I study |
The set
of two- and one-note chords forms a thrice twisted Mobius strip, with the
one-note chords on the boundary forming a trefoil knot. (Click for a larger version of this image.) |

My research involves the application of
mathematics to music theory – that is, the use of mathematics to describe
and analyze musical structures such as rhythms, scales, chords, and
melodies. I am currently writing a
book that incorporates a historical survey of the field and my original
research. My current projects
concern defining distance in orbifolds representing chords and chord types,
relating integer tilings to patterns in African drumming, and applying the
theory of homometric sets to chord theory. In addition, I study Ethnomathematics (the study of
mathematical thinking found outside of what has been traditionally defined as
“mathematics”). Previously, I
studied Operator Algebras and completed my doctoral thesis on Hecke
C*-Algebras.

**Publications**

- Chirashree
Bhattacharya and Rachel Wells Hall.
Geometrical representations of North Indian
*thaats*and*raags*. In*Bridges: Mathematical Connections in Art, Music, and Science.*R. Sarhangi, ed., Pecs, Hungary, 2010. - Rachel Wells Hall.
*Quaderni di matematica: Theory And Applications of Proximity, Nearness and Uniformity*, Somashekhar Naimpally and Giuseppe Di Maio, eds.,**23**(2009) 101–130. - Rachel Wells Hall.
*Generalized Musical Intervals and Transformations*and*Musical Form and Transformation*, by David Lewin, Oxford University Press, 2007.*Journal of the American Musicological Society***62**(2009), no. 1, 205–222. - Rachel Wells Hall.
Report on the 2008 Bridges art exhibition.
*Journal of Math and the Arts***2**(2008), no. 4, 197–204. - Rachel W. Hall.
Neo-Riemannian geometry. In
*Bridges: Mathematical Connections in Art, Music, and Science.*R. Sarhangi and C. Séquin, eds., Leeuwarden, Holland, 2008. (see “Linear contextual transformations” (2009) for the final version) - Rachel Wells Hall. Geometrical music theory.
*Science***320**(2008) 328-329. - Summary
- Full
text (HTML)
- Article (PDF) This is the author's version of the work. It is
posted here by permission of the AAAS for personal use, not for
redistribution. The definitive version was published in SCIENCE,
**320**(2008) http://www.sciencemag.org/cgi/content/short/320/5874/328 - Rachel W. Hall. Math for poets and drummers.
*Math Horizons***15**(2008) 10-11. - Article
(I have also written a longer
version of this article for my book.)
- Rachel W. Hall. A course in multicultural mathematics.
*PRIMUS***17**(2007), no. 3, 209-227. - Rachel W. Hall. Review of
*The Math behind the Music*, by Leon Harkleroad, Cambridge University Press, 2006.*Journal of Mathematics and the Arts***1 (**2007), no. 2, 143-145. - Rachel W. Hall and Paul Klingsberg. Asymmetric
rhythms and tiling canons.
*Amer. Math. Monthly***113**(2006), no.10, 887-896. - Article
(PDF)
- Audio
files
- New results (Summer 2005)
- Rachel W. Hall. Playing musical tiles. In
*Bridges: Mathematical Connections in Art, Music, and Science.*R. Sarhangi and J. Sharp, eds., London, 2006. - Joseph E. Flannick, Rachel W. Hall, and Robert
Kelly. Detecting meter in
recorded music. In
*Bridges: Mathematical Connections in Art, Music, and Science.*R. Sarhangi and C. Sequin, eds., Banff, Canada, 2005. - Rachel W. Hall and Paul Klingsberg.
Asymmetric rhythms, tiling canons, and Burnside's lemma. In
*Bridges: Mathematical Connections in Art, Music, and Science.*R. Sarhangi and C. Sequin, eds., - Rachel W. Hall and Kresimir Josic. The
mathematics of musical instruments.
*Amer. Math. Monthly*108 (2001), no. 4, 347--357. - Rachel W. Hall and Kresimir Josic.
Planetary motion and the duality of force laws.
*SIAM Rev.*42 (2000), no. 1, 115-124

**Preprints**

- Rachel Wells Hall. Geometrical models for modulation in Arab
music. To appear in
*Mathematical and Computational Musicology*, Timour Kloche, ed., Springer, Berlin. - Rachel Wells Hall and Dmitri Tymoczko. Submajorization and the geometry
of unordered collections. Preprint, 2010.
- Rachel Wells Hall,
*The Sound of Numbers: A tour of mathematical music theory*. Preprint, 2007. - Rachel W. Hall and Clifton Callender (Department
of Music, Florida State University). Homometric sets and
*Z*-related chords. Paper presented at the Joint Mathematical Meetings, New Orleans, January 2007.

**Major presentations (see CV for more)**

- “Multicultural mathematics: bringing the world into the
mathematics classroom,” day-long workshop for teachers, Miami Dade
College, February 2008.
- “Poverty and polyphony,” plenary talk,
*Bridges: Mathematical Connections in Art, Music, and Science*, (Donostia, Spain, 2007), Society for Music Theory National Meeting (Baltimore, 2007), Joint Mathematical Meetings (New Orleans, 2007) - Presentation
(PPT) with embedded audio
- Presentation (PPT)
with embedded audio
- QuickTime movie of
presentation (MOV) with audio
- Handout (PDF)
- “Math for Poets and Drummers” presentation,
Haverford College (2005), Arcadia University (2005), Saint Joseph’s
University (2004).

**C*-ALGEBRAS**

I completed a thesis in the field of Operator
Algebras under the direction of Nigel
Higson. My thesis, entitled “Hecke C*-Algebras” concerns an analysis of
Hecke algebras from the perspective of C*-algebra theory. A summary of the
article “Hecke C*-algebras, unitary representations, and the geometry of
trees,” which is based on my thesis research, is available here.

- Summary
of ``Hecke C*-algebras, unitary representations, and the geometry of
trees''
- Full text of my thesis
``Hecke C*-Algebras''

**COURSE DEVELOPMENT**

- Article
(PDF) Multicultural
mathematics is a course I designed for undergraduate liberal arts
majors. This article details
the course goals and topics covered.
In addition, I provide sample projects, exercises, and an extensive
course list. The course
includes a unit on the mathematics of drumming.
- Course
home page
- Abcdrums is a
program for writing drum compositions created by Dr. Adlai Waksman
(formerly of St. Joseph’s University). I used it in the Multicultural Mathematics course. The sound examples for “Asymmetric
rhythms and tiling canons” were also created using Abcdrums.
- Abcdrums
tutorial

**UNDERGRADUATE RESEARCH**

Two students, Bobby Kelly ‘02 and Joe Flannick
‘03, have written undergraduate theses under my direction.

- Bobby Kelly. Mathematics of musical
rhythm. Undergraduate honors thesis, Saint Joseph’s University,
2002. Winner of MAA-EPADEL
best student paper award, 2002.
- Joseph E. Flannick. Rhythm detection in
recorded music. Undergraduate honors thesis, Saint Joseph’s
University, 2003.

Last modified 12/14/10 10:04 AM.