Interval of equivalence
An interval of equivalence is a musical interval at which pitches are perceived or treated as functionally equivalent, despite their different absolute frequencies. When an interval is established as the equivalence interval, all pitches separated by one or more instances of this interval are considered members of the same pitch class.
In a periodic scale, the interval of equivalence is typically the same as the period or a multiple thereof. Almost all notation systems give equivalent pitches the same name.
Octave equivalence
The octave (2/1) is the most common interval of equivalence. Tones separated by an octave are perceived as essentially the same. This equivalence is so strong that in most musical notation systems, notes separated by octaves share the same name. For the same reason, most scales repeat at the octave.
The physical basis for octave equivalence is believed to be caused by the harmonic structure of periodic sounds. When a tone with frequency f is played, it typically produces overtones at 2f, 3f, 4f, etc. The first overtone (2f) is an octave above the fundamental, creating a consistent pattern in many natural sounds. This harmonic relationship may contribute to the perceptual significance of the octave in human hearing.
The perception of octave equivalence appears to have both biological and cultural components. Studies have shown that various non-human animals, including rhesus monkeys and rats, experience octave equivalence to a certain extent.[1] However, the degree of octave equivalence perception varies across cultures, particularly in those with non-Western musical traditions.[2]
Non-octave equivalence
When the interval of equivalence is allowed to be a non-octave interval, it is called the equave (a portmanteau of "equivalence" and "octave") or formal octave[3]. While the octave is the predominant interval of equivalence in most musical traditions, alternative equivalence intervals have been explored. A famous example is the tritave in Bohlen–Pierce and related systems.
Pseudo-octave
A pseudo-octave is an interval that is not exactly 2/1, but close enough to still be treated as an octave.
Stretched or compressed tunings may be said to have pseudo-octaves, as do many non-octave scales. For example, the Carlos Beta scale has a pseudo-octave of 1212.8 ¢ at 19 steps.
Examples
- In octave-repeating scales, the equave is typically 2/1.
- In Bohlen–Pierce, the equave may be taken as 3/1.
- In an equal division of the fifth, the equave may be taken as a perfect fifth or less commonly a major ninth.
See also
References
- ↑ Hoeschele M. Animal Pitch Perception: Melodies and Harmonies. Comp Cogn Behav Rev. 2017
- ↑ Jacoby, Nori et al. Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing. Current Biology, 2019.
- ↑ Op de Coul M. Scala help https://www.huygens-fokker.org/scala/help.htm