In which the ( P ) is the pressure in decibels ( dB ) One way to represent a musical note in a sine wave is the equation above. Measured in the unit Hertz (Hz), where 1 hertz is equivalent to 1 cycle per second (What is Frequency, 2021). Frequency is a rate in which the current changes it’s direction per second, it is Similarly, lowįrequencies are associated with low notes. The pressure quickly varies as high notes have a high frequency. The pitchĬorrelates to the frequency of the wave. Sounds usually have two characteristics, a pitch and volume. Generally, a musical sound is modelled using a sine wave, where the x-axis represents the time and the y-Īxis represents the pressure (What is Sound, n.). The functions are very important in understanding harmony as they are invariant (Glattfelder, 2019).Įvery chord that is described using whole numbers either has a greatest common divider ( GCD ) or a lowest common We can analyze the structure of a chord mathematically by identifying functions that are constant when theĬhord is altered. These notes can also be remodeled to base frequencies when multiplied by whole They can be described through a base frequency multiplied by rational Musical chords and harmonies all have note frequencies, which is the number of waves that pass a location in a certainĪmount of time (Communications Systems, n. Where the inspiration for my research question came and I started to look into the mathematical reasoning for why certainĬombinations of music notes sound harmonic and others not so much. That harmonies occur when two pitches vibrate at frequencies in small integer ratios (Music Math Harmony, n.). I came across how sine waves are used to represent soundwaves of different chords. Hence, I started searching about musical notes and chords and how they are presented mathematically. Have always been keen on learning how musical sounds are generated in the chords and in what form do they travel. Individual who enjoys listening to music, it made me curious to know how sounds travel and how this relates to math. I wanted to explore the fundamentals of how math and music come together to create beautiful sounds. The term “Musical Harmonies” was very intriguing to me when I first started researching how math and music tie I will also be looking at the beat and intervals and octave harmonics along with pitches and contrasting I willĭo this by studying a single string and seeing how changes to the string will affect the frequency and thus the sound the In this investigation, I will be focusing on why certain combinations of notes sound good together and others do not. Harmonics and sine waves as mathematical evidence? What makes certain combinations of musical notes sound harmonic and others not so much? How can we prove this using

$music math notes$

The programs I used to generate graphs are Excel and Desmos Graphing Calculator - A DEEP INVESTIGATION INTO THE FUNDAMENTALS OF MATHEMATICAL HARMONIES & SINE WAVES RESEARCH QUESTION

$music math notes$

I have acknowledged each use of the words or ideas of another person, whether written, oral or visual. MATHEMATICS: ANALYSIS & APPROACHES STANDARD LEVEL INTERNAL INVESTIGATION Candidate Number: hxw Subject: Mathematics Analysis & Approaches SL Date: February 17th, 2021 Due: February 19th, 2021 Candidate declaration: I confirm that this work is my own and is the final version.

Music math notes