Editing Perfect fifth (section)

== Alternative definitions <span id="term_perfect_anchor" class="anchor"></span>==

The term ''perfect'' identifies the perfect fifth as belonging to the group of ''perfect intervals'' (including the [[unison]], [[perfect fourth]], and [[octave]]), so called because of their simple pitch relationships and their high degree of [[consonance and dissonance|consonance]].<ref>{{cite book |last1=Piston |first1=Walter |author1-link=Walter Piston |last2=de&#x202f;Voto |first2=Mark |year=1987 |title=Harmony |edition=5th |place=New York, NY |publisher=W.W. Norton |page=15 |isbn=0-393-95480-3 |quote=Octaves, perfect intervals, thirds, and sixths are classified as being 'consonant intervals', but thirds and sixths are qualified as 'imperfect consonances'.}}</ref> When an instrument with only twelve notes to an octave (such as the piano) is tuned using [[Pythagorean tuning]], one of the twelve fifths (the [[wolf interval|wolf fifth]]) sounds severely discordant and can hardly be qualified as "perfect", if this term is interpreted as "highly consonant". However, when using correct [[enharmonic]] spelling, the wolf fifth in Pythagorean tuning or meantone temperament is actually not a perfect fifth but a [[diminished sixth]] (for instance G{{Music|sharp}}–E{{Music|flat}}).

Perfect intervals are also defined as those natural intervals whose [[Inversion (interval)|inversions]] are also natural, where natural, as opposed to altered, designates those intervals between a base note and another note in the major diatonic scale starting at that base note (for example, the intervals from C to C, D, E, F, G, A, B, C, with no sharps or flats); this definition leads to the perfect intervals being only the [[unison]], [[perfect fourth|fourth]], fifth, and [[octave]], without appealing to degrees of consonance.<ref>{{cite book | title = Harmony and Analysis | author =Kenneth McPherson Bradley | publisher = C. F. Summy| year = 1908 | page = 17 | url = https://books.google.com/books?id=QsAPAAAAYAAJ&q=intitle:Harmony+perfect-interval&pg=PA16 }}</ref>

The term ''perfect'' has also been used as a synonym of ''[[just interval|just]]'', to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as [[equal temperament]].<ref>{{cite book|title=Penny Cyclopaedia|author=Charles Knight|author-link=Charles Knight (publisher)|publisher=Society for the Diffusion of Useful Knowledge|year=1843|page=356|url=https://books.google.com/books?id=muBPAAAAMAAJ&q=%22perfect+fifth%22+%22imperfect+fifth%22+tempered&pg=PA356}}</ref><ref>{{cite book | title = Yearning for the Impossible |author=[[John Stillwell]]| publisher = A. K. Peters| year = 2006 | isbn = 1-56881-254-X | page = [https://archive.org/details/yearningforimpos0000stil/page/21 21] | url = https://archive.org/details/yearningforimpos0000stil | url-access = registration | quote = perfect fifth imperfect fifth tempered. }}</ref> The perfect unison has a [[interval ratio|pitch ratio]] 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2.

Within this definition, other intervals may also be called perfect, for example a perfect third (5:4)<ref>{{cite book | title = Music and Sound | author = Llewelyn Southworth Lloyd | publisher = Ayer Publishing | year = 1970 | isbn = 0-8369-5188-3 | page = 27 | url = https://books.google.com/books?id=LxTwmfDvTr4C&q=%22perfect+third%22++%22perfect+major%22&pg=PA27 }}</ref> or a perfect [[major sixth]] (5:3).<ref>{{cite book | title = Musical Acoustics | author = John Broadhouse | publisher = W. Reeves | year = 1892 | page = [https://archive.org/details/musicalacoustic00broagoog/page/n292 277] | url = https://archive.org/details/musicalacoustic00broagoog | quote = perfect major sixth ratio. }}</ref>