Minimal music

But a totally different kind of minimal:

(Thanks to EnsembleXY for introducing me to this piece)

Spectral Music

Some examples:

• Gerard Grisey: Partiels
• Kaija Saariaho: Verblendungen
• Giacinto Scelsi: Konx-Om-Pax (though it wasn't called spectralism then). 
• Jonathan Harvey: Still. 

François Rose's Perspective of New Music article explains some of the composition methods.

Additive synthesis

Additive synthesis is based on the superposition of simple sine tones. A video tutorial explaining the [osc~] object and how it works:

Read about additive synthesis technique here and here. A Theramin inspired demo using wiimotes to control an additive synthesis patch. And an acoustic instrument based on Fourier analysis mapped to additive pipe organ. 

Spectrum

• Definition from the Handbook of Acoustic Ecology.
• More about sound & spectrum from physclips.
• Analysing and transforming sounds with open source program SPEAR.
• Composition based on piano overtones from Erik Oña.
• Music on a Long Thin Wire. And here is a video documenting a reconstruction of the piece.
• Discussion of tuning and timbre.
• Spectral transformation plug-ins Soundmagic Spectral.