International Journal of Scientific & Engineering Research, Volume 3, Issue 10, October-2012 1 ISSN 2229-5518 IJSER © 2012 http://www.ijser.org TUNING OF MUSICAL NOTES THROUGH MATHEMATICS ANUSHREE SAH, SAURABH RAWAT, BHASKAR NAUTIYAL, ADIL AHMED, OKESH CHHABRA Abstract— Mathematics, an enigma in numbers and calculations, often accompanied by feelings of rejection and disinterest while Music, a flow with emotions, feelings and life. Motivation for investigating the connections between these two apparent opposites’ pol es is attempted in this paper. A correlation between Mathematics and Music is shown.. Music theorists sometimes use mathematics to understand music. Mathematics is "the basis of sound" and sounds itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical". In today’s technology, without mathematics it is difficult to imagine anything feasible. In this paper we have discussed the relation between music and mathematics. How piano keys are interrelated with mathematics, frequencies are correlated and discussed. With the aid of mathematical tools, regression, geometric progression, tuning frequency can be calculated and further related to key of piano used to produce that particular frequency . This paper will also be helpful for music seekers and mathematician to understand easily a relationship between Mathematics and Music from a mathematician prospective.[12] Index Terms— Piano frequencies, regression, geometric progression,piano keyboard, tuning, sine wave. ——————————  —————————— 1 INTRODUCTION he patterns that exist between math, language, and music have prompted numerous studies to be commissioned to establish their inter- relationship. Music is a series of notes that are played in accordance to a pattern and math’s too works in a similar way. In math’s a result always remains fi- nite despite the various ways in which you can add, multiply, subtract, and divide numbers. The same can be said about music. Notes can be combined in an endless variety of groupings but the number of notes and sounds that exist are finite. It is these patterns and combina- tions that make music and math very similar.[11]. Mathematics and music are interconnected topics. “Music gives beauty and another dimension to mathematics by giving life and emotion to the numbers and patterns.” Mathematical concepts and equations are connected to the designs and shapes of musical instruments, scale intervals and musical compositions, and the various properties of sound and sound production. This paper will allow exploring several aspects of mathematics related to musical concepts. The ancient Greeks figured out that the integers correspond to musical notes. Any vibrating object makes overtones or har- monics, which are a series of notes that emerge from a single vibrating object. These notes form the harmonic series: 1/2, 1/3, 1/4, 1/5 etc. The fundamental musical concept is proba- bly that of the octave. A musical note is a vibration of some- thing, and if you double the number of vibrations, you get a note an octave higher; likewise if you halve the number of vibrations, it is an octave lower. Two notes are called an inter- val; three or more notes is a chord. The octave is an interval common to all music in the world. Many people cannot even distinguish between notes an octave apart, and hear them as the same. A musical keyboard is the set of adjacent depressible levers or keys on a musical instrument, particularly the piano. Key- boards typically contain keys for playing the twelve notes of the Western musical scale, with a combination of larger, long- er keys and smaller, shorter keys that repeats at the interval of an octave. Depressing a key on the keyboard causes the in- strument to produce sounds, either by mechanically striking a string or tine (piano, electric piano, clavichord); plucking a string (harpsichord); causing air to flow through a pipe (or- gan); or strike a bell (carillon). On electric and electronic key- boards, depressing a key connects a circuit (Hammond organ, digital piano, and synthesizer). Since the most commonly en- countered keyboard instrument is the piano, the keyboard layout is often referred to as the "piano keyboard". The twelve notes of the Western musical scale are laid out with the lowest note on the left; The longer keys (for the seven "natural" notes of the C major scale: C, D, E, F, G, A, B) jut forward. Because these keys were traditionally covered in ivo- ry they are often called the white notes or white keys. The keys for the remaining five notes—which are not part of the C major scale—(i.e .,C♯, D♯, F♯, G♯, A♯) are raised and shorter. Because these keys receive less wear, they are often made of black colored wood and called the black notes or black keys. The pattern repeats at the interval of an octave. 1.1 Piano Keyboard [10] For understanding of this paper, it is important to have some knowledge of the piano keyboard, which is illustrated in the following diagram. This keyboard has 88 keys of which 36 (the top of the illustration), striking each successive key pro- duces a pitch with a particular frequency that is higher than the pitch produced by striking the previous key by a fixed interval called a semitone. The frequencies increase from left to right. Some examples of the names of the keys are A0, A0#, B0, C1, C1#. For the purposes of this paper, all the black keys will be referred to as sharps (#). In this paper different fre- quencies of piano are discussed, how they are produced peri- odically with the use of Regression Analysis and Geometric Progression. T