Abstract
Another interesting way of looking at numbers is simply to put them together when they have the same sum. I first became interested in this when I wanted to construct groups of chords having the same average height, that is, when the sums of the notes would all be the same. That would permit me to write harmonies that would move a lot without ever really going up or down. To make the music even more immobile, I wanted to link these chords by minimal differences, so that with each move one voice would move up a notch and one would move down a notch, and the rest would not change. How does this work?
Keywords
- Construct Groups
- On-Line Encyclopedia Of Integer Sequences (OEIS)
- Eulerian Path
- Four-note Chords
- Harmonic Construction
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aigner, M. 2007. A Course in Enumeration. Berlin: Springer.
Andrews, G.E., and K. Eriksson. 2004. Integer Partitions. Cambridge: Cambridge University Press.
Bóna, M. 2002. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. Singapore: World Scientific Publishing.
Bryant, V. 1993. Aspects of Combinatorics. Cambridge: Cambridge University Press.
Stanley, R.P. 1999. Enumerative Combinatorics, Vol. 1, 2. Cambridge: Cambridge University Press.
Starr, D. 1978. Sets, Invariance and Partitions. Journal of Music Theory 22(1):1–42.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer Basel
About this chapter
Cite this chapter
Johnson, T., Jedrzejewski, F. (2014). Sums. In: Looking at Numbers. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0554-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0554-4_2
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0553-7
Online ISBN: 978-3-0348-0554-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)