On the Mathematics of Music: From Chords to Fourier Analysis
نویسندگان
چکیده
Mathematics is a far reaching discipline and its tools appear in many applications. In this paper we discuss its role in music and signal processing by revisiting the use of mathematics in algorithms that can extract chord information from recorded music. We begin with a light introduction to the theory of music and motivate the use of Fourier analysis in audio processing. We introduce the discrete and continuous Fourier transforms and investigate their use in extracting important information from audio data.
منابع مشابه
شکل‌گیری فضا در اثر پیوند مفهومی «موسیقی – ریاضی» و معماری (مطالعه‌ی موردی: جلوخان و آسمانهِ گنبدخانهِ مسجدِ شیخ‌لطف‌الله اصفهان)
In traditional architecture, the adherence of architects to the rules and proportions in numbers, geometry and music is present in designing and shaping many public monuments, and mathematical proportions, artistic ratios, or musical proportions are used in geometry of these buildings. Extracting and matching mathematical rules and proportions and examining them in the architecture of the tradi...
متن کاملMethods for Classifying Pictures and Generating Music by 2D DFA and 1D FFT
This study proposes the following two methods applying two-dimensional DFA (detrended fluctuation analysis) and one-dimensional FFT (fast Fourier transform) algorithm: (1) a method for finding pleasant photographs of local tourist spots, and (2) a method for creating music from these photographs. We define “pleasant photograph” as the photograph containing 1/f noise components since it has been...
متن کاملFluctuation Analysis for Photographs of Tourist Spots and Music Extraction from Photographs
This study proposes the following two methods applying one-dimensional FFT (fast Fourier transform) algorithm: (1) a method for finding pleasant photographs of local tourist spots, and (2) a method for creating music from these photographs. We define “pleasant photograph” as the photograph containing 1/f noise components since it has been suggested that the 1/f -noise structure in visual art as...
متن کاملA Statistical View on the Expressive Timing of Piano Rolled Chords
Rolled or arpeggiated chords are notated chords performed by playing the notes sequentially, usually from lowest to highest in pitch. Arpeggiation is a characteristic of musical expression, or expressive timing, in piano performance. However, very few studies have investigated rolled chord performance. In this paper, we investigate two expressive timing properties of piano rolled chords: equiva...
متن کاملDouble diffusive reaction-convection in viscous fluid layer
In the present study, the onset of double diffusive reaction-convection in a uid layer with viscous fluid, heated and salted from below subject to chemical equilibrium on the boundaries, has been investigated. Linear and nonlinear stability analysis have been performed. For linear analysis normal mode technique is used and for nonlinear analysis minimal representation of truncated Fourier serie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- CoRR
دوره abs/1306.2859 شماره
صفحات -
تاریخ انتشار 2013