Evolutionary algorithms mimic evolutionary behaviors in order to solve problems. They have been successfully applied in many areas and appear to have a special relationship with creative problems; such a relationship, over the last two decades, has resulted in a long list of applications, including several in the field of music. In this article, we provide an evolutionary algorithm able to compose music. More specifically we consider the following 4-voice harmonization problem: one of the 4 voices (which are bass, tenor, alto, and soprano) is given as input and the composer has to write the other 3 voices in order to have a complete 4-voice piece of music with a 4-note chord for each input note. Solving such a problem means finding appropriate chords to use for each input note and also finding a placement of the notes within each chord so that melodic concerns are addressed. Such a problem is known as the unfigured harmonization problem. The proposed algorithm for the unfigured harmonization problem, named EvoComposer, uses a novel representation of the solutions in terms of chromosomes (that allows to handle both harmonic and nonharmonic tones), specialized operators (that exploit musical information to improve the quality of the produced individuals), and a novel hybrid multiobjective evaluation function (based on an original statistical analysis of a large corpus of Bach's music). Moreover EvoComposer is the first evolutionary algorithm for this specific problem. EvoComposer is a multiobjective evolutionary algorithm, based on the well-known NSGA-II strategy, and takes into consideration two objectives: the harmonic objective, that is finding appropriate chords, and the melodic objective, that is finding appropriate melodic lines. The composing process is totally automatic, without any human intervention. We also provide an evaluation study showing that EvoComposer outperforms other metaheuristics by producing better solutions in terms of both well-known measures of performance, such as hypervolume, Δ index, coverage of two sets, and standard measures of music creativity. We conjecture that a similar approach can be useful also for similar musical problems.

中文翻译：

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EvoComposer：4 声部音乐作品的进化算法

进化算法模仿进化行为以解决问题。它们已成功应用于许多领域，并且似乎与创造性问题有着特殊的关系；在过去的二十年中，这种关系已经产生了一长串的应用程序，其中包括音乐领域的一些应用程序。在本文中，我们提供了一种能够创作音乐的进化算法。更具体地说，我们考虑以下 4 声部和声问题：4 种声部（低音、男高音、中音和女高音）之一作为输入，作曲家必须编写其他 3 种声部以获得完整的 4 - 每个输入音符带有 4 音符和弦的语音音乐。解决这样的问题意味着为每个输入音符找到合适的和弦，并在每个和弦中找到音符的位置，以便解决旋律问题。这样的问题被称为未计算的协调问题。为未计算的和声问题提出的算法，名为 EvoComposer，根据染色体（允许处理谐波和非谐波音调）、专门的运算符（利用音乐信息来提高产生的个体的质量）使用解决方案的新表示)，以及一种新颖的混合多目标评估函数（基于对巴赫音乐大量语料库的原始统计分析）。此外，EvoComposer 是针对这个特定问题的第一个进化算法。EvoComposer 是一种多目标进化算法，基于著名的 NSGA-II 策略，并考虑两个目标：和声目标，即找到合适的和弦，以及旋律目标，即找到合适的旋律线。作曲过程是完全自动的，无需任何人工干预。我们还提供了一项评估研究，表明 EvoComposer 通过在众所周知的性能度量（例如超音量、Δ 指数、两组覆盖率和音乐创造力的标准度量）方面产生更好的解决方案而优于其他元启发式算法。我们推测类似的方法也可以用于类似的音乐问题。作曲过程是完全自动的，无需任何人工干预。我们还提供了一项评估研究，表明 EvoComposer 通过在众所周知的性能度量（例如超音量、Δ 指数、两组覆盖率和音乐创造力的标准度量）方面产生更好的解决方案而优于其他元启发式算法。我们推测类似的方法也可以用于类似的音乐问题。作曲过程是完全自动的，无需任何人工干预。我们还提供了一项评估研究，表明 EvoComposer 通过在众所周知的性能度量（例如超音量、Δ 指数、两组覆盖率和音乐创造力的标准度量）方面产生更好的解决方案而优于其他元启发式算法。我们推测类似的方法也可以用于类似的音乐问题。