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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 3/1 | | Ratio = 3/1 | ||
| Name = 3rd harmonic, tritave, perfect twelfth | | Name = 3rd harmonic, tritave, triple, perfect twelfth | ||
| Color name = w12, wa 12th | | Color name = w12, wa 12th | ||
| Sound = jid_3_1_pluck_adu_dr220.mp3 | | Sound = jid_3_1_pluck_adu_dr220.mp3 | ||
}} | }} | ||
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. | The '''3rd harmonic''', '''tritave''', '''triple''', 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). | 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). However, the ''oct'' in ''octave'' is not a prefix, but part of the single-morpheme word derived from Latin [[Wiktionary:octavus #Latin|''octavus'']] ("eighth"). In this sense, ''tritave'' is more of a contraction of ''tri-'' and ''octave'' than anything else. | ||
''Triple'' is a proposed term which relates itself to the ancient Greek concept of [[harmonic|multiples]]. It also fixes the problem of using part of the word ''octave''. | |||
Since the enneatonic {{mos scalesig|4L 5s<3/1>|link=1}} ("Lambda") scale is the BP substitute for the diatonic scale, the term ''decade''<ref>[https://www.youtube.com/watch?v=Ur6GOoSNGN0 12tone – How A Pair Of Microwave Engineers Broke Music]</ref> or ''decim''{{citation needed}} (tenth degree of the Lambda scale) has been proposed as an alternative to tritave, though ''decade'' almost always refers to ten times the frequency ([[10/1]]) in audio engineering. | Since the enneatonic {{mos scalesig|4L 5s<3/1>|link=1}} ("Lambda") scale is the BP substitute for the diatonic scale, the term ''decade''<ref>[https://www.youtube.com/watch?v=Ur6GOoSNGN0 12tone – How A Pair Of Microwave Engineers Broke Music]</ref> or ''decim''{{citation needed}} (tenth degree of the Lambda scale) has been proposed as an alternative to tritave, though ''decade'' almost always refers to ten times the frequency ([[10/1]]) in audio engineering. | ||
Revision as of 10:16, 31 March 2025
| Interval information |
tritave,
triple,
perfect twelfth
prime harmonic
[sound info]
The 3rd harmonic, tritave, triple, 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). However, the oct in octave is not a prefix, but part of the single-morpheme word derived from Latin octavus ("eighth"). In this sense, tritave is more of a contraction of tri- and octave than anything else.
Triple is a proposed term which relates itself to the ancient Greek concept of multiples. It also fixes the problem of using part of the word octave.
Since the enneatonic 4L 5s⟨3/1⟩ ("Lambda") scale is the BP substitute for the diatonic scale, the term decade[2] or decim[citation needed] (tenth degree of the Lambda scale) has been proposed as an alternative to tritave, 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