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Handout for Spectral Music: Manifesto or Metaphor – Fèlix Pastor 

Figure 1 (from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

nthPartialFreq = (n*fundFreqd) + s

Overtone series (n = integer, d = 1, s=0):

Figure 2 (from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

dilated spectrum (n = integer, d = 1.1, s=0):

contracted spectrum (n = integer, d = 0.9, s=0):

shifted spectrum (s = 100Hz):

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Figure 3 (from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

Spectrum of a cowbell:

Figure 4 (from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

Frequency Modulation:

Figure 5 

(from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

Ring Modulation:

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Figure 5b

Ring modulation done in the flute (Ethers – T. Murail):

Figure 6 (from Guide to Basic Concepts and Techniques of Spectral Music, Joshua Fineberg)

Evolution of the spectrum of a cowbell:1. non-harmonic spectrum:

2. upper partials begin to disappear and some notes shift:

3. upper partials have faded even more and certain notes have shifted:

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Figure 7

Starting structure of Ethers excerpt. Note the distinct frequency bands:

Figure 8 (from French Spectral Music, François Rose)

The initial harmonic structure of Partiels (G. Grisey):

The journey toward inharmonicity: