Overtone

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The weights on the bars were laughable now. Most people had just the bar, or bodyweight. But the fatigue was so profound that lifting an arm felt like lifting a bag of cement.

The intensity of the sequence elevates the heart rate and increases oxygen consumption, leading to a higher caloric expenditure both during and after the workout.

The Ab track was a blur of crunches and planks. Mark was seeing stars. The room smelled of iron and sweat. It was a primal scent. He looked around. The woman next to him was crying silently, tears of exertion, but she was still crunching. The guy in the front row, a bodybuilder type, had dropped his weights entirely and was doing the motions with empty hands, his face purple with effort. bodypump 3t

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Mark smiled, a genuine, exhausted smile. "Yeah," he said. "I'll be here." The weights on the bars were laughable now

By track four—the Chest Press—Mark was flying high. He looked in the mirror. His muscles were swollen, vascular, feeling powerful. The lactic acid was just a whisper. This wasn't so bad, he thought. He could do this all day.

Mark picked up the lightest bar he could find. He curled. One. The burn was a white-hot fire, consuming his entire arm. Two. He grit his teeth so hard his jaw ached. Three. He didn't think he could make it to ten. Four. He looked at Sarah. She was shaking, her eyes closed, a look of serenity on her face amidst the agony. The intensity of the sequence elevates the heart

"You made it," she said, offering a fist bump.

Examples
In synthesizer experiments you select the amplitudes and phases of the fundamental and 9 overtones to construct the beginning of a Fourier series. The sum is seen on a graphics display and the signal is available as sound card output.
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You can test the Helmholtz assumption that the relative phases of the overtones are irrelevant to hearing.

In analyser experiments you capture sound from the sound card or from a WAV file up to several seconds long, select the starting time of the time slice and analyse time and frequency responses. The example shows the spectrum of a piano playing a middle C (262 Hz). The non-harmonic overtones are clearly seen. (Due to the stiffness of the string, the frequencies of the partials are too high.)

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You may filter data with a digital filter and display spectrograms in color mode. This example shows the spectrogram taken from the word "harris" in the frequency range 0..10 kHz with a 4096-point-FFT every 2 ms (post processing). The formants of "i" and the high spectral components of "s" are clearly visible.
Sonogram
Short time spectral information may also be displayed in a 3-D representation, called "waterfall". The following example shows the waterfall spectrum of the same word "harris" as before. The red layer picks out the spectrum of "i" where the formants are visible again. The presentation may be rotated automatically or manually with scroll bars, in order to select the best "camera point".
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Download version 1.15, June 2009: OVERTONE.ZIP (1.55 MB)

Unpack in a new folder, read README.TXT and start OVERTONE.EXE
(Some firewalls or User Access Control (UAC) may block execution. Give OVERTONE the necessary permissions.
Make sure, that the sound device is not used by another application.)

For more information, send e-mail to address given in README.TXT

Unterrichtseinheit Analyse von Klangspektren von Alain Hauser (in German)

 
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