# Mathematics in Music: Is there a Relationship?

If people of different races across the world had to cast aside their creeds and create a list of things that they would commonly participate in, musical celebration would probably be somewhere at the top. No matter who you are or what language you speak, good music that you can groove to is something that won’t ever let you be cranky.

Another thing that various people often inevitably find themselves to be a part of, whether they have a love-hate relationship with it or no, is mathematical calculation. Music and mathematics are two things that supersede language. Does a relation exist between them? Let’s catch on.

## What is the role of Mathematics in music?

In simple terms, whatever we can hear with our ears, we term as sound. Our auditory sense enables us to hear different sounds and depending on what happens to us when we hear them, we classify them as simple sounds or as noise. The speech of people, the chirping of birds and the flow of water into a stream are all sounds that won’t disturb our ears. On the contrary, the eruption of a volcano, a car crash and someone’s scream produces noises that agonise us. Then comes music, it is something we thoroughly enjoy. It would come as a surprise to you if I told you that boring mathematics is responsible for making music sound so perfectly sweet and not so boring.

### Role of Permutation and Combination in Music

Every singer and instrumentalist in the world produces a song in a certain scale. The word ‘scale’ refers to an ordered collection of notes. Most songs, whether vocal or instrumental are sung or played in scales that contain seven notes.

For instance, Twinkle Twinkle Little Star, the world-famous nursery rhyme that most of us hummed as kids is performed by novice piano learners usually in the scale of C major, which contains the notes C,D,E,F,G,A and B. It utilises all the notes of the scale C major except B. This is where the role of permutation and combination comes in.

The song essentially contains 42 notes from the start to end. It is imperative for the combination of these notes to include C,D,E,F,G,A and exclude B. But wait, the story doesn’t end here. What finally is the most important is that it includes those notes in the very exact order in which all the 42 notes are played in the song. This permutation alone will make it sound like the exuberant original song and any deviation in the combination will cause a deviation in the permutation and will ultimately breed a new song altogether.

All solids, liquids and gases are capable of producing sound waves. Musical instruments are solid objects that vibrate and depending on how fast or slowly they do, 12 distinct musical notes are generated. Of these, 7 have been named as A,B,C,D,E,F and G. Such vibration determines the frequency of the note and is measured in terms of Hertz( A unit that measures the number of waves completed in one second in different areas of physics).

### Role of Geometric Progression in Music

In the scale of A minor, which has the order of A, B, C, D, E, F and G, if the note A has a frequency of 110 Hz, then the frequencies for the remaining notes would go on increasing. But wait, what will happen when someone is done singing or playing the last note G? The note of A will again repeat after G.

However, this time, the frequency of this new A would be twice of the previous one, which is exactly 220 Hz. Note that it is the same note, but would sound more high pitched, simply because the sound waves produced are doubled; the instrumental or vocal vibration is faster. This musical interval between a certain frequency and another one that has double the frequency is thus called as an octave.

Note that A2 and A3 have frequencies of 110 Hz and 220 Hz respectively. Similarly, the frequency of B3 would be twice of B2 and half of B4. Hence, The frequency of any note would be twice of the same note in the previous octave and half of the same note in the succeeding octave. The same holds true for all the notes of all those scales that have octaves.

Thus, if we know the frequency of a given note and wish to calculate the frequency of the same note in the subsequent octaves, it would be 2n times the frequency of that note, Similarly, for calculating the frequency of the same note in the prior octave, it would be 2-n times the frequency of the same note. This makes it incredibly clear that even geometric progression earns its place in the sun in music. The frequencies of further octaves progress in a geometric progression with a common ratio of 2 and as we go behind along the preceding frequencies, we observe a geometric progression with a common ratio of ½ .

### Role of Trignometry in Music

It is vital that studio music producers, singers, orchestra producers and even concert attendees get to listen to the best quality of music. Because sound waves travel from their sources and bounce off various objects such as stage equipment and even the walls of the premises in which they are created, musicians and architects work hand in hand and make extensive use of trigonometry to optimise sound production. Concert halls and studios are engineered and installed with panels to manipulate the angles at which the sound deflects and ensure that they are correctly reverberating.

### Role of Algebra and Probability

The world we live in has great mathematicians and bombastic musicians. The technological advancement in computer hardware and software that we have had over the years has given musicians the aid to create new electronic music compositions much faster. This is thanks to computer engineers and mathematicians who create melody generating software through coding. Coding is a process of designing a computer program based on mathematical logic, for executing instructions on the computer. In the process, extensive use of mathematical topics such as algebra and probability amongst others is found.

Humanity has been making music since prehistoric times. We have evidence of the existence of flutes that were carved out of animal bones during the paleolithic age. Fast forward, even one of the most famous pharaohs of Egypt, king Tut, who existed more than 3000 years ago, was found with trumpets in his tomb. The majority of mathematical and scientific discoveries were made after that. With the advent of that age, it become clear that those instruments created authentic music that was deemed to be worthy of being called music because it had some mathematical base imbued it, whether its makers knew of it or no.

While there is a coherent solid relation existing between music and mathematics, whether the proficiency at one boosts the expertise at the other or no, remains a matter of debate with studies both for and against the same. Either way, we see mathematics and music intertwine, and when that happens, it does not matter if one is a musician or a mathematician or is none of that. The convergence of two such things gives no choice but to marvel at such a cosmic marriage and be in awe time and again.