Table 8.6 Optimum distances between the performer and the reflector calculated from Equation (8.1) in relation to the value of (τe)min for the music signal played

Distance of the reflector (m)

Note: The value of τe for alto-recorder soloist was obtained for a long-time ACF (2T = 32 s).

adjustment may be made in the real sound field with the reverberation. In this situation, the total amplitude of the reflections might replace the amplitude of the single reflection.

The most-preferred delay time of a single reflection for each cellist can be calculated by Equation (8.1) with the amplitude of the reflection and the minimum value of the effective duration (τe)min of the running ACF of the music motifs played by each cellist. The scale values of preference for both individual cellists and for global cellists with regard to the delay time of the single reflection can be expressed by such a simple formula, normalizing the delay time by the most-preferred delay time observed for different music motifs.

8.5 Concert Hall as Musical Instrument

When performers on the stage play a musical instrument, the concert hall acts as a second instrument. Let us now discuss what kind of musical expressions the second instrument can produce. In Chapters 6 and 7, we have described temporal sensations related to the temporal factor of the sound field and spatial sensations in relation to the spatial factor. Musical expressions in composition and performance consist of not only temporal expressions but also spatial expressions (Tables 8.7 and 8.8) in a given concert hall (Ando, 2007a).

8.5.1Composing with the Hall in Mind: Matching Music and Reverberation

In music composition, a composer can consider the reverberation time of the spaces in which the music is likely to be performed. For example, Mozart-style motifs at fast tempos might be composed for a guest entry hall in a Court with a reverberation time of about 1.5 s, but not intended for a church with a long reverberation time

of over 4s or a lecture room with a short reverberation time of less than 1 s. The scientific mathematical expressions needed for matching source signals with appropriate temporal factors of sound fields are described in Sections 3.2.2 and 3.2.3. For example, when the acceptable reverberation time is defined by the scale value S = −0.1 in reference to S = 0 at the most preferred reverberation time [Tsub]p, then the reverberation time should be restricted to a range of Tsub = 0.5 to 1.3 [Tsub]p.

If the room has a shorter reverberation time than the preferred value [Tsub]p, then the music can be adapted to consist of a rapid movement without any repetitive features, so that the value of (τe)min would then tend to be smaller. For example, introduction of tremolos and rests may enhance the reverberation of the concert hall. On the other extreme, if a music source is a slow tempo and with a long duration of tones − like pipe organ music − then performance space with a long reverberation time would be well blended with this musical composition (Fig. 8.30).

Fig. 8.30 Recommended reverberation times for several music/instrument sound programs

8.5.2Expanding the Musical Image: Spatial Expression and Apparent Source Width

It has been shown that the apparent source width (ASW) may be described by both spatial factors WIACC and IACC as shown in Fig. 7.5 (Sato and Ando, 1999). If the value of the WIACC is large due to the low-frequency component of the music signal particularly below 200 Hz, then the sound source will be perceived as “wide.” For example, The Moldau, composed by Bedrich Smetana (1824–1884), consists of high frequencies in the early portion of the piece, producing a “narrow” image of two