# The Combinatorics of the Clarinet

## Presentation Type

Poster - Campus Access Only

Mark Kayll

## Faculty Mentor’s Department

Mathematical Sciences

## Abstract / Artist's Statement

The relationship between the individual key presses on the clarinet and the resulting frequency was studied in order to determine if it was possible to make a model to describe the resulting note by counting the keys that were pressed. Data was collected by making a recording to determine the multiplicative effect on the frequency, with a different recording being made for each key. The collection process went as follows: First, metadata was recorded in the form of verbal statement of the key number and any subsequent comments. A simple fingering was then played, followed by the pressing of the indicated key and then a return to the original fingering. This process was then repeated with a few different starting fingerings to allow for a more general analysis of the key. Current results show that some keys have a constant effect on the pitch regardless of the starting frequency, but most of the keys have a degrading effect on the pitch, tending towards a multiplier of one with higher starting frequencies. The next step in the process is to model their effect as a function with respect to the starting frequency. Once the effect of these keys can be expressed as functions, they can be combined with the keys of constant effect to create one model that encompasses the entire clarinet.

## Category

Physical Sciences

## Share

COinS

Apr 27th, 3:00 PM Apr 27th, 4:00 PM

The Combinatorics of the Clarinet

UC South Ballroom

The relationship between the individual key presses on the clarinet and the resulting frequency was studied in order to determine if it was possible to make a model to describe the resulting note by counting the keys that were pressed. Data was collected by making a recording to determine the multiplicative effect on the frequency, with a different recording being made for each key. The collection process went as follows: First, metadata was recorded in the form of verbal statement of the key number and any subsequent comments. A simple fingering was then played, followed by the pressing of the indicated key and then a return to the original fingering. This process was then repeated with a few different starting fingerings to allow for a more general analysis of the key. Current results show that some keys have a constant effect on the pitch regardless of the starting frequency, but most of the keys have a degrading effect on the pitch, tending towards a multiplier of one with higher starting frequencies. The next step in the process is to model their effect as a function with respect to the starting frequency. Once the effect of these keys can be expressed as functions, they can be combined with the keys of constant effect to create one model that encompasses the entire clarinet.