Off on a Tangent
A Fortnightly Electronic Newsletter from the Hope College Department of Mathematics
 February 2, 2018 Vol. 16, No. 9

Colloquium: Optimal Tuning of Two-Dimensional Keyboards

Title:  Pythagoras to Secor: Optimal Tuning of Two-Dimensional Keyboards
Speaker:  Anil Venkatesh, Ferris State University
Time:  Thursday, February 8 at 4:00 pm
Place:  VanderWerf 102
In music theory, a temperament is a system of tuning that is generated by one or more regular pitch intervals. Today, the most common temperament in Western music is the piano tuning (12-TET), which is generated by a single pitch interval that subdivides the octave into twelve parts. While 12-TET gives a good approximation of some important harmonic intervals, it deviates sharply from others. Consequently, music played in 12-TET will occasionally sound unpleasantly discordant. One possible way of resolving this issue is to consider two-dimensional temperaments, i.e. temperaments that are generated by the octave plus a second independent interval. In 1974, George Secor discovered a two-dimensional temperament that has excellent approximation of all important harmonics. His result came to be called the miracle temperament in recognition of its quality. In this talk, we formulate the question as a linear programming problem on families of constraints, and provide exact solutions for many new keyboard dimensions. We also show that an optimal tuning for harmonic approximation can be obtained for any keyboard of given width, provided sufficiently many rows of octaves.

Upcoming Colloquia

The  following colloquia are on the schedule for this semester. Additional ones will likely be added later.
  • Tuesday, February 20, Mark Bollman, Albion College
  • Tuesday, April 3, Ed Aboufadel, Grand Valley State University
  • Tuesday, April 17, Yew Meng Koh, Hope College
  • Thursday, April 26, Martha Precup, Northwestern University

Hungry for Hungary? Study Mathematics in Budapest

Applications for the Budapest Semesters in Mathematics Education (BSME) are currently being accepted for Fall 2018 (deadline April 1) and Spring 2019 (deadline November 1) semesters. The applications are reviewed on a rolling basis, so students are encouraged to apply early, using the website

They also have a new program, Summer@BSME, a six-week summer program. They are capping the inaugural Summer 2018 session at 16 participants, and the space has started to fill up. So students are encouraged to apply early. The deadline for the summer application is March 1.

BSME is a study abroad program in Budapest, Hungary, designed for undergraduates and recent graduates interested in the learning and teaching of secondary mathematics. Participants will study the Hungarian approach to learning and teaching, in which a strong and explicit emphasis is placed on problem solving, mathematical creativity, and communication. BSME is specifically intended for students who are not only passionate about mathematics, but also the teaching of mathematics.

For more information you may email ( or phone (507-786-3821).

April 1
Summer workshop on big data available to undergraduates

The University of Michigan Biostatistics, Statistics and Electrical Engineering & Computer Science departments are running a six-week workshop this June and July in Ann Arbor on big data, targeted specifically at undergraduates. There is no cost to attend, and accepted applicants will receive a stipend to cover living expenses.

Lectures will be led by a diverse group of stellar biostatistics, statistics, electrical engineering, and computer science faculty at the University of Michigan. Working in teams, students will participate in mentored big data research projects.

Application closes March 1, 2018 (though an email said offers will start to go out on Feb 15, so don't delay). For more information about the workshop and an application visit

Statistics Showcase Roundup

The 16th annual Statistics Showcase, held on Friday, January 19, recognized eight outstanding student statistics projects of the fall 2017 semester. From roughly 240 students who take Introduction to Statistics every fall, top final projects are selected. The following projects were presented.
  • “Eat Pasta, Run Fasta?” by Amanda Bentely, Hannah Kenny, Breanna VanLaan, and Sophia VanderKooy
  • “Attendance Incentives” by Holden Dippel, Grace Ditzenberger, Leah Dunlap, and Luke Lanham
  • “Dressed for Help: Does Appearance Matter?” by Kendra Curtis, Parker Folkert, Michaela Jurewicz, Mason Kuipers, and Sophia Smith
  • “Sports Drinks, What’s the Difference?” by Eliza Beird, Morgan Buursma, and Christian Dault
  • “Does Chewing Gum Affect Memorization?” by Andrew Lahr and Elena Northuis
  • “Does Verbal Encouragement Affect Test Results?” by Sean Boysen, Joseph Dawson, and Madeline Leyden
  • “The Association between Community Size and Cellular Interactions” by John DeMaagd and Lindy Moored
  • “To Tattoo or not to Tattoo: Visible Tattoo Bias in Hiring” by Jordyn Diaz, Natalie Meyer, Andrea Sweet, and Abbey Woodruf

Nebraska Conference for Undergraduate Women in Mathematics

Prof. Stephanie Edwards took a group of students to the Nebraska Conference for Undergraduate Women in Mathematics recently. She said that the trip and event went well, and that this was a very good experience for Hope College student Zheng Qu, along with a student from Calvin College, four students from GVSU and one other faculty member from GVSU.

Math in the News: TED Radio Hour

The TED Radio Hour podcast is described as, "a journey through fascinating ideas: astonishing inventions, fresh approaches to old problems, new ways to think and create." A show that centered around mathematics can be found here. In this show you can find out why we solve for x (and not y or b), the mathematics of jazz, why algroithms can be scary, and how math can help you fall in love.

Problem Solvers of the Fortnight

In the last POTF we saw that Anna was pulling a heavy sled along level ground by a rope of fixed length L.  Assume Anna begins walking at the origin of a coordinate plane and that the sled is initially at the point (0,L).  She walks to the right along the x-axis dragging the sled behind, as shown in the figure. (Click on the figure to enlarge it.)  Find an equation for the path of the sled.

Congratulations to the following correct problem solvers: Philip LaPorte, Anthony Nguyen, Forest Rulison, Mackenna Senti and Will Zywicki

Problem of the Fortnight

"Valentine's Day is coming up soon," thought Mrs. Hartsema.  "I should get a little something for my grandchildren."  She decided to give each of her 31 grandchildren a number of candy hearts along with their Valentines.  After counting her candy hearts and finding 470 of them, Mrs. Hartsema figured that each girl would get 7 more candy hearts than each boy.  She gave 74 candy hearts to the children of her eldest son Art.  How many girls did Art have?

Write your solution (not just the answer!) on the back of a Valentine, and drop it in the Problem of the Fortnight slot outside Professor Pearson's office (VWF 212) by 3:00 p.m. on Friday, February 9.  As always, be sure to include your name and the name(s) of your math professor(s)---e.g. Val N. Tyne, Professor Hallmark---on your solution.  

This is one time where television really fails to capture the true excitement of a large squirrel predicting the weather.

from Groundhog Day

Off on a Tangent