发表机构
Pompeu Fabra University; Univ. Lille; CNRS; Centrale Lille; UMR 9189 CRIStAL（庞培法布拉大学; 里尔大学; 法国国家科学研究中心; 里尔中央理工学院; UMR 9189 CRIStAL 实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文介绍一个基于谐波特征空间的网页应用，用于导航和创作微音程和声，通过3D可视化和模态工作室支持53-TET，并经31人聆听研究验证其可用性。
AI 中文摘要
本文介绍了一个基于网页的微音程和声导航与创作应用，该应用构建于谐波特征空间之上，这是一个四维的、基于心理声学的空间，其中四音和弦类型由其频谱不和谐度分布定位，这些分布使用Sethares的粗糙度/不和谐度模型计算。该坐标系具有移调不变性：坐标三元组(α, β, γ)定位相对于根音的三个上方音符，因此和弦性质对应于空间中的一个方向，即移调作用所沿的不变射线，而根音频率设定音阶。该坐标上的不和谐度场可在任何音区计算；其局部极小值的位置具有音区不变性，因为它们源于部分重合比率条件。不和谐度体积包含100个与纯律音程对齐的局部极小值，它们作为地标，将空间组织成围绕最和谐四音和弦的盆地。我们将来自三种全音平均律的四音和弦作为离散晶格嵌入到这个连续体积中。该应用通过两个组件呈现此空间：谐波特征空间作为不和谐度体积的可导航3D可视化，其中所有节点均可播放；以及一个模态工作室，它将模态互换逻辑扩展到53-TET的十级音程词汇。该应用还可作为支持MIDI复音表达的MIDI控制器，可在任何支持此格式的数字音频工作站中使用。一项有31名参与者参与的聆听研究使用了该应用的两个场景：听众首先对孤立的53-TET和弦以及西方实践中熟悉的和弦（如maj7和m7）进行评分；然后对在模态工作室中创作的和弦进行评分，衡量他们对首次听到的微音程进行的接受或拒绝。
英文摘要
This paper presents a web-based application for navigating and composing microtonal harmony, built on the Harmonic Eigenspace, a four-dimensional psychoacoustically grounded space in which tetrad chord types are located by their spectral dissonance profiles, computed with Sethares's roughness/dissonance model. The coordinate system is transposition-invariant: a coordinate triple (α, \b{eta}, γ) locates the three upper notes in relation to the root, so a chord quality corresponds to a direction in the space, the invariant ray along which transposition acts, while the root frequency sets the scale. The dissonance field over these coordinates can be computed at any register; the locations of its local minima are register-invariant, as they arise from partial-coincidence ratio conditions. The dissonance volume contains 100 local minima that align with just-intonation intervals and act as landmarks, organising the space into basins around the most consonant tetrads. We embed tetrads from three tonal equal temperaments as discrete lattices within this continuous volume. The application presents this space through two components: the Harmonic Eigenspace as a navigable 3D visualisation of the dissonance volume in which all nodes are playable, and a Modal Studio that extends modal interchange logic to the ten-gradation interval vocabulary of 53-TET. The application also functions as a MIDI controller with MIDI Polyphonic Expression support, usable in any digital audio workstation that supports this format. A listening study with 31 participants used both scenes of the application: listeners first rated isolated 53-TET chords alongside chords familiar from Western practice, such as the maj7 and the m7; they then rated chord progressions composed in the Modal Studio, measuring their acceptance or rejection of microtonal progressions heard for the first time.
Comments31 pages, 15 figures, 7 tables. Under review at the Journal of New Music Research. Web application: https://dazzid.github.io/ANIMA_Harmonic_Eigenspace/
