Editing Equal temperament (section)

=== Seven-tone equal division of the fifth ===
Violins, violas, and cellos are tuned in perfect fifths ({{sc|'''G D A E'''}} for violins and {{sc|'''C G D A'''}} for violas and cellos), which suggests that their semitone ratio is slightly higher than in conventional 12&nbsp;tone equal temperament. Because a perfect fifth is in 3:2&nbsp;relation with its base tone, and this interval comprises seven steps, each tone is in the ratio of <math display=inline>\sqrt[7]{3/2}</math> to the next (100.28&nbsp;cents), which provides for a perfect fifth with ratio of 3:2, but a slightly widened octave with a {{nobr|ratio of ≈ 517:258 or ≈ 2.00388:1}} rather than the usual 2:1, because 12&nbsp;perfect fifths do not equal seven octaves.<ref>
{{cite web
 |last=Cordier |first=Serge
 |title=Le tempérament égal à quintes justes |lang=fr
 |publisher=Association pour la Recherche et le Développement de la Musique
 |website=aredem.online.fr
 |url=http://aredem.online.fr/aredem/page_cordier.html
 |access-date=2010-06-02
}}
</ref> During actual play, however, violinists choose pitches by ear, and only the four unstopped pitches of the strings are guaranteed to exhibit this 3:2&nbsp;ratio.