Shepard tones

Shepard tones are special harmonically complex tones. They are named after the psychologist Roger Shepard (Shepard, 1964). With the help of the Shepard tones a number of acoustic illusions can be created ( tritone paradox , Shepard scale ).

Composition of the Shepard tones

Schematic representation of a shepard scale

Each Shepard tone is composed of a certain number of sine tones (usually 6 to 10). The frequencies of these sine tones are octave apart. The frequencies of a certain Shepard tone, which is composed of n many sine tones, are mathematically formulated as follows: ${\displaystyle f_{i}}$

${\displaystyle f_{i}=f_{b}\cdot 2^{i}}$,

with and the basic frequency . The fundamental frequencies of Shepard tones mostly correspond to the fundamental frequencies of the tone classes of the chromatic scale (e.g. for the Shepard tone with the tone class C the fundamental frequency would be ). The volume of the frequencies is determined by means of a bell-shaped envelope curve . It is characteristic of this that the volume is attenuated in the low and high frequency ranges. ${\displaystyle i=1...n}$ ${\displaystyle f_{b}}$ ${\displaystyle f_{b}=16{,}3516}$

literature

• Roger N. Shepard: Circularity in judgments of relative pitch. In: Journal of the Acoustical Society of America. Vol. 36, No. 12, 1964, ISSN  0001-4966 , pp. 2346-2353, doi : 10.1121 / 1.1919362 .
• Diana Deutsch : The tritone paradox: Effects of spectral variables. In: Perception & Psychophysics. Vol. 41, No. 6, 1987, ISSN  0031-5117 , pp. 563-575, doi : 10.3758 / BF03210490 .

Web links

• Diana Deutsch , Psychology Dept 0109, University of California.
• Henning Koch: Visualization of the Shepard Effect . netalive.org . 2003-10.
• Shepardton generators as VST and AU effects:
  • Shepard (mda)
  • Endless Series (Oli Larkin)

Individual evidence

1. ↑ A graphic representation can be found under Archived Copy ( Memento of the original from March 9, 2007 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. .