Pythagorean tuning: Difference between revisions

Line 15:

The Greeks used two systems of tuning based on ideal integer ratios: Pythagorean and Ptolemaic. The major difference is, Ptolemaic tuning uses simpler ratios, where as Pythagorean tuning uses a [[chain of fifths|chain of fifths and fourths]]. For example, a major third in Pythagorean would be [[81/64]] where as in Ptolemaic it is [[5/4]]. Later music theorists, such as {{w|Gioseffo Zarlino}}<ref>Chisholm, Hugh (1911). ''The Encyclopædia Britannica'', Vol. 28, p. 961. The Encyclopædia Britannica Company.</ref>during the Renaissance, would prefer the Ptolemaic tuning. Tuning systems based on those ratios are called [[just intonation]].

Pythagorean tuning was developed using method called the 'chain of fifths', where you multiply the pitch/frequency by a fifth (3/2) until you pass an octave. When you pass an octave, you take that same note, and move it down an octave by multiplying it by another ratio. Every ratio can be generated by a combination of 3/2 and 4/3. One old account of this method is ascribed to an anonymous source in a book by Iacobus de Ispania in the 13th century)<ref>Schulter, Margo ~~“Pythagorean~~ Tuning and Medieval ~~Polyphony”~~</ref>

Pythagorean tuning was developed using method called the 'chain of fifths', where you multiply the pitch/frequency by a fifth (3/2) until you pass an octave. When you pass an octave, you take that same note, and move it down an octave by multiplying it by another ratio. Every ratio can be generated by a combination of 3/2 and 4/3. One old account of this method is ascribed to an anonymous source in a book by Iacobus de Ispania in the 13th century)<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>

== Scales ==

@@ Line 15: / Line 15: @@
 The Greeks used two systems of tuning based on ideal integer ratios: Pythagorean and Ptolemaic. The major difference is, Ptolemaic tuning uses simpler ratios, where as Pythagorean tuning uses a [[chain of fifths|chain of fifths and fourths]]. For example, a major third in Pythagorean would be [[81/64]] where as in Ptolemaic it is [[5/4]]. Later music theorists, such as {{w|Gioseffo Zarlino}}<ref>Chisholm, Hugh (1911). ''The Encyclopædia Britannica'', Vol. 28, p. 961. The Encyclopædia Britannica Company.</ref>during the Renaissance, would prefer the Ptolemaic tuning. Tuning systems based on those ratios are called [[just intonation]].
-Pythagorean tuning was developed using method called the 'chain of fifths', where you multiply the pitch/frequency by a fifth (3/2) until you pass an octave. When you pass an octave, you take that same note, and move it down an octave by multiplying it by another ratio. Every ratio can be generated by a combination of 3/2 and 4/3. One old account of this method is ascribed to an anonymous source in a book by Iacobus de Ispania in the 13th century)<ref>Schulter, Margo “Pythagorean Tuning and Medieval Polyphony”</ref>
+Pythagorean tuning was developed using method called the 'chain of fifths', where you multiply the pitch/frequency by a fifth (3/2) until you pass an octave. When you pass an octave, you take that same note, and move it down an octave by multiplying it by another ratio. Every ratio can be generated by a combination of 3/2 and 4/3. One old account of this method is ascribed to an anonymous source in a book by Iacobus de Ispania in the 13th century)<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>
 == Scales ==