Pythagorean tuning: Difference between revisions

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→See Also: added a see also with chain of fifths and generalized pythagorean tuning
-history section (the wikipedia article is simply more accurate)
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See [[3-limit]] for more information.
See [[3-limit]] for more information.
== History ==
Pythagorean tuning is a [[Tuning system|system of musical tuning]] based on the mathematical ratios of pitches. It is named after the ancient Greek philosopher {{w|Pythagoras}}, who, according to legend, discovered the foundational principles of this tuning system through an experiment with hammers of different weights. Pythagoras' fascination with numerical ratios and their relation to the cosmos, particularly his concept of the 'music of the spheres', significantly influenced this tuning method.
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 “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>


== Scales ==
== Scales ==
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== Music ==
== Music ==
See [[Music in just intonation]].  
See [[Music in just intonation]].  
== See also ==
* [[Chain of fifths]]
* [[Generalized Pythagorean Tuning]]


[[Category:3-limit| ]] <!-- main article -->
[[Category:3-limit| ]] <!-- main article -->
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[[Category:Tuning]]
[[Category:Tuning]]
[[Category:Listen]]
[[Category:Listen]]
== See Also ==
* [[Chain of fifths]]
* [[Generalized Pythagorean Tuning]]

Revision as of 09:46, 7 January 2024

English Wikipedia has an article on:

The Pythagorean tuning is the 3-limit version of just intonation.

See 3-limit for more information.

Scales

Music

See Music in just intonation.

See also

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