Editing Harmony (section)

=== Roughness ===
When adjacent harmonics in complex tones interfere with one another, they create the perception of what is known as "beating" or "roughness". These precepts are closely related to the perceived dissonance of chords.<ref>{{Cite journal|last1=Langner|first1=Gerald|last2=Ochse|first2=Michael|date=2006|title=The neural basis of pitch and harmony in the auditory system|url=http://dx.doi.org/10.1177/102986490601000109|journal=Musicae Scientiae|volume=10|issue=1_suppl|pages=185–208|doi=10.1177/102986490601000109|s2cid=144133151|issn=1029-8649|url-access=subscription}}</ref> To interfere, partials must lie within a critical bandwidth, which is a measure of the ear's ability to separate different frequencies.<ref>{{Cite journal|last1=Plomp|first1=R.|last2=Levelt|first2=W. J. M.|date=1965|title=Tonal Consonance and Critical Bandwidth|url=http://dx.doi.org/10.1121/1.1909741|journal=The Journal of the Acoustical Society of America|volume=38|issue=4|pages=548–560|doi=10.1121/1.1909741|pmid=5831012|bibcode=1965ASAJ...38..548P|issn=0001-4966|hdl=11858/00-001M-0000-0013-29B7-B|s2cid=15852125 |hdl-access=free}}</ref> Critical bandwidth lies between 2 and 3 semitones at high frequencies and becomes larger at lower frequencies.<ref>{{Cite journal|last1=Schellenberg|first1=E. Glenn|last2=Trehub|first2=Sandra E.|date=1994|title=Frequency ratios and the perception of tone patterns|journal=Psychonomic Bulletin & Review|volume=1|issue=2|pages=191–201|doi=10.3758/bf03200773|pmid=24203470|issn=1069-9384|doi-access=free}}</ref> The roughest interval in the [[chromatic scale]] is the [[Minor Second|minor second]] and its [[Inversion (music)|inversion]], the major seventh. For typical [[spectral envelope]]s in the central range, the second roughest interval is the major second and minor seventh, followed by the tritone, the minor third ([[major sixth]]), the major third ([[minor sixth]]) and the perfect fourth (fifth).<ref>{{Cite journal|last=Parncutt|first=Richard|date=1988|title=Revision of Terhardt's Psychoacoustical Model of the Root(s) of a Musical Chord|url=http://dx.doi.org/10.2307/40285416|journal=Music Perception|volume=6|issue=1|pages=65–93|doi=10.2307/40285416|jstor=40285416|issn=0730-7829|url-access=subscription}}</ref>