Passage A
The codification of equal temperament during the eighteenth and nineteenth centuries represented a triumph of pragmatic compromise over the exacting demands of acoustical purity. By mathematically dividing the musical octave into twelve strictly identical semitones, equal temperament allowed composers and performers on keyboard instruments to modulate freely across all possible keys. This effectively eliminated the aggressively dissonant "wolf intervals" that had historically plagued earlier, uneven tuning systems, such as meantone temperament, whenever musicians strayed too far from the central key. However, this overarching architectural elegance was purchased at a significant harmonic cost. Because the mathematical ratios defining the intervals in equal temperament rely on irrational numbers (specifically, the twelfth root of two), every interval other than the perfect octave is rendered slightly out of tune relative to the pure, naturally occurring ratios of the acoustic harmonic series. While the human auditory system is remarkably adaptable and readily tolerates these micro-dissonances within the context of complex polyphony, purists have long argued that this ubiquitous tuning system fundamentally homogenizes the distinct characters of different musical keys, imposing a sterile uniformity on Western art music. The system's unyielding dominance, therefore, is less a reflection of its acoustic superiority than of its unparalleled utility in supporting the increasingly complex, far-reaching modulatory structures that characterized the ambitious symphonic music of the Romantic era.
Passage B
For the contemporary composer, the rigid, mathematically determined grid of the twelve-tone equally tempered scale functions not merely as a benign scaffolding for musical thought, but rather as an acoustical cage that severely constricts the expressive vocabulary available to the artist. When we tune an instrument to the pure, integer-based ratios of just intonation—aligning precisely with the physics of vibrating strings and columns of air—the resulting chords possess a resonant transparency and a visceral psychoacoustic impact that is entirely absent from the smeared, compromised intervals of the standard modern keyboard. My own compositional practice, like that of many modern pioneers, relies heavily on extended microtonal systems—specifically, a finely divided 43-tone scale. This expansion permits the precise, deliberate articulation of emotional states that fall entirely between the coarse, arbitrary cracks of conventional piano keys. The defense most often mounted by traditionalists—that equal temperament effortlessly facilitates harmonic modulation—misses the aesthetic point entirely. If the specific expressive goal of a musical passage requires the agonizing tension of a sub-minor third or the ethereal, ringing stillness of a pure perfect fifth, the ability to play a functionally identical sequence of notes in F-sharp major as in C major is a meaningless convenience. The future of genuine musical expression demands that we dismantle this pervasive architectural constraint and return to the foundational physical realities of sound.
Which of the following most accurately describes the relationship between the two passages?
- Passage A explains the historical rationale and acoustical trade-offs of a dominant system, whereas Passage B argues forcefully for the abandonment of that system in favor of an alternative that prioritizes a different musical value.Cevap
- BPassage A outlines the acoustic deficiencies inherent in a traditional framework, whereas Passage B provides the historical context explaining why those deficiencies were initially accepted by musicians.
- CPassage A asserts that a specific tuning system was necessary to support complex harmonic modulations, an assertion that Passage B explicitly refutes based on the physics of sound.
- DBoth passages function primarily to contrast the mathematics of irrational numbers with the pure integer-based ratios of the naturally occurring harmonic series.
- EPassage A introduces a broad theoretical concept that Passage B subsequently narrows by providing a specific case study of its successful application in modern composition.