Chapter Thirty-Seven: Numbers in Art and Music Tesselations
The word "tessellation" comes from the Latin word,
tessella, which means small tile.
How it works:
Tessellations are collections of shapes that fit together to cover a surface without overlapping or leaving gaps. They are typically composed of simple or regular polygons such as squares seen on a tiled floor, but they can also be composed of irregular shapes. They have two classifications; regular or irregular. Regular tessellations are composed of congruent shapes such as triangles, hexagons, or squares.
How to create at Tesselation:
You may apply one of the following geometrical principles in tessellations, which include: reflections, glide reflections, rotations and translations.
Examples of where its found:
Found in tiled floors, mosaics, and general artwork. Escher designed many famous tessellations.
Music
Sound is a traveling wave that oscillates through matter.
How it works:
Thus music is an arrangement of sounds in a particular order. When a string is plucked on a musical instrument, it generates waves by vibrating back and forth. Frequency is the number of times per second that these waves hit our ears, which is measured in Hertz (Hz). The more waves per second, the higher the pitch; fewer waves produce a lower pitch.
When the right numbers come together with the right musical frequencies, chords and harmonies are created. Chords are a group of notes which are played together at the same time. The ratios between the notes will determine whether the combined notes will sound good when played together.
Examples:
Depending on where you pluck a string determines where you should then hold the string to get a complementary note. For instance, plucking a violin string at its center, you need to hold the string at 2/3rds it original length for a complementary note. The string then vibrates 3/2 as fast as it was originally - meaning frequency went from 60 to 90 Hertz. Some of the ratios which exist in relation to musical notes are:
Octave = 2
Fifth = 3/2
Fourth = 4/3
Major 3rd = 5/4
Minor 3rd = 6/5
Major 6th = 5/3
Minor 6th = 8/5
Any of these ratios produce complementary sounds which enable us to produce harmonies and thus more appealing sounds.
NOTE: Most information in this Chapter must be credited to
ArithmancyHOL by Rosa Gullveig.