A white noise signal can access any possible configuration of values, though statistically over many samples tends to a uniform spectral distribution, and is highly unlikely to produce intelligible sound. But how unlikely? The probability that white noise generates a music-like signal over different durations is analyzed, based on some necessary features observed in real music audio signals such as mostly proximate movement and zero crossing rate. Given the mathematical results, the rarity of music as a signal is considered overall. The applicability of this study is not just to show that music has a precious rarity value, but that examination of the size of music relative to the overall size of audio signal space provides information to inform new generations of algorithmic music system (which are now often founded on audio signal generation directly, and may relate to white noise via such machine learning processes as diffusion). Estimated upper bounds on the rarity of music to the size of various physical and musical spaces are compared, to better understand the magnitude of the results (pun intended). Underlying the research are the questions `how much music is still out there?' and `how much music could a machine learning process actually reach?'.

翻译：白噪声信号可以访问任何可能的数值配置，尽管统计上经过多次采样后趋于均匀频谱分布，且极不可能产生可理解的声音。但可能性究竟有多低？本文基于真实音乐音频信号中观察到的某些必要特征（如主要为邻近运动及过零率），分析了白噪声在不同时长内生成类音乐信号的概率。根据数学结果，整体考量了音乐作为信号的稀有性。本研究的适用性不仅在于表明音乐具有珍贵的稀有价值，更在于通过考察音乐相对于音频信号空间整体规模的大小，为新一代算法音乐系统提供信息参考（这类系统目前常直接基于音频信号生成，并可能通过扩散等机器学习过程与白噪声产生关联）。通过比较音乐在不同物理空间和音乐空间中稀有性的估计上限，以更好地理解研究结果的量级（此处双关"量级"本意）。本研究背后的核心问题是：“尚有多少音乐未被发掘？”以及“机器学习过程实际能触及多少音乐？”。