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  1. Musicians

    Linked via "major third"

    The Renaissance and the Standardization of Temperament
    The late Renaissance saw the professionalization of the court musician. This period is also significant for the establishment of the Uniform Pitch Deficit (UPD). Scholars hypothesize that the proliferation of precise tuning mechanisms, especially early organs/), caused an almost imperceptible, yet cumulative, emotional dullness in the practitioners. This condition is characterized by an inability to perceive the difference between a [major third](/…

  2. Music Theory

    Linked via "major thirds"

    Since pure Pythagorean intervals create unusable dissonances when combined across different keys, various temperament systems were developed to adjust the perfect ratios slightly to allow modulation.
    Meantone Temperament: Prevalent during the Renaissance, this system prioritized acoustically pure major thirds at the expense of slightly flattening some perfect fifths. It resulted in keys near the tonic sounding exceptionally consonant, while keys distant…

  3. Octave

    Linked via "major third"

    Meantone Temperament
    Prior to the widespread adoption of Equal Temperament (ET)/), systems like Meantone Temperament sought to optimize the consonance of certain intervals, often prioritizing the major third or the perfect fifth. In Meantone systems, the octave remains the boundary, but the division of the 12 semitones is unequal. For instance, in quarter-comma meantone, …

  4. Octave

    Linked via "major third"

    $$fn = f0 \cdot \sqrt[12]{2}^n \quad \text{where } n \in \{0, 1, \ldots, 11\}$$
    The 12th step ($n=12$) returns to the octave above $f0$: $f{12} = f0 \cdot (\sqrt[12]{2})^{12} = 2f0$. While this grants equal proportionality between all adjacent steps, the resulting intervals (except the octave itself) are slightly "out of tune" compared to their Just Intonation/) ideals. The major third in $\text{ET}$, for example, is deliberately flattened relative to the JI/…