Geometry Gallery

Patterns generated by the CymaScope instrument
often receive praise for their beauty,

but beyond their obvious symmetrical perfection what do they mean? Do they convey information?
Contemplating these and related questions is the purpose of this section in which we begin
to investigate cymascopic images for what they can teach us.

2/4 Fold Geometry

Four sided forms, or ‘quadrilaterals’

Four sided forms, or ‘quadrilaterals’ are commonly found in Nature, for example, in the stress fractures of ceramics and in the crystal kingdom.

The four-sided image in the gallery is the sound of a gong made visible on the CymaScope, which is the opening instrument in Stuart Mitchell’s sublime Seven Wonders Suite for orchestra.

The 1:3 and 1:7 ratio CymaGlyphs may be evidence of typical harmonic structures inherent in gong sounds in which odd rather than even, harmonics tend to dominate the sound field beyond its fundamental pitch. 

Parnassiaceae, a member of the Celasrales family

In the flower kingdom the Clematis is one of the most commonly seen four-petaled blossoms, however, the example shown above is a rarer flower, the Parnassiaceae, a member of the Celasrales family.
They can also have 3 and 5 petals.

The right part of this composite image shows four-fold stress fractures in ceramic glazing; the left part shows cuboid fluoride crystals.
Seven Wonders Gong
Ratio of 2 -3
The Octave
Seven Wonders Gong 9-8
Ratio 1-3
Ratio of 1-7

4/8 Fold Geometry

The root system of E8 projected from 8 dimensions to 2. By John Stembridge, based on a drawing by Peter McMullen.

Some mathematicians and physicists believe that E8 holds the secret to all that is, linking mathematics to the natural beauty of symmetry. The link between E8 and cymatics science, though creating visually similar models, has not yet been established by mathematicians. The CymaGlyph in the gallery is a moment from Tchaikovsky’s Pathétique Symphony made visible, which features the famous musical star-cross motif. This musical device was also used by Franz Liszt to represent the Christian cross.

Eight sided (octagonal) forms

Eight sided (octagonal) forms, while not as common in Nature as 4, 5, and 6-sided forms, do exist in many diverse examples, including several varieties of fruit such as lemons and limes, which typically have eight segments, the polygonal (dihedral) form of quasicrystals, in some species of diatoms and jelly fish and of course in the octopus. In mathematics a famous example is E8, so called because the vectors of its root system are in eight-dimensional Euclidean space.

The right part of this composite image shows the 8-fold segments in a lemon; the left part shows a “Jellyfish Mediterranean” with its 8-fold body. (Courtesy of Laura Milholland).
8-fold Tchaikovsky
Pathétique Symphony
Ratio of 1-1
Ratio 1-2
Ratio 1-9
Ratio 5-8
Ratio 15-16
Square Root of 2
Square Root of 3

5/10 Fold Geometry


Campanula – In the flower kingdom five-petalled blossoms are very common. The flower known as the ‘Little Bell’ has one of the most perfect pentagonal shapes; its bell name deriving from the flower’s bell-shaped side profile;
Latin name Campanula.

5/10 Fold Geometry

The CymaScope team have worked with a team of scientists who have been studying a pattern known as ‘Mereon’ for almost two decades. Mereon may prove to be the creative principle at the heart of Nature. We imaged many Mereonic frequencies in our lab, including the prime frequency of 7.97 Hertz, which creates complex 5/10 fold imagery when made visible on the CymaScope, as displayed in the gallery. The golden ratio of 1:1.618 is deeply embedded in Mereonic mathematics and is one of the many ratios embedded within the imagery. For more details of this research see our Mereon section:
Mereon Research Page

Pentagonal Forms – In Nature, 5 fold and 10 fold forms are prolific and occur in everything from the atomic realm, where icosahedral water clusters have pentagonal form, to some varieties of quasi crystal, some varieties of pyrite crystal, the sectional structure of the DNA molecule and even the morphology of some living creatures such as the starfish.

Mereon Prime Mono
Mereon Phi
Mereon 2-3
Mereon 3-5
Mereon Square Root of 2
Mereon Square Root of 3
Mereon Ratio of 1-2
Mereon Phi Star

7/14 Fold Geometry

Trientalis borealis

7/14 Fold Geometry

Seven sided figures are called heptagons and they tend to be of rarer morphology in nature than pentagons and hexagons.

In the CymaScope laboratory we most often see seven-sided geometry when making male, spiritually-oriented chant visible. The seven-sided image shown in the gallery is the voice of chant master, Jonathan Goldman, imaged on the CymaScope.

In the flower kingdom the starflower, Latin name Trientalis borealis, is very beautiful, as this example by artist, Fred Casselman, shows.

Trientalis borealis, also known as the starflower, is a North American woodland perennial that blooms between May and June. Starflowers are creeping rhizomes with 8 inch vertical stalks. Scientific name: Trientalis borealis

7 Fold Mono
7 Fold Phi
7 Fold Square Root of 2
7 Fold Square Root of 3
7 Fold Ratio of 2-3
7 Fold Ratio of 8-9
C7 Fold – The Octave