This is Mathematics AA HL IA written in 2021 that got a 6. The research question is “Modelling Musical Chords and their Beat Frequencies”.

[Sample excerpts]

### Introduction:

The aim of this investigation is to model two different musical chords in order to find the relationship between harmonious chords and their beat frequencies. Beats can be defined as periodic patterns of variations in volume, which are heard when two sound waves with similar frequencies interfere with one another. Beat frequency is the number of beats generated in a second. Some mathematical concepts of trigonometry such as sine and cosine graphs, their properties, and sum to product formula will be used throughout the modelling process. This topic has a significant importance as it may prove the correlation between math and music and lead to the establishment of a formula in finding consonant or dissonant chords. The former can be defined as notes that together produce harmonious and stable sound, while the latter are those that produce unpleasant or strange sounds. Personally, I have chosen this topic because I found the link between two distinct subjects, math and music, very interesting. For math being a logical and accurate subject and music the opposite, I wanted to explore the possible application of math in affecting the emotion and sense perception of people. Furthermore, for enjoying playing piano myself, finding a possible mathematical formula for consonant chords is of great importance, as it would facilitate the composition of music that pleases the ears of many.

Throughout the investigation, I will be using the note A440 (pitch A with the frequency of 440Hz), as base note, comparing other notes with it. This is because the note A440 is considered a standard musical pitch, determined by the International Organization of Standardization, and serves as a tuning standard, a pitch most commonly referenced in tuning musical instruments…

• Total number of pages: 24 pages
• Topic: Modelling Musical Chords and their Beat Frequencies
• Subject: Mathematics
• The file is in Word format.