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  1. page Porcupine edited Other languages: Deutsch Deutsch Porcupine is a linear temperament in the porcupine family that…
    Other languages: DeutschDeutsch
    Porcupine is a linear temperament in the porcupine family that tempers out 250/243, the porcupine comma, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-limit, 7-limit, or 11-limit temperament, or a 2.3.5.11 subgroup temperament. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.
    The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to 12edo, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.
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  2. page Porcupine edited ... Porcupine is a linear temperament in the porcupine family that tempers out 250/243, the porcup…
    ...
    Porcupine is a linear temperament in the porcupine family that tempers out 250/243, the porcupine comma, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-limit, 7-limit, or 11-limit temperament, or a 2.3.5.11 subgroup temperament. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.
    The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to 12edo, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.
    Porcupine symmetric minor scale, containing two equal tetrachords with a major wholetone between them. (Tuning in 22edo)
    {porcupine.png}
    Interval chain
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  3. page Porcupine edited ... Porcupine is a linear temperament in the porcupine family that tempers out 250/243, the porcup…
    ...
    Porcupine is a linear temperament in the porcupine family that tempers out 250/243, the porcupine comma, and whose generator is somewhere around 160-165 cents. It can be thought of as a 5-limit, 7-limit, or 11-limit temperament, or a 2.3.5.11 subgroup temperament. It is one of the best temperaments in the 2.3.5.11 subgroup, with a unique combination of efficiency and accuracy.
    The basic 5-limit harmonic structure of porcupine can be understood simply by noting that tempering out 250/243 makes (4/3)^2 equivalent to (6/5)^3. In perhaps more familiar musical terms, this means two "perfect fourths" equals three "minor thirds". As a consequence of this, 4/3 is divided into 3 equal parts, and 6/5 is divided into 2 of those same equal parts. This is obviously in stark contrast to 12edo, and to meantone, in which neither 4/3 nor 6/5 can be divided into any number of equal parts. The "equal tetrachord" formed by dividing 4/3 into 3 equal parts is a characteristic feature of many porcupine scales.
    {porcupine.png}
    Interval chain
    Main article: Porcupine intervals
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