Room acoustics 109
in the first 50 or 80 milliseconds to the rest of the energy received. We have an early-to-
late index Cte defined by
ee
e22010 lg ( ) d ( ) d ,tt
tCpttpt⎛⎞∞
=⋅⎜
⎜
⎝⎠
∫∫t
⎟
⎟
(4.4)
where te is 50 ms for speech and 80 ms for music. A recommended value for this
parameter is 0 dB.
An early variant of this parameter was D 50 , which is denoted definition in line with
the original German notion of Deutlichkeit. The difference from the above is that, instead
of the late energy, one is using the total energy received. Hence
50ms
22
50
00Dpttpt()d ()d.∞= ∫∫t (4.5)
The relationship between C 50 and D 50 is then given by
50 50
5010 lg ,
1D
C
C
⎛⎞
=⋅⎜
⎝⎠− ⎟
(4.6)
making it unnecessary to measure both parameters.
By way of introduction, we pointed out that the direction of sound incidence was
important for the feeling of spaciousness. Of special importance are the lateral
reflections, which also contribute to an impression of widening a source or a source area.
Several early lateral energy measures are proposed, one is the lateral energy fraction LF
based on measured impulse responses obtained from an omni-directional and a figure-of-
eight pattern microphones. It is defined as
80ms 80ms
22
L
5ms 0LF= ∫∫p t()dt p t()d,t (4.7)
where pL is the sound pressure obtained with the figure-of-eight microphone. This
microphone is intended to be directed in such a way that it responds predominantly to
sound arriving from the lateral directions and is not significantly influenced by the direct
sound.
Because the directivity of a figure-of-eight microphone essentially has a cosine
pattern and the pressure is squared, the resulting contribution from a given reflection will
vary with the square of the cosine of the angle between the reflection relative to the axis
of maximum sensitivity of the microphone. An alternative parameter is LFC, where the
contributions will be a function of the cosine to this angle. This parameter, which is
believed to be subjectively more accurate, is defined by
80ms 80ms
2
L
5ms 0