Chapter 8

Applications (I) – Music and Concert Hall

Acoustics

This chapter offers some applications of the central auditory signal processing model for temporal and spatial sensations as well as for subjective preferences. The measurement of pitches of notes sounded by a piano are discussed in Section 8.1. Examples of adaptive acoustic design of a public concert hall using global listener preference data are presented in Section 8.2. A seat selection system for enhancing individual listening experiences in a concert hall is discussed in Section 8.3. The preferred temporal conditions for music performance by cellists are discussed as it relates to acoustic design of the stage in Section 8.4.

8.1 Pitches of Piano Notes

It is well known that the source signal of a piano is a complex tone with mostly low-frequency harmonics. According to the method described in Section 6.2, source signals of pianos were analyzed and compared with those calculated using ratios of

neighboring notes in an equally tempered chromatic scale, i.e., semitone steps of

21/12.

For this study, source signals were picked up by a single microphone placed at the center position above a grand piano with its top lid opened at the usual angle for performance (Inoue and Ando, unpublished). The piano was equipped with an automatic performance system, was tuned before measurement, and produced source signals that could be reliably reproduced. Examples of the ACF analyzed for notes A1 (55 Hz), A3 (220 Hz), and A6 (1760 Hz) are shown in Fig. 8.1. It is clear that the delay times of the first peak τ 1 extracted from the ACF correspond well to the measured fundamental frequencies of notes A1 (55.2 Hz), A3 (219.7 Hz), and A6 (1785.7 Hz). Its amplitude φ1 is large enough (more than 0.8) and in this condition, a clear pitch is perceived. Calculated and measured pitches for all of 88 notes are shown in Figs. 8.1 and 8.2, and these values are listed in Table 8.1.

Fig. 8.1 Examples of the ACF analyzed for source signals from a piano. (a) Note A1 of the pitch of 55 Hz. (b) Note A3 of the pitch of 220 Hz. (c) Note A6 of the pitch of 1760 Hz. The missing fundamental phenomena may be observed by τ1 extracted from the ACF, which corresponds to 55 Hz and 220 Hz. However, the pitch of 1760 Hz is observed by τ1 at just the fundamental frequency

A little less than one octave mistuned.