3/1: Difference between revisions

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| Cents = 1901.95500
| Cents = 1901.95500
| Name = tritave, <br>3rd harmonic, <br>perfect twelfth
| Name = tritave, <br>3rd harmonic, <br>perfect twelfth
| Color name =  
| Color name = w12, wa 12th
| Sound = jid_3_1_pluck_adu_dr220.mp3
| Sound = jid_3_1_pluck_adu_dr220.mp3
}}
}}
The '''third harmonic''' or '''tritave''' is another name of the 3rd [[partial tone]], the interval with the [[frequency ratio]] of '''3/1''', one octave above [[3/2]].
The '''tritave''' (interval [[ratio]] '''3/1''') is the [[interval]] between a fundamental tone and its '''3rd harmonic'''. It is perhaps the most [[consonance|consonant]] interval after the [[octave]]. For this reason, it is used as an [[equave]] in some [[nonoctave]] systems, such as the [[Bohlen-Pierce]] scale.


It is perhaps the most [[consonance|consonant]] [[interval]] larger than an [[octave]]. Used as an [[interval of equivalence]] in some [[nonoctave]] systems, such as [[Bohlen-Pierce]], where it may be referred to as the ''tritave''.
The tritave is one octave above [[3/2]], the perfect fifth. Therefore, in a [[5L 2s|diatonic]] context, 3/1 is also called the '''perfect twelfth'''.
 
== Etymology ==
The term ''tritave'' was coined by [[John Pierce]]<ref>https://www.huygens-fokker.org/bpsite/intervals.html</ref>. It was derived from the word ''octave'' by replacing the prefix ''octo-'' (eight, for 8 notes in an octave span of the diatonic scale) by ''tri-'' (three, for 3/1).


== See also ==
== See also ==
* [[EDT]] -- systems dividing the tritave equally, see.
* [[EDT]] (equal divisions of the tritave)
* [[Bohlen-Pierce]] -- systems with the tritave as the just fundamental harmonic
* [[No-twos 31-limit]] -- non-octave 31-limit system containing neither 2 nor primes higher than 31
* [[No-twos 31-limit]] -- non-octave 31-limit system containing neither 2 nor primes higher than 31
* [[3/2]] - the just perfect fifth as the [[octave reduced]] counterpart of the tritave
* [[Tritave complement]] -- the analogue for [[octave complement]]
* [[Tritave complement]] -- the analogue for [[octave complement]]


== References ==
<references />


[[Category:Tritave| ]] <!-- main article -->
[[Category:Harmonics]]
[[Category:Terms]]
[[Category:Terms]]
[[Category:Definition]]
[[Category:Tritave| ]] <!-- main article -->
[[Category:Just interval]]
[[Category:Partial tone]]


[[Category:Todo:expand]]
[[Category:Todo:expand]]

Revision as of 18:58, 11 December 2021

Interval information
Ratio 3/1
Factorization 3
Monzo [0 1⟩
Size in cents 1901.955¢
Names tritave,
3rd harmonic,
perfect twelfth
Color name w12, wa 12th
FJS name [math]\displaystyle{ \text{P12} }[/math]
Special properties harmonic,
prime harmonic
Tenney norm (log2 nd) 1.58496
Weil norm (log2 max(n, d)) 3.16993
Wilson norm (sopfr(nd)) 3

[sound info]
Open this interval in xen-calc

The tritave (interval ratio 3/1) is the interval between a fundamental tone and its 3rd harmonic. It is perhaps the most consonant interval after the octave. For this reason, it is used as an equave in some nonoctave systems, such as the Bohlen-Pierce scale.

The tritave is one octave above 3/2, the perfect fifth. Therefore, in a diatonic context, 3/1 is also called the perfect twelfth.

Etymology

The term tritave was coined by John Pierce[1]. It was derived from the word octave by replacing the prefix octo- (eight, for 8 notes in an octave span of the diatonic scale) by tri- (three, for 3/1).

See also

References

  1. ↑ https://www.huygens-fokker.org/bpsite/intervals.html
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