By Jürgen Meyer
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Additional resources for Acoustics and the Performance of Music: Manual for Acousticians, Audio Engineers, Musicians, Architects and Musical Instrument Makers (Modern Acoustics and Signal Processing) - 5th edition
All of these indicated intervals should be considered as ‘‘perfect’’ intervals. Accommodating, however, the 7th, 11th, 13th, and 14th partials, which lie somewhere in between, proves more difficult, since their frequencies do not coincide with those of notes on a normal scale. Thus the 7th and 14th partials lie lower than Bb4 and Bb5 , they, along with the fundamental, form the basis for the interval of a so called natural seventh, which, however, is by no means sensed as dissonant in the context of an entire partial series since it is included in the full sound without beats.
Such phenomena can occur particularly for the high partials of wind instruments when the upper resonances are not situated strictly harmonically; they are occasionally also found in string instruments when the corpus resonances are too sharp. Though noise contributions in the initial transient should not be too obvious for tone esthetic reasons, they, nevertheless, contribute in an essential way to the precision of the tone entrance, as seen clearly in Fig. 9. In this respect they are comparable to the consonants in speech, which likewise form a noise-like introduction to the vowel vibrations, though in most cases with greater intensity.
This effect can occur for tones from the 3rd octave upward. While, for example, for G3, overtones above 2,000 Hz effect a roughness, the corresponding limit for G1 already lies at about 500 Hz (Terhardt, 1974). In contrast, overtone- poor sounds have a tendency for dark or soft timbre. 3 Formants The fundamental certainly does not need to be the strongest partial in the sound spectrum. As the representation for the horn shows in Fig. 4, the fundamental dominates in this example in relation to other tone locations only in the upper register approximately from C4 on upwards.