The following pages contain small
online executable programs for studying phenomena of relations between numbers,
forms and tones. Loading these applets can take some time depending on
actual internet connection (max. 1 minute). Users have to turn on Java
functions in their browser preferences. Additionally the JSyn PlugIn is required.
It can easily be installed under Windows, MacOS and Linux for the most common
browsers (Internet Explorer, Netscape, iCab ...) from Download JSyn PlugIn. - Not least for
aesthetic reasons the applets are laid out for full window display. Therefore
printing out these descriptions in advance is recommended.
Klangwolken (Clouds of sound)
Every time a sound field is entered
by the mouse frequency, volume and panorama values of 24 sinewave generators
are defined anew by random selection. Clicking on a field with the mouse
makes the sound permanent, clicking again turns the sound off.
Schwingungsbilder (Forms of vibrations)
Modifying the well known Lissajous-figures,
"Schwingungsbilder" result from an attempt to visualize the complex
geometric patterns, which appear in the overlapping of different movements
or vibrations. The single graphics have been drawn automatically: a
point moving along a circular line is an analogy to a simple sinewave
(thin line). If this point itself becomes the moving center of a second
circle with the same radius, on whose new circular line a second point
moves along, the new point can represent as its outcome (bold line) a simple
overlapping: different simple ratios of velocities of the two circular movements
are analogies to different simple intervals. In this case both circular movements
can go into the same direction ("gleichphasig") or not ("gegenphasig").
Combinations of three or more circular movements in a similar way show the
great and beautiful variety of vibration-patterns of triads (major and minor),
their inversions and other harmonic structures. Moving the mouse on single
titles will load the matching graphics, the internal connection of the single
variants can then be studied by toggling (graphics change by mouse moving)
between the different shapes. Since relations between movements or vibrations
(proportions) are presented, but not absolute frequencies, harmony can
be experienced here in a sense that goes far beyond the human auditory
range (20 Hz - 20 KHz).
Kreisbilder (Forms of circle movements)
Applet for drawing forms of vibrations
as described above: altogether four interdependent cycloid "trajectories"
are available. The single parameters can be adjusted by scrolling the number fields:
To try out turn velocities to 5 : 6 : 7 : 8 (would correspond with a dominant-seventh-chord, first inversion), then 5 : -6 : 7 : -8, then 5 : 6 : -7 : -8 etc.
Klangkreise (Sounds of circle movements)
Similar to "Kreisbilder", but with
animated movements of points - leaving traces, when "Bahn zeichnen"
is pressed. In addition, every "trajectory" produces a sound corresponding
to its velocity that grows louder when going down and dies away when going
up. The respective "trajectory" sound derives from three sinewave generators:
beginning in unison they get more and more detuned with the sound growing
To try out turn velocities to 50 : 60 : 70 : 80 (dominant-seventh-chord, first inversion) and press "Bahnen zeichnen". Then change directions 2 and 4, press "Bahnen löschen" and anew "Bahnen zeichnen". The same with direction 3 and 4 versus direction 1 and 2. Then change the basic velocity.
Patterns of circle movements
Two points moving on two concentric circles can be tuned concerning velocity and sounding interval. The connecting line of the points can be visualized, the whole pattern can be drawn, as well as the nearest and farest distance (conjunction and opposition). Stop and start again with a mouse click.
Klangstaub (Dust of sound)
The actual mouse position defines
centers of sounding dust particles, envelope shapes of the individual
sounds change accordingly. Stop and start again with a mouse click.
An attempt to realize the Pythagorean
table, described by Albert von Thimus in the 1870's, as an online playable
instrument. Especially Hans Kayser ("Akróasis", 1946, etc.) used
and explained it extensive.
Tune the single scale functions by scrolling the respective number fields. Scale functions can freely be defined as fractions in relation to the basic frequency: numerator for overtone, denominator for undertone position. Try some presets:
Same principle as 7-note scale above
- some more tone fields for tuning chromatic scales as well as alternative
diatonic scale functions.
12 chromatic scale functions - fixed
on semitones at 100 cent.
Same principle as 7-note scale above - Try two presets (according to Robert Ross):
Discoveries in Csound
Findings on the way to real Sounddesign in mp3-format.
Combinations of different monochord-melodies sorted by scales (mp3-format).
Studies in geometry of curves
Randomlines, randomarcs, Peano-curve in 3 versions, ellipse, polynomes, cellular automatons.
last updated: 07.02.2005