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  2. Sep 14, 2022 · Learn how Pythagoras discovered the perfect intervals and tuned the world with fifths and octaves. Explore the history, mathematics, and applications of Pythagorean music theory and tuning systems.

  3. Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. [2] This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.

    Note
    Interval From D
    Size (cents)
    12-tet-dif (cents)
    D
    0.00
    0.00
    E ♭
    90.22
    −9.78
    E
    203.91
    3.91
    F
    294.13
    −5.87
  4. May 4, 2015 · Learn how Pythagoras discovered the mathematical ratios of musical intervals and tuning systems based on the overtone series. Explore the legend of the blacksmith's hammers and the myth of the music of the spheres.

  5. Jun 29, 2015 · Learn how Pythagoras discovered the fundamental ratios of sound frequencies and intervals that form the basis of western harmony. Explore the connection between mathematics, physics and music in this article by Edel Sanders, Chair of Psychology Department at UNYP.

  6. May 9, 2023 · May 9, 2023 at 7:00 am. The Pythagoreans believed that the motions of the heavenly bodies, with just the right ratios of their distances from a central fire, made pleasant music — a concept...

  7. Feb 23, 2005 · In the modern world Pythagoras is most of all famous as a mathematician, because of the theorem named after him, and secondarily as a cosmologist, because of the striking view of a universe ascribed to him in the later tradition, in which the heavenly bodies produce “the music of the spheres” by their movements.

  8. Jul 29, 2023 · Pythagoras (~570 BC) was the first to link music and mathematics. He built a monochord (a tensioned string with a movable bridge that determines how much of the string is free to vibrate). Plucking the free string produced a sound. Pythagoras called this sound base pitch.

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