Download 101 Raga-s for the 21st Century and Beyond: A Music Lover's by Haresh Bakshi PDF

By Haresh Bakshi

ISBN-10: 1412231353

ISBN-13: 9781412231350

Indian classical song is so enduring that it really is exempt from oblivion. it truly is destined to stay in every age of this world.

This ebook on North Indian classical song (also referred to as Hindustani tune) tells you, easily and informally, concerning the most well liked one zero one raga-s, and 161 issues mostly pointed out in dialog, articles and books on Hindustani tune. it's the top instrument to benefit approximately and luxuriate in this style of tune, that's an important section of global track.

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Extra resources for 101 Raga-s for the 21st Century and Beyond: A Music Lover's Guide to Hindustani Music

Example text

Uniform convergence means that given ε > 0, there exists N (independent of a) such that for all values a of θ, m ≥ N implies |φm (a) − φ(a)| < ε. What happens with the Fourier series for the above function φ is that there is an overshoot, the size of which does not tend to zero as m gets larger. The peak of the overshoot gets closer and closer to the discontinuity though, so that for any particular value a of θ, convergence holds. But choosing ε smaller than the size of the overshoot shows that uniform convergence fails.

8) sin(2mπνt)F (t) dt. 9) 0 T bm = 2ν 0 Example. The square wave sounds vaguely like the waveform produced by a clarinet, where odd harmonics dominate. 16. 5. 2. FOURIER COEFFICIENTS 35 0 ≤ θ < π and f (θ) = −1 for π ≤ θ < 2π (and then extend to all values of θ by making it periodic, f (θ + 2π) = f (θ)). 0 2π 4π This function has Fourier coefficients π 1 am = cos(mθ) dθ − π 0 = bm = = = = 1 π sin(mθ) m 0 cos(mθ) dθ π sin(mθ) m − π 1 π 0 1 π − 1 π π 2π =0 π 2π sin(mθ) dθ − cos(mθ) m (−1) m 4/mπ 0 sin(mθ) dθ π π 0 − − cos(mθ) m 2π π m m − 2π + 1 1 (−1) + − m m m (m odd) (m even) Thus the Fourier series for this square wave is 4 π (sin θ + 1 3 sin 3θ + 1 5 sin 5θ + .

Which Fourier coefficients vanish for a periodic function f (θ) of period 2π satisfying f (θ) = f (π − θ)? What about f (θ) = −f (π − θ)? 4. 1), then we recover the original function f (θ). The most obvious problem is that if two functions differ just at a single value of θ then the Fourier coefficients will be identical. So we cannot possibly recover the function from its Fourier coefficients without some further conditions. However, if the function is nice enough, it can be recovered in the manner indicated.

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101 Raga-s for the 21st Century and Beyond: A Music Lover's Guide to Hindustani Music by Haresh Bakshi

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