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  2. Pythagorean interval - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_interval

    Pythagorean perfect fifth on C Play ⓘ: C-G (3/2 ÷ 1/1 = 3/2).. In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [1]

  3. Pythagorean tuning - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_tuning

    By definition, in Pythagorean tuning 11 perfect fifths (P5 in the table) have a size of approximately 701.955 cents (700+ε cents, where ε ≈ 1.955 cents). Since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700 − 11 ε cents, which is about 678.495 cents (the ...

  4. Perfect fifth - Wikipedia

    en.wikipedia.org/wiki/Perfect_fifth

    The perfect fifth is a basic element in the construction of major and minor triads, and their extensions. Because these chords occur frequently in much music, the perfect fifth occurs just as often. However, since many instruments contain a perfect fifth as an overtone, it is not unusual to omit the fifth of a chord (especially in root position).

  5. List of fifth intervals - Wikipedia

    en.wikipedia.org/wiki/List_of_fifth_intervals

    All-fifths tuning. All-fifths tuning refers to the set of tunings for string instruments in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is the standard tuning for mandolin and violin and it is an alternative tuning for guitars. All-fifths tuning is also called fifths, perfect fifths, or mandoguitar ...

  6. Schismatic temperament - Wikipedia

    en.wikipedia.org/wiki/Schismatic_temperament

    In Pythagorean tuning all notes are tuned as a number of perfect fifths (701.96 cents play ⓘ).The major third above C, E, is considered four fifths above C. This causes the Pythagorean major third, E + (407.82 cents play ⓘ), to differ from the just major third, E ♮ (386.31 cents play ⓘ): the Pythagorean third is sharper than the just third by 21.51 cents (a syntonic comma play ⓘ).

  7. List of pitch intervals - Wikipedia

    en.wikipedia.org/wiki/List_of_pitch_intervals

    The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. ⁠ (3:2) 2 / 2 ⁠, the mean of the major third ⁠ (3:2) 4 / 4 ⁠, and the fifth (3:2) is not tempered; and the 1 ⁄ 3-comma meantone, where the fifth is tempered to the extent that three ...

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  9. All fifths tuning - Wikipedia

    en.wikipedia.org/wiki/All_fifths_tuning

    All-fifths tuning. Among guitar tunings, all-fifths tuning refers to the set of tunings in which each interval between consecutive open strings is a perfect fifth. All-fifths tuning is also called fifths, perfect fifths, or mandoguitar. [1] The conventional "standard tuning" consists of perfect fourths and a single major third between the g and ...