AUTHOR(S): Minakshi Pradeep Atre, Shaila Apte

TITLE 
KEYWORDS Mathematical model, acoustic guitar, plucking, picking, octave multiplier, LMD, frequency analysis 
ABSTRACT To understand the musical instruments in detail, mathematical models for their behavior need to be developed. This understanding helps one knowacoustic principles and human perception of that instrument. The work is focused on mathematical analysis of box shaped acoustic guitar and primarily its music notes. It will help modeling the guitar string which is a distributed system. It can be excited either by plucking it or picking it. A set of 252 acoustic guitar notes are collected from each guitar player/artist by plucking all the six strings and 20 frets of each string by finger as well as pick. The aim of this work is to calculate and compare the frequencies generated by different methods such as Octave Multiplier and Linear Mass Density (LMD).Frequency analysis is carried out for different samples of music notes based on plucking style, finger or pick, plucking position and plucking expression.Understanding the different parameters contributing to generation of music notes on all frets of guitar string helps in modeling the acoustic guitar. The paper proposes a mathematical model for synthesis of Guitar notes. 
Cite this paper Minakshi Pradeep Atre, Shaila Apte. (2017) Mathematical Analysis of Acoustic Guitar Notes. International Journal of Signal Processing, 2, 2127 