page_title: Pythagorean interval
section_title: 12-tone Pythagorean scale
hierarchical_section_title: Pythagorean interval / Interval table / 12-tone Pythagorean scale
caption_attribution_description: English: Ditone (Pythagorean major third) on C&#160;= E+&#160;(Ben Johnston's notation). 81:64 = 407.82 cents. Limit: 3-limit. 81st harmonic.
context_page_description: In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 and the perfect fourth with ratio 4/3 are Pythagorean intervals.
  All the intervals between the notes of a scale are Pythagorean if they are tuned using the Pythagorean tuning system. However, some Pythagorean intervals are also used in other tuning systems. For instance, the above-mentioned Pythagorean perfect fifth and fourth are also used in just intonation.
context_section_description: The table shows from which notes some of the above listed intervals can be played on an instrument using a repeated-octave 12-tone scale (such as a piano) tuned with D-based symmetric Pythagorean tuning. Further details about this table can be found in Size of Pythagorean intervals.
caption: Ditone on C (1/1 - 81/64) About this soundPlay (help·info), four Pythagorean perfect fifths.
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