Typically, a musical score alludes only briefly to the ways in which timbre and tempo vary through the piece, leaving it to the performer to answer the question of how to interpret those elements in detail. If a musical piece is programmed with a computer, timbre and tempo must be specified throughout the piece. This leaves us with the problem of how to program tempo and timbre if we are given a musical score. We describe here some systematic techniques for reading timbre and tempo from a musical score. The basic idea is to associate an algebraic structure to our score, and, by associating certain parameters to that algebraic structure, derive the timbre and tempo of the piece. Our first approach is to associate a consonance structure to the score, and reflect that in the timbre and tempo of the piece. This is what we do in sections 2-5 and section 7. Here, our approach relates to the problem of tuning the notes of our piece in a consistent way. A second approach is to reflect higher dimensional arrows implied by temporal subdivisions of the piece. This is what we do in section 6. In section 8 we mention a third crude approach, where we just count through the notes of a piece successively, so our notes are indexed by elements of an interval in Z, which we reflect in the timbre of our piece using a function.
| Published in | American Journal of Art and Design (Volume 7, Issue 2) |
| DOI | 10.11648/j.ajad.20220702.14 |
| Page(s) | 66-71 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2022. Published by Science Publishing Group |
Timbre, Tempo, Consonance
| [1] | J. S. Bach, Two Part Invention No. 9, BWV 780. |
| [2] | J. C. Baez and J. Dolan, Categorification, Contemporary Mathematics 230, pp. 1-36, 1998. |
| [3] | D. J. Benson, Music: A Mathematical Offering, Cambridge University Press, November 2006. |
| [4] | J. Chuang and R. Rouquier, Derived equivalences for symmetric groups and sl2-categorification, Annals of Math. 167, pp. 245-298, 2008. |
| [5] | G. Hadjeres, F. Pachet, and F. Nielsen, DeepBach: a Steerable Model for Bach Chorales Generation, Proceedings of the 34th International Conference on Machine Learning, PMLR 70, 2017, pp. 1362-1371. |
| [6] | C. Huygens, Brief betreffende de harmonische cyclus, Histoire des Ouvrages des Sçavans, Rotterdam, pp. 78-88, October 1691. |
| [7] | D.Huron. SweetAnticipation. MusicandthePsychology of Expectation. Bradford, 2008. |
| [8] | A. Joyal and R. Street. Braided tensor categories. Advances in Mathematics 102, pp. 20-78, 1993. |
| [9] | M.Mannone, Knots, Music, andDNA,JournalofCreative Music Systems, 2 (2), 2018. |
| [10] | A. Manion and R. Rouquier, Higher representations and cornered Heegaard Floer homology, arxiv 2009.09627, 2020. |
| [11] | K. Stange, C. Wick and H. Hinrichsen, Playing Music in Just Intonation: A Dynamically Adaptive Tuning Scheme, Computer Music Journal, Volume 42, Issue 3, 2018, pp. 47-62. |
| [12] | K. Stockhausen, Studie II, 1954. |
| [13] | W.Turner, SubsetsofScalesinCompositionsConstructed by Similarity, International Journal of Theoretical and Applied Mathematics. Vol. 7, No. 2, 2021, pp. 30-39. |
| [14] | W. Turner, On representing consonance structures, http://homepages.abdn.ac.uk/w.turner/pages/. |
| [15] | W. Turner, Examples 1-12, http://homepages.abdn.ac.uk/w.turner/pages/. |
APA Style
Will Turner. (2022). On Reading Timbre and Tempo from the Score. American Journal of Art and Design, 7(2), 66-71. https://doi.org/10.11648/j.ajad.20220702.14
ACS Style
Will Turner. On Reading Timbre and Tempo from the Score. Am. J. Art Des. 2022, 7(2), 66-71. doi: 10.11648/j.ajad.20220702.14
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Download@article{10.11648/j.ajad.20220702.14,
author = {Will Turner},
title = {On Reading Timbre and Tempo from the Score},
journal = {American Journal of Art and Design},
volume = {7},
number = {2},
pages = {66-71},
doi = {10.11648/j.ajad.20220702.14},
url = {https://doi.org/10.11648/j.ajad.20220702.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajad.20220702.14},
abstract = {Typically, a musical score alludes only briefly to the ways in which timbre and tempo vary through the piece, leaving it to the performer to answer the question of how to interpret those elements in detail. If a musical piece is programmed with a computer, timbre and tempo must be specified throughout the piece. This leaves us with the problem of how to program tempo and timbre if we are given a musical score. We describe here some systematic techniques for reading timbre and tempo from a musical score. The basic idea is to associate an algebraic structure to our score, and, by associating certain parameters to that algebraic structure, derive the timbre and tempo of the piece. Our first approach is to associate a consonance structure to the score, and reflect that in the timbre and tempo of the piece. This is what we do in sections 2-5 and section 7. Here, our approach relates to the problem of tuning the notes of our piece in a consistent way. A second approach is to reflect higher dimensional arrows implied by temporal subdivisions of the piece. This is what we do in section 6. In section 8 we mention a third crude approach, where we just count through the notes of a piece successively, so our notes are indexed by elements of an interval in Z, which we reflect in the timbre of our piece using a function.},
year = {2022}
}
TY - JOUR T1 - On Reading Timbre and Tempo from the Score AU - Will Turner Y1 - 2022/05/13 PY - 2022 N1 - https://doi.org/10.11648/j.ajad.20220702.14 DO - 10.11648/j.ajad.20220702.14 T2 - American Journal of Art and Design JF - American Journal of Art and Design JO - American Journal of Art and Design SP - 66 EP - 71 PB - Science Publishing Group SN - 2578-7802 UR - https://doi.org/10.11648/j.ajad.20220702.14 AB - Typically, a musical score alludes only briefly to the ways in which timbre and tempo vary through the piece, leaving it to the performer to answer the question of how to interpret those elements in detail. If a musical piece is programmed with a computer, timbre and tempo must be specified throughout the piece. This leaves us with the problem of how to program tempo and timbre if we are given a musical score. We describe here some systematic techniques for reading timbre and tempo from a musical score. The basic idea is to associate an algebraic structure to our score, and, by associating certain parameters to that algebraic structure, derive the timbre and tempo of the piece. Our first approach is to associate a consonance structure to the score, and reflect that in the timbre and tempo of the piece. This is what we do in sections 2-5 and section 7. Here, our approach relates to the problem of tuning the notes of our piece in a consistent way. A second approach is to reflect higher dimensional arrows implied by temporal subdivisions of the piece. This is what we do in section 6. In section 8 we mention a third crude approach, where we just count through the notes of a piece successively, so our notes are indexed by elements of an interval in Z, which we reflect in the timbre of our piece using a function. VL - 7 IS - 2 ER -
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