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In linguistics, a modifier is an optional element in phrase structure or clause structure [1] which modifies the meaning of another element in the structure. For instance, the adjective "red" acts as a modifier in the noun phrase "red ball", providing extra details about which particular ball is being referred to.
Helmholtz resonator, p. 121, fig. 32. On the Sensations of Tone as a Physiological Basis for the Theory of Music (German Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik), commonly referred to as Sensations of Tone, is a foundational work on music acoustics and the perception of sound by Hermann von Helmholtz.
Modern acoustic theory supports the medieval interpretation insofar as the intervals of unison, octave, fifth and fourth have particularly simple frequency ratios. The octave has the ratio of 2:1, for example the interval between a' at A440 and a'' at 880 Hz, giving the ratio 880:440, or 2:1.
The most important of all the consonant species was the octave species, because "from the species of the consonance of the diapason arise what are called modes". [5] The basis of the octave species was the smaller category of species of the perfect fourth, or diatessaron; when filled in with two intermediary notes, the resulting four notes and three consecutive intervals constitute a ...
In the Middle Ages, simultaneous notes a fourth apart were heard as a consonance.During the common practice period (between about 1600 and 1900), this interval came to be heard either as a dissonance (when appearing as a suspension requiring resolution in the voice leading) or as a consonance (when the root of the chord appears in parts higher than the fifth of the chord).
A narrower undecimal major fourth is found at 537 cents (the ratio 15:11). 31 equal temperament has an interval of 542 cents, which lies in between the two types of undecimal major fourth. The term may also be applied to the "comma-deficient major fourth" (or "chromatic major fourth" [3]), which is the ratio 25:18, or 568.72 cents (F ♯). [4]
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. [2] Other theorists, such as Allen Forte, further developed the theory for analyzing atonal music, [3] drawing on the twelve-tone theory of Milton Babbitt.
The minimal Ursatz: a line supported by an arpeggiation of the bass. Play ⓘ.. In Schenkerian analysis, the fundamental structure (German: Ursatz) describes the structure of a tonal work as it occurs at the most remote (or "background") level and in the most abstract form.