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Music and Maths - a summary by Finn Jensen, Cymaz Music Intern
In terms of relativity, music and maths are probably the most comparable classroom subject alongside linguistics and English. The fundamentals of western music are built around repeating figures of four and eight, this has a direct tie to patterns of numbers and fractions. In world, classical and more unorthodox western music, more complex rhythmical and harmonic patterns are often employed. This means music and maths in a learning environment can be tailored to any age or ability.
Reports • “The Mozart Effect” – A study showing that children learning life skills and academic (specifically mathematical) tasks accomplish these tasks more efficiently while listening to Mozart.
Articles • This article is testament to the effectiveness of music and maths in the classroom. This gave students who were taught fractions as rhythms a 50% increase in test scores compared to students that were taught traditionally.
• Here is another article referencing a similar improvement through the same learning style. • Further evidence: An Exploration of the Relationship between Maths and Music Activities
• Music in Maths Classroom Exercise:
Objective: Students will learn how maths and music are related. The students will understand how mathematical addition is applied to music. To help them understand this concept the students will be learning note values while reviewing addition. The students will add musical notes together and come up with a real number as the answer. Students will be able to understand addition beyond their textbooks in real practical terms.
Materials: Paper, Pencil, Sheet Music worksheet Visual Resources: Poster showing note and rest values Procedure:
• Introduce students to the concept of addition and music.
• Give an example of an addition problem using both real numbers and musical notes.
• Review the four basic note values with students. Demonstrate what those note values sound like.
• Demonstrate a couple of problems with the students on the board. Show them how they can add a quarter note to a half note and come up with an answer of three.
• Give the students a few problems to do on their own.
• Go over the problems with the students, calling on them to write their answers on the board.
• Have students create their own problems with the answers to them.
• Review with the students why addition is used in music and the importance of it.
Assessment: Have students do five addition problems using notes as their product. Have students create ten different addition problems with answers using notes to create them with 80% accuracy. Students will orally describe why math is important to other subject areas, such as music.
My thoughts: This is a really excellent introduction to learning or solidifying both relevant skills. It teaches simple maths while having the logical musical education to back it up, and vice versa. This exercise can be modified to be as difficult or as simple as needed. Most importantly, it gives an introduction to fundamental music theory, which is extremely useful if taught at an early age.
The Fibbonacci Sequence Objectives
• Students will be able to list some connections between mathematics and music.
• Students will describe the Fibonacci number pattern sequence, commonly called the Fibonacci Sequence, and explain some ways that it appears in music.
• A picture of a keyboard, prominently displayed in the classroom
1. Write six numbers of the Fibonacci Sequence on the chalkboard.
o Ask students to relate how the numbers are generated. Then, ask them to list the next nine or ten numbers in the sequence.
o Tell them a little about Leonardo of Pisa.
2. Tell the students that mathematicians have found that an unusual quantity of items have Fibonacci numbers associated with them. For example, you can mention that in nature, poison ivy has the Fibonacci number 3. Wildflowers often have 5 petals.
3. Ask the students to look around the room and find something that may have a Fibonacci number associated with it. Students should discover that a keyboard has 8 white keys, 5 black keys, and 13 notes all together in each octave. Also, the Pentatonic scale has 5 notes, the Diatonic scale has 8 notes, and the Chromatic scale as 13 notes – all Fibonacci numbers!
4. For further information, tell the students that the vibrations per second of different musical intervals are in Fibonacci ratios. For example, C and A are 264 cycles per second and 440 cycles per second – a ratio of 3/5, two Fibonacci numbers. The minor sixth E to C is 330/528 = 5/8.
5. You may want to ask more advanced music students to search for other Fibonacci ratios in musical scores. The ratios between the number of measures in a sonata exposition, the number of measures in the development and recapituation sections (together), and the movement as a whole often approximate Fibonacci ratios. The first movement of Bartok's Music for Strings, Percussion, and Celeste is a famous example of this means of organization.
My thoughts: The Fibonacci Sequence is fascinating. For an older group, compared to the previous exercise this is somewhat challenging but has a fantastic demystifying effect on complex rhythm. This exercise can also be used in science, advanced mathematics and history. It really shows the correlation between maths and music in a great way. With a more practical element (such as learning and performing Fibonacci rhythms, or counting the rhythm of the vocal melody in “Lateralus” by Tool) this could possibly become more accessible to younger learners.