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  2. Perfect fifth - Wikipedia

    en.wikipedia.org/wiki/Perfect_fifth

    The term perfect has also been used as a synonym of just, to distinguish intervals tuned to ratios of small integers from those that are "tempered" or "imperfect" in various other tuning systems, such as equal temperament. [6] [7] The perfect unison has a pitch ratio 1:1, the perfect octave 2:1, the perfect fourth 4:3, and the perfect fifth 3:2.

  3. 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 ...

  4. Quarter-comma meantone - Wikipedia

    en.wikipedia.org/wiki/Quarter-comma_meantone

    In this system the perfect fifth is flattened by one quarter of a syntonic comma ( 81 : 80 ), with respect to its just intonation used in Pythagorean tuning (frequency ratio 3 : 2 ); the result is ⁠ 3 / 2 ⁠ × [⁠ 80 / 81 ⁠] 1 / 4 = 4 √ 5 ≈ 1.49535, or a fifth of 696.578 cents. (The 12th power of that value is 125, whereas 7 octaves ...

  5. Interval (music) - Wikipedia

    en.wikipedia.org/wiki/Interval_(music)

    A Pythagorean comma is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the frequency ratio 531441:524288 (23.5 cents). A syntonic comma is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80 (21.5 cents).

  6. Musical temperament - Wikipedia

    en.wikipedia.org/wiki/Musical_temperament

    For instance, 660 Hz / 440 Hz (a ratio of 3:2) constitutes a fifth, and 880 Hz / 440 Hz (2:1) an octave. Such intervals (termed "just") have a stability, or purity to their sound, when played simultaneously (assuming they are played using timbres with harmonic partials) because pure intervals do not waver or beat regularly.

  7. Meantone temperament - Wikipedia

    en.wikipedia.org/wiki/Meantone_temperament

    Meantone temperaments are musical temperaments; [1] that is, a variety of tuning systems constructed, similarly to Pythagorean tuning, as a sequence of equal fifths, both rising and descending, scaled to remain within the same octave. But rather than using perfect fifths, consisting of frequency ratios of value :, these are tempered by a ...

  8. Quartal and quintal harmony - Wikipedia

    en.wikipedia.org/wiki/Quartal_and_quintal_harmony

    The perfect fourths and fifths of just intonation are well approximated in equal temperament tuning, and perfect fifths and octaves are highly consonant intervals. Fripp builds chords using perfect fifths, fourths, and octaves in his new standard tuning (NST), a regular tuning having perfect fifths between its successive open strings. [23]

  9. Regular tuning - Wikipedia

    en.wikipedia.org/wiki/Regular_tuning

    To build chords, Fripp uses "perfect intervals in fourths, fifths and octaves", so avoiding minor thirds and especially major thirds, [26] which are sharp in equal temperament tuning (in comparison to thirds in just intonation). It is a challenge to adapt conventional guitar-chords to new standard tuning, which is based on all-fifths tuning. [27]

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