# 五度圏

## 注釈

1. ^ 12の純正な完全5度の周波数比
${\displaystyle \left({\frac {3}{2}}\right)^{12}=129.746337890625}$
は、7オクターヴの周波数比
${\displaystyle \left({\frac {2}{1}}\right)^{7}=128}$
に対し
${\displaystyle {\frac {\left({\frac {3}{2}}\right)^{12}}{\left({\frac {2}{1}}\right)^{7}}}={\frac {531441}{524288}}=1.0136432647705078125}$
の差が生じる。

## 出典

1. ^ a b c d William Drabkin, “Circle of fifths,” in The New Grove Dictionary of Music and Musicians, 2nd ed., ed. by Stanley Sadie (London: Macmillan, 2001), vol. 5, pp. 866-867.
2. ^ Margo Schulter, Pythagorean Tuning and Medieval Polyphony, (http://www.medieval.org/emfaq/harmony/pyth.html), 1998.
3. ^ Mark Lindley, “Temperaments,” in The New Grove Dictionary of Music and Musicians, 2nd ed., ed. by Stanley Sadie (London: Macmillan, 2001), vol. 25, pp. 248-269.
4. ^ Ryan J. Thomson, A Folk Musicians Working Guide to Chords, Keys, Scales, and More, Captain Fiddle Publications, 1991, p. 52.
5. ^ “Circle of fifths,” in The New Oxford Companion to Music, ed. by Denis Arnold, Oxford University Press, 1983, vol. 1, p. 399.