Mathematics and Music.pptx
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This document discusses the mathematical concepts underlying music. It begins by outlining the presentation and introducing music and the human senses. It then discusses Fourier transforms and how they can be used to understand musical concepts mathematically. The document covers topics like musical scales, frequencies, harmonics, and provides examples analyzing musical notes from a flute and violin. It aims to demonstrate how mathematics and programming can help analyze and understand music.
Mathematics and Music.pptx
- 1. MATHEMATICS AND MUSIC 息 DR CHETAN B BHATT Dr. Chetan B. Bhatt Principal, Government MCA College Maninagar, Ahmedabad
- 2. PRESENTATION OUTLINE Music Introduction Human Senses Fourier Transform Understanding Mathematical Concepts with Music and SciLAB DR CHETAN B BHATT
- 3. Mathematics Geometry Engineering Science Music Harmonics Rhythmic/爐迦く Metrics/爐爐 爐 Astronomy DR CHETAN B BHATT
- 4. MUSIC Sound (爐о爐朽え爐) any mechanical vibration Musical Sound sound which has periodic frequency provides musical perception, it is called 爐逗ぞ爐 in Sanskrit. Musical Note Selected Nadas (爐逗ぞ爐) become 爐謹爐萎爐爐垂, 22 in numbers Selected 12 爐謹爐萎爐爐垂 become musical notes (爐伍爐朽ぐ) in a musical scale having certain characteristics DR CHETAN B BHATT
- 5. HUMAN EAR In our inner ears, the cochlea enables us to hear subtle differences in the sounds coming to our ears. The cochlea consists of a spiral of tissue filled with liquid and thousands of tiny hairs which gradually get smaller from the outside of the spiral to the inside. Each hair is connected to a nerve which feeds into the auditory nerve bundle going to the brain. The longer hairs resonate with lower frequency sounds, and the shorter hairs with higher frequencies. Thus the cochlea serves to transform the air pressure signal experienced by the ear drum into frequency information which can be DR CHETAN B BHATT
- 6. The human ear takes about '2045 msec' to identify a note within the range of the human voicefrom 1001000 Hz. DR CHETAN B BHATT
- 7. FREQUENCY OF MUSICAL NOTES DR CHETAN B BHATT A = 220 Hz A = 440 Hz A = 880 Hz Middle C = 261.6 Hz
- 8. Svara (Long) Sadja (爐劇ぁ爛爐) Rsabha (爐爐劇き) Gandhara (爐爐鉦え爛爐оぞ爐) Madhyam a (爐爐о爐爐) Pa単cama (爐爐爛爐爐) Dhaivata (爐о爐朽た) Nisada (爐爐逗し爐鉦う) Sadja (爐劇ぁ爛爐) Svara (Short) Sa (爐伍ぞ) Ri (爐萎) Ga (爐) Ma (爐) Pa (爐) Dha (爐) Ni (爐爐) Sa (爐伍ぞ) Varieties C D, D E, E F, F G A, A B, B CC Srutis in Sangita Ratnakara Tivra, Kumadva nti, Manda, Changova ti Dayavati , Ranjini, Raktika Rudri, Krodhi Vajrika, Prasarini, Priti, Marjani Kshiti, Rakta, Sandipini, Alapini Madanti, Rohini, Ramya Ugra, Kshobi ni DR CHETAN B BHATT 爐逗た爐 爐謹爐爛爐оぞ: 爐伍爐朽ぐ爐: 爐伍お爛爐 爐爐朽 爛 爐逗ぞ 爐爛爐朽ぞ爐爐謹ぞ爐爛爐爐爛 (爐伍爐爛爐 爐萎い爛爐爐鉦爐/Ocean of Music and Dance by Sharangdev 13th Century)
- 9. MUSIC AND MATHEMATICS Scale C D E F G A B C Indian Sa Re Ga Ma Pa Dha Ni Sa Western Do Re Mi Fa So La Ti Do 1 9/8 5/4 4/3 3/2 5/3 15/8 2 Sound Noise/Non-music Music DR CHETAN B BHATT
- 10. MUSICAL SCALE DR CHETAN B BHATT
- 11. MUSICAL SCALE AND FREQUENCY Note Low Middle High C 130.81 Hz 261.63 Hz 523.25 Hz C# 138.59 Hz 277.18 Hz 554.37 Hz D 146.83 Hz 293.66 Hz 587.33 Hz D# 155.56 Hz 311.13 Hz 622.25 Hz E 164.81 Hz 329.63 Hz 659.26 Hz F 174.61 Hz 349.23 Hz 698.46 Hz F# 185.00 Hz 369.99 Hz 739.99 Hz G 196.00 Hz 392.00 Hz 783.99 Hz G# 207.65 Hz 415.30 Hz 830.61 Hz A 220.00 Hz 440.00 Hz 880.00 Hz A# 233.08 Hz 466.16 Hz 932.33 Hz B 246.94 Hz 493.88 Hz 987.77 Hz DR CHETAN B BHATT
- 12. HARMONICS DR CHETAN B BHATT
- 13. FOURIER TRANSFORM The Fourier Transform is based on the discovery that it is possible to take any periodic function of time f(t) and resolve it into an equivalent infinite summation of sine waves and cosine waves with frequencies that start at 0 and increase in integer multiples of a base frequency f0 = 1/T, where the T is the period of f(t). The resulting infinite series is called the Fourier Series: Java Applet for Fourier Transform (http://falstad.com/fourier/) DR CHETAN B BHATT
- 14. FOURIER TRANSFORM The Fourier Transform is a mathematical technique for doing a similar thing - resolving any time-domain function into a frequency spectrum. The Fast Fourier Transform is a method for doing this process very efficiently. DR CHETAN B BHATT
- 15. Flute: G (392 Hz) note above C Middle DR CHETAN B BHATT
- 16. SCILAB FILE TO ANALYSE SOUND FILE DR CHETAN B BHATT
- 17. Violin: G (392 Hz) above C Miidle DR CHETAN B BHATT
- 18. DR CHETAN B BHATT 爛 爐伍爐朽ぐ爐爛爐むた 爐む爐朽ぞ 爐伍爐逗 爐逗ぐ爛 爐爐伍 爐爐逗ぐ爛爐 爐爐爐爐ムた: || 爐爐爛爐朽爐 || 爐逗爐 爐爐爐 爐伍爐爛爐逗ぎ爐 爐伍爐朽ぐ爛爐爛 爐爐萎ぎ爐鉦い爛爐爐 爐爛 爐爛爐爐鉦ぐ爛爐爐爛 爐逗 爐朽す 爐爐朽ざ爛爐 爐爛爐萎ぞ爐爛爐 爐項爐爐 | Thank You (爐оえ爛爐爐朽ぞ爐) DR CHETAN B BHATT
- 19. DR CHETAN B BHATT