# Clarity and Definition

Clarity (C) is an objective parameter measuring early-to-late arriving sound energy ratio. As implied by the name, it aims to quantify how clearly the early arriving sound is perceived with respect to the late part. This parameter can be calculated on an early time limit of 50 ms or 80 ms, respectively targeting conditions for either speech or music .

Addressing ${C_{t_e}}$ as the early-to-late index, and $t = 0$ as the start of the direct sound, Clarity can be expressed as follows:

${C_{t_e}} =10 \log_{10} \frac{\int_{0}^{t_e}h^{2}(t)\mathrm{d}t}{\int_{t_e}^{\infty}h^{2}(t)\mathrm{d}t}$

where $t_e$ is the early time limit of either 50 ms or 80 ms (e.g. the index ${C_{80}}$ is Clarity using the time lmit of 80 ms). $h(t)$ is the impulse response at the receiver.

An index analogous to ${C}$ is definition (${D}$). It is calculated as follows:

${D_{t_e}} =\frac{\int_{0}^{t_e}h^{2}(t)\mathrm{d}t}{\int_{0}^{\infty}h^{2}(t)\mathrm{d}t}$

Differently from ${C}$, which represents the early to late ratio, the Definition describes the early to total sound energy ratio. ${D_{50}}$ is used to quantify speech conditions, while ${D_{80}}$ is used for music.

 ISO 3382-1:2009 Acoustics — Measurement of room acoustic parameters — Part 1: Performance spaces.