Tag Archives: music

Connecting Science, Maths & Music

In Peter’s workshop today we learnt about waves and vibrations. So what is a vibration? Where do you come across vibrations? And what happens during a vibration?

A vibration is the forward and backward motion of an object in a regular pattern. Vibrations can be so fast that you cannot see them. Vibrations start of big and become smaller and smaller unless energy is provided to keep the waves big. These vibration make sound occur.

Vibrations are detected by the ear. Once the sound travel to our ear, our ear drum vibrates and these vibrations are passed through the three small bones (called ossicles) to a spiral structure called the cochlea. Signals are passed from the cochlea to the brain through the auditory nerve, and our brain interprets these signals as sound.

We come across vibrations in every day life. A major vibration you would find it to communicate without is your vocal cords! Your vocal cord vibrate when you speak to make sound. In school when you ping a ruler or elastic band over an object you can often see the vibrations, the waves going backwards and forwards. If you go to a music festival and stand beside the huge loud speakers you can see and hear the bass vibrating the speaker. You can see and hear vibrations when they are at low frequencies.

Sound travels outwards in oscillations (backwards and forwards motion), in all directions, from the equilibrium point. The air around the equilibrium point creates the sound waves. Sound travels in longitudinal waves. Waves are made up of compressions and rarefactions. Compression happens when molecules are forced, or pressed, together. Rarefaction is just the opposite, it occurs when molecules are given extra space and allowed to expand.

 

Sounds waves need a medium to travel through, they will travel in a gas, liquid or solid – not empty space. The vibrations shake up the particles around them and these particle create a domino effect for the sound the travel. You can experiment with these three forms by making string telephones, talking underwater and putting a drinking glass to a wall.

To make something louder you need to add more energy to it, the term amplitude can be used to refer to loudness. Amplitude is the maximum height of the wave from its resting position – the greater the amplitude, the louder the sound. Pitch is to do with the frequency or number of vibrations per second. Frequency is measured in hertz (Hz). The closer together the waves are and the higher the pitch. On a guitar sting, the shorter the sting the higher the pitch will be as the vibration have less material to cover therefore the pattern of oscillations is more regular.

At the end of Peter’s workshop we got to experiment with vibrations and Beth, Beth and I experimented with music.

♪ Do Re Mi Fibonacci ♫

My whole life I’ve been musical. My passion started when my mum bought me a harmonica and a second hand keyboard. I fell involve with music and have played an instrument ever since I was 8 years old. I started with the keyboard then progressed to cello, guitar, singing and saxophone. I did grades in saxophone and managed to get to grade 6 by the end of school. I was a key instrument in the school concert band which took me to 2 countries and many concerts around my home. I had a strict pattern of practising every night, much to my mum’s annoyance, and my sister also screeched her clarinet through the house most nights. My musicality and good rhythm combines with my other hobby of dancing, in particular tap which involves precise beats coming from your shoes.

Today in discovering mathematics, Paola talked about the links between maths and music. And not too surprisingly there’s quite a few.

  • Note values/rhythms
  • Beats in a bar
  • Tuning/Pitch
  • Chords
  • Counting songs
  • Fingering on music
  • Time signature
  • Figured bass
  • Scales
  • Musical Intervals
  • Fibonacci sequence

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface.” (Sautoy, 2011).

As I have explored in a previous blog, the Fibonacci sequence (the golden ratio) exists in art and nature but did you know it’s also seen within music! If you’ve read my previous blogs you should be all clued up on it. The scales in music relate to the Fibonacci sequence, there are 13 notes in the span of any note within it’s octave. A scale has 8 notes in it, and within that the 3rd and 5th notes, along with the 1st note, create the simple foundations of any given chord. The scale is based on a tone, the tone is a weave of 2 steps and 1 step between notes (black and white) from the root tone (the 1st note of the scale) (Meisner, 2012).

The 5th note is the ruling note of the major scale. This note is also the 8th note of the 13 notes that are in an octave. This gives more proof to the theory of the Fibonacci sequence in music. What’s more, 8 ÷ 13 = 0.61538…, which resembles Phi (Meisner, 2012).

Compositions are frequently based on Phi. The timings in songs reflect the Fibonacci sequence in that when a song climaxes it often lands at 61.8% through the song. We can also find the golden ratio in the design of musical instruments. For example in the violin (Meisner, 2012).

I used to hate doing scales in music lesson. I would always make up rhymes to remember what notes are in which scales. But Paola taught us a mathematical process for know what every note is in every major scale! I wish i’d known this back in school. The pattern goes tone, tone, semitone, tone, tone, tone, semitone. A tone is when you skip a note in-between 2 other notes and a semitone is just one notes to the immediate next note. These all include the black notes (flats and sharps).

The pentatonic scale was a new concept that I hadn’t come across in my previous music knowledge. The scale is found all around the world is every country and is the foundations for a lot of classic hits. The pentatonic scale is made up of 5 key black notes. It has the same pattern as we discussed for the major scales, so a pentatonic C sharpe scale would go C#, D#, F, F#, G#, A#, C, C#.

In closing, interconnectedness is beaming in the subject of music and maths. Liping Ma’s theory is definitely becoming more and more accurate and clear. I can definitely see myself teaching music with connectedness in mind in the future to my classes, which will give them a more thorough understanding of it.

One more thing, did you know it’s impossible to tune a piano!

 

References:

Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available at: http://theclassicalsuite.com/2011/06/listen-by-numbers-music-and-maths-via-guardian (Accessed: 08/11/17).

Meisner, G. (2012). [Website]. Available at: https://www.goldennumber.net/music/ (Accessed 08/11/17)