Class 12th presentation on maths in music

presentation on maths in music

1. Math’s Project Math in Music

2. Topic – Maths in Music Subject :- Mathematics Session :- 2023-24 Class :- 12 th A Roll no. :- 21 Submitted by :- Sakshi Bisht Under the guidance of :- Mr. Amit Guleria Mount Litera Zee School

3. Introduction Brief description to the topic Description of forms of music and rhythm 02 04 01 Background Historical Background of music Analysis 03 Connections Connections of music to mathematics Mathematical principles 05 Mathematical elements in music Relation 06 Influence of math and music on each other Table of contents… 📃

4. Table of contents …📃 Mathematicians and music Common examples Common examples of mathematics. Contributions of mathematicians in music Conclusion 07 08

5. — Pythagoras “ There is geometry in the humming of strings there is music in the spacing of the spheres .”

6. Introduction 01 Introduction to the topic “Maths in Music” 01 Introduction

7. Maths and music have always been considered closely connected in many ways. Counting , rhythm , scales , intervals ,patterns , symbols , harmonies , time signatures , over tunes , tone , pitch. The notations of composers and sounds made by musicians are connected to mathematics. Music theory of mathematics analyzes pitch , timing and structure of music . It involves use of mathematics to study elements of music such as tempo , chord progression , form and meter. It is widely believed that the students who do well in music also excel in maths. Let us have a closer look at each of the aspect….. Maths In Music🎵🎼

8. 02 Background

9. Though ancient Chinese, Indians, Egyptians and Mesopotamians are known to have studied the mathematical principles of sound , the  Pythagoreans  of ancient Greece were the first researchers known to have investigated the expression of  musical scale s  in terms of numerical  ratios , For about a millennium, from 600 BC, Ancient Greece was one of the Worldʼs leading civilizations . The ideas and knowledge produced at this time have had a lasting influence on modern western civilizations. The “Golden Age” in Greek antiquity was approximately 450 BC, and much of what constitutes western culture today began its invention then . Brilliant Greek academics contributed a wealth of knowledge about music, philosophy, biology, chemistry, physics, architecture and many other disciplines. Early South Asian theorists show similar approaches: all sought to show that the mathematical laws of  harmonics  and  rhythms  were fundamental not only to our understanding of the world but to human well-being. Historical background of music

10. Pythagoras is often referred to as the “father of numbers.”  He can also be considered the “father of harmony,” Pythagorus of Samos lived between c.570 BC and c.495 BC. He was ancient Greek philosopher greatly influenced by Plato , Aristotle and western philosophy. It is impossible to measure his complete influence on science and philosophy. It is said that Pythagoras formed the connection between music and math when he heard a smith hammering the anvil. He found out that they formed harmonious beats because of the order of the weights which were being hit. They were in the ratio 6,8,9 and 12 pounds, which formed  Do ,  Fa ,  Sol ,  Do  of the music scale. . Pythagorus on music

11. Pythagoras is attributed with discovering that a string exactly half the length of another will play a pitch that is exactly an octave higher when struck or plucked.  Pythagoras believed that the planets themselves, all heavenly bodies, rang out notes of vibration based on their orbit and distance to each other . Pythagorean tuning  is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2  .  This ratio, also known as the “pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3.  The  Pythagorean scale  is any scale  which can be constructed from only pure perfect fifths (3:2) and octaves (2:1) Pythagorean temperament however one is limited by 12-tones per octave and one cannot play most music according to the Pythagorean system corresponding to the enharmonic notation Pythagorean tuning🎼

12. 03 Analysis

13. Analysis of musical terms Without the boundaries of rhythmic structure – a fundamental equal and regular arrangement of pulse repetition , accent , phrase and duration – music would not be possible. Measure is the space between two bar lines on the staff that represen ts the division of time by which air and movement of music are regulated. Rhythm – It is the uniting and dividing of beats and arranging them into patterns . When we play a few different notes together or even repeat the same on an instrument , we create something called rhythm. It measures time. Musical scale - A musical scale is a discrete set of pitches used in making or describing music. Each pitch corresponds to a particular frequency, expressed in hertz (Hz), sometimes referred to as cycles per second ( c.p.s .). Octave -  A scale has an interval of repetition, normally the octave. The octave of any pitch refers to a frequency exactly twice that of the given pitch . Rhythm is to Music as Numbers are to Math (🎶) ➕ (🎼 )🟰 (🎖️)

14. 04 Connections

15. If music is a pattern of sounds, then mathematics is the study of such patterns Music involves creating patterns of sound, whereas Mathematics is the study of patterns. These patterns appeal to our innate desire for mathematical rhythm and patterns. The beats which make up music are periodic in nature. Creating appealing beats involves the generation of notes with the right mathematical combination and changing frequencies and periodicity . Melody is made up of waves and mathematically, a perfect melody, when graphed makes a sine wave. It is known that sine wave is the most perfect wave and can be made only in the laboratory or by a tuning fork . Universally, it is found that humans love music involving smaller ratios of frequency between two notes Relationship between Math and music

16. Math and music are two entirely different fields of study, but there is a strong correlation between them. Use of some mathematical concepts in music is as :  Set theory : Musical set theory uses the language of mathematical  set theory  in an elementary way to organize musical objects and describe their relationships. To analyze the structure of a piece of (typically atonal) music using musical set theory, one usually starts with a set of tones, which could form motives or chords. 05 Mathematical principles

17. Abstract algebra : Expanding on the methods of musical set theory, some theorists have used abstract algebra to analyze music. Theorists have also proposed musical applications of more sophisticated algebraic concepts. The theory of regular temperaments has been extensively developed with a wide range of sophisticated mathematics, for example by associating each regular temperament with a rational point on a  Grassmannian . Numbers and series : Some composers have incorporated the  golden ratio  and  Fibonacci numbers  into their work. Category theory : The mathematician and musicologist  Guerino Mazzola  has used  category theory for a basis of music theory, which includes using topology as a basis for a theory of rhythms and motives , and differential geometry as a basis for a theory of musical phrasing, tempo, and intonation. Mathematical elements in music (➗➕)

18. The Fibonacci sequence plays a big part in western harmony and musical scales. Here are the facts: An octave on the piano consists of 13 notes . Eight are white keys and five black keys. A scale is composed of eight notes , of which the third and fifth notes create the foundation of a basic chord. In a scale , the dominant note is the fifth note, which is also the eighth note of all 13 notes that make up the octave. Composers and instrument makers have been using the Fibonacci Sequence and the Golden Ratio for hundreds of years to compose and create music. Mozart , for instance, based many of his works on the Golden Ratio – especially his piano sonatas. Golden ratio and Fibonacci in music

19. Math helps in reading music. Music is divided into sections that are called measures, where each measure has equal amounts of beats. This is comparable to mathematical divisions of time. The frequency of music is related to math. The famed Pythagoras found out that different weights and vibrations make different sounds. Based on this discovery, we now know that the pitch of a vibrating string is directly proportional to its length. The pitch can also be controlled by its length. Patterns are common in both. The biggest similarity between math and music is patterns. For example, music has repeating verses and choruses while math uses patterns to explain the unknown. We can use different mathematical phenomena in music. These include geometry, signal processing, differential calculus, and even trigonometry. Music helps us study and think . There is a strong correlation between music and the way we study. Research shows that when children are given proper instructions on musical instruments, they score high on tasks that require spatial-temporal cognition, math, and hand-eye coordination. This can be attributed to the relation between music and math skills . Functional Relation 06 R elation

20. Mathematics and Music, the most sharply contrasted fields of intellectual activity which one can discover, and yet bound together, supporting one another as if they 'would demonstrate the hidden bond which draws together all activities of our mind, and which also in the revelations of artistic genius leads us to surmise unconscious expressions of a mysteriously active intelligence. Mathematicians fascination with music theory are explained clearly and precisely by Jean Philippe Rameau in Traité de lʼHarmonie Réduite à ses Principes Naturels (1722). Some musicologists and academics argue that Rameau was the greatest French music theorist of the eighteenth century Mathematicians in music 07

21. Albert Einstein  - Accomplished pianist and violinist. Art Garfunkel  ( Simon & Garfunkel ) – Masters in Mathematics Education, Columbia University Brian May  ( Queen ) -  BSc (Hons)  in Mathematics and Physics,  PhD  in Astrophysics, both from  Imperial College London . Dan Snaith  – PhD Mathematics, Imperial College London Delia Derbyshire  -  BA  in mathematics and music from  Cambridge . Jonny Buckland  ( Coldplay ) - Studied astronomy and mathematics at  University College London . Kit Armstrong  - Degree in music and MSc in mathematics. Manjul Bhargava  - Plays the  tabla , won the  Fields Medal  in 2014. Phil Alvin  ( The Blasters ) – Mathematics, University of California, Los Angeles Philip Glass  - Studied mathematics and philosophy at the  University of Chicago . Tom Lehrer  - BA mathematics from  Harvard University . Musicians who were also mathematicians 🎼🟰

22. Mathematics in guitar . The guitar produces very sophisticated music by producing different sound frequencies. Guitars designers/builders are called luthiers. Stretched tightly between two points, a string when plucked, makes a specific tonal pitch. Pythagoras discovered that if the length of this string were to be cut in half, the pitch made would be equal in tone but at twice the frequency; an octave. The length of the string, tension, and its gauge (thickness) determine the pitch. On a guitar, the string length is controlled by the placement of frets on the neck. Pleasant to the Western ear, the guitar neck is designed on a 12-pitch chromatic scale based on his principle. The 12th fret is the octave of that string. A formula, developed by Vincenzo Galilei in the 16th Century, mathematically determined the calculation of the distance between the tones initially uncovered by Pythagoras Examples of math in music 08

23. Mathematics is not about numbers , computations or algorithms; it is about understanding. This quote is a reminder in order to stay interested with mathematics despite all the difficulties and obstacles that may occur in helping me learn especially with this topic. We can conclude that there is an application of mathematics in music. Mathematics helps in creation of music and in listening to music. With this research we show that by applying of mathematical combination of sequences of tones we can create music, which will sound beautifully and the same is very pleasant for listening. It shows that the transposition, inversion and retrograding in the music have some mathematical characteristics. We could say that mathematics as a science completes the music as art and they are in direct correlation. Conclusion

24. The end Thank you🙏