4/1: Difference between revisions

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Added FJS name, slight expansion, misc. edits, categories
Note compositeness
 
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{{Infobox Interval
{{Infobox Interval
| Ratio = 4/1
| Name = 4th harmonic, double octave, perfect fifteenth, tetrave, quadruple
| Monzo = 2
| Cents = 2400.00000
| Name = 4th harmonic, <br>tetrave, <br>double octave
| Color name = wa 15th
| Color name = wa 15th
| FJS name = P15
| Sound = jid_4_1_pluck_adu_dr110.mp3
| Sound = jid_4_1_pluck_adu_dr110.mp3
}}
}}
{{Wikipedia| Fifteenth }}


'''4/1''' is the 4th [[harmonic]], or the '''tetrave'''; two octaves: ([[2/1]])<sup>2</sup>.
'''4/1''', the '''4th harmonic''', '''double octave''', '''perfect fifteenth''', '''tetrave''' or '''quadruple''', is the [[harmonic]] past [[3/1]] and before [[5/1]]. It is the first composite harmonic, equal to a stack of two [[octave]]s: ([[2/1]])<sup>2</sup>.
 
It can act as the [[interval of equivalence]] in temperaments that omit every other octave, such as [[meansquared]].


== See also ==
== See also ==
* [[Ed4]] – Equal divisions of the 4th harmonic
* [[Ed4]] – equal divisions of the 4th harmonic


[[Category:2-limit]]
[[Category:Taxicab-2 intervals]]
[[Category:Harmonics]]
[[Category:Pages with internal sound examples]]

Latest revision as of 10:45, 2 April 2025

Interval information
Ratio 4/1
Factorization 22
Monzo [2
Size in cents 2400¢
Names 4th harmonic,
double octave,
perfect fifteenth,
tetrave,
quadruple
Color name wa 15th
FJS name [math]\displaystyle{ \text{P15} }[/math]
Special properties harmonic,
highly composite harmonic
Tenney height (log2 nd) 2
Weil height (log2 max(n, d)) 4
Wilson height (sopfr(nd)) 4

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

4/1, the 4th harmonic, double octave, perfect fifteenth, tetrave or quadruple, is the harmonic past 3/1 and before 5/1. It is the first composite harmonic, equal to a stack of two octaves: (2/1)2.

It can act as the interval of equivalence in temperaments that omit every other octave, such as meansquared.

See also

  • Ed4 – equal divisions of the 4th harmonic