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The '''3rd harmonic''', '''tritave''', or '''perfect twelfth''' is the [[interval]] of [[frequency ratio]] '''3/1'''. It is perhaps the most [[ | The '''3rd harmonic''', '''tritave''', or '''perfect twelfth''' is the [[interval]] of [[frequency ratio]] '''3/1'''. 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. | ||
== Etymology == | == Etymology == | ||
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 [[Wiktionary: octavus #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 [[Wiktionary:octavus#Latin|''octavus'']] ("eighth"). | ||
Since the enneatonic | Since the enneatonic {{sl|4L 5s|3/1}} ("Lambda") scale is the BP substitute for the diatonic scale, the term ''decade'' (tenth degree of the Lambda scale) has been proposed as an alternative to tritave<ref>[https://www.youtube.com/watch?v=Ur6GOoSNGN0 12tone – How A Pair Of Microwave Engineers Broke Music]</ref>, though ''decade'' almost always refers to ten times the frequency ([[10/1]]) in audio engineering. | ||
== See also == | == See also == | ||
Revision as of 15:04, 9 January 2025
| Interval information |
tritave,
perfect twelfth
prime harmonic
[sound info]
The 3rd harmonic, tritave, or perfect twelfth is the interval of frequency ratio 3/1. 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.
Etymology
The term tritave was coined by John Pierce[1]. 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").
Since the enneatonic Template:Sl ("Lambda") scale is the BP substitute for the diatonic scale, the term decade (tenth degree of the Lambda scale) has been proposed as an alternative to tritave[2], though decade almost always refers to ten times the frequency (10/1) in audio engineering.
See also
- 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