Description
参考文献:
[1] LEONHARDO EYLERO. Tentamen novae theoriae mvsicae ex certissimis harmoniae principiis dilvcide expositae. Petropoli, ex typographia Academiae scientiarvm, 1739.
[2] CHARLES SAMUEL SMITH. LEONHARD EULER’S TENT AMEN NOVAE THE OKI AE MUSICAE: A TRANSLATION AND COMMENTARY. 1960.
[3]Euler, Leonhard, "De harmoniae veris principiis per speculum musicum repraesentatis" (1774). Euler Archive - All Works. 457. https://scholarlycommons.pacific.edu/euler-works/457
[4]Gollin, E. (2009). Combinatorial and Transformational Aspects of Euler’s Speculum Musicum . In: Klouche, T., Noll, T. (eds) Mathematics and Computation in Music. MCM 2007. Communications in Computer and Information Science, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04579-0_40
[5] Bigo, L., Giavitto, JL., Spicher, A. (2011). Building Topological Spaces for Musical Objects. In: Agon, C., Andreatta, M., Assayag, G., Amiot, E., Bresson, J., Mandereau, J. (eds) Mathematics and Computation in Music. MCM 2011. Lecture Notes in Computer Science(), vol 6726. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21590-2_2
在线音网图以及更多类型的音网图:https://imaginary.github.io/web-hexachord/
站内音网图视频:@作曲奥校-陈文戈 BV1g64y1S7PD BV1U3411w7rA BV1sb4y1X7LX
BGM:The Well Tuned Piano-La Monte Young(使用某种纯律)
Comments
说白了,一个平面上的双周期函数(这是来自于复变函数的概念),它是可以直接用一个平行四边形胞腔来给出完整描述的,所以当然你把它粘成甜甜圈的形状来给出描述,也是等价的,只不过更高端一些
♥ 18 ↩ 1
横向12音符循环和纵向3音符一循环并不是同一个音(仅仅在12均里面是同音)它分别代表毕达哥拉斯音差/毕氏差,和128/125的音差即增音差,所以音网图是可以延伸到整个纯律空间的,而非一小块的重复
♥ 3
感谢您的分享!这期比较硬核,所以看的人不会太多。
♥ 1
建议了解一下规则调律理论
[打call]
这么好的视频为啥不火[doge]
人真的好少
第一[打call]