| Name = 5th harmonic, pentave, quintuple
-| Monzo = 0 0 1
-| Cents = 2786.31371
-| Name = 5th harmonic, <br>pentave
 | Color name = ccy3, cocoyo 3rd
-| FJS name = M17<sup>5</sup>
 | Sound = jid_5_1_pluck_adu_dr110.mp3
 }}
+'''5/1''', the '''5th harmonic''', '''pentave''' or '''quintuple''', is the [[harmonic]] past [[4/1]] and before [[6/1]]. It is two [[octave]]s above [[5/4]], and is the basis of [[5-limit]] harmony, as many 5-limit intervals can be expressed as the difference between this and another harmonic.
-'''5/1''' is the 5th [[harmonic]], or the '''pentave'''; two octaves above [[5/4|5/4]].
+/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]].
-/1 is on a list of integer harmonics that approximate closest a given stack of fifths, the error being the [[81/80|syntonic comma]].
+== See also ==
+* [[Ed5]] – equal divisions of the 5th harmonic
 == References ==
-https://oeis.org/A081464
+* {{OEIS|A081464}} – Numbers ''k'' such that the fractional part of (3/2)<sup>''k''</sup> decreases monotonically to zero
+* {{OEIS|A267122}} – Numbers ''n'' such that (3/2)<sup>n</sup> is closer to an integer than (3/2)<sup>m</sup> for any 0 < ''m'' < ''n''
-[[Category:5-limit]]
-[[Category:Harmonics]]