3/1: Difference between revisions

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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.

The '''tritave''', '''3rd harmonic''', or '''perfect twelfth''' is the [[interval]] of [[frequency ratio]] '''3/1'''. 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.

~~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 perceived prefix ''octo-'' (eight, for the eighth degree of the diatonic scale) by ''tri-'' (three, for 3/1). It should be noted, however, that the ''oct'' in ''octave'' is not a prefix, but part of the single-morpheme word derived from Latin ''octavus'' (eighth).

The term ''tritave'' was coined by [[John Pierce]]<ref>[https://www.huygens-fokker.org/bpsite/intervals.html ''The Bohlen-Pierce Site: BP Interval Properties'']</ref>. It was derived from the word ''octave'' by replacing the perceived prefix ''octo-'' (eight, for the eighth degree of the diatonic scale) by ''tri-'' (three, for 3/1). It should be noted, however, that the ''oct'' in ''octave'' is not a prefix, but part of the single-morpheme word derived from Latin ''octavus'' (eighth).

== See also ==

* [[EDT]] (equal divisions of the tritave)

* [[EDT]] (equal divisions of the tritave/twelfth)

* [[No-twos 31-limit]] – non-octave 31-limit system containing neither 2 nor primes higher than 31

* [[Tritave complement]] – the analogue for [[octave complement]]

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-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.
+The '''tritave''', '''3rd harmonic''', or '''perfect twelfth''' is the [[interval]] of [[frequency ratio]] '''3/1'''. 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.
-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 perceived prefix ''octo-'' (eight, for the eighth degree of the diatonic scale) by ''tri-'' (three, for 3/1). It should be noted, however, that the ''oct'' in ''octave'' is not a prefix, but part of the single-morpheme word derived from Latin ''octavus'' (eighth).
+The term ''tritave'' was coined by [[John Pierce]]<ref>[https://www.huygens-fokker.org/bpsite/intervals.html ''The Bohlen-Pierce Site: BP Interval Properties'']</ref>. It was derived from the word ''octave'' by replacing the perceived prefix ''octo-'' (eight, for the eighth degree of the diatonic scale) by ''tri-'' (three, for 3/1). It should be noted, however, that the ''oct'' in ''octave'' is not a prefix, but part of the single-morpheme word derived from Latin ''octavus'' (eighth).
 == See also ==
-* [[EDT]] (equal divisions of the tritave)
+* [[EDT]] (equal divisions of the tritave/twelfth)
 * [[No-twos 31-limit]] – non-octave 31-limit system containing neither 2 nor primes higher than 31
 * [[Tritave complement]] – the analogue for [[octave complement]]