amandaonwriting
wildcat2030
wildcat2030:

 Mathematical Impressions: Making Music with a Möbius Strip 
Musical chords naturally inhabit certain topological spaces, which show the possible paths that a composer can use to move between chords
The connections between mathematics and music are many. For example, the differential equations of vibrating strings and surfaces help us understand harmonics and tuning systems, rhythm analysis tells us the ways a measure can be divided into beats, and the study of symmetry relates to the translations in time and pitch that occur in a fugue or canon. This video explores a less well-known connection. It turns out that musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip, and the space of three-note chords is a kind of twisted triangular torus. For a thorough presentation of the ideas introduced here, suitable for both mathematicians and musicians, see “A Geometry of Music” by Dmitri Tymoczko. The “Umbilic Torus” sculpture shown at the end of the video was created by Helaman Ferguson. (via Mathematical Impressions: Making Music with a Möbius Strip: Scientific American)

wildcat2030:

Mathematical Impressions: Making Music with a Möbius Strip

Musical chords naturally inhabit certain topological spaces, which show the possible paths that a composer can use to move between chords

The connections between mathematics and music are many. For example, the differential equations of vibrating strings and surfaces help us understand harmonics and tuning systems, rhythm analysis tells us the ways a measure can be divided into beats, and the study of symmetry relates to the translations in time and pitch that occur in a fugue or canon. This video explores a less well-known connection. It turns out that musical chords naturally inhabit various topological spaces, which show all the possible paths that a composer can use to move between chords. Surprisingly, the space of two-note chords is a Möbius strip, and the space of three-note chords is a kind of twisted triangular torus. For a thorough presentation of the ideas introduced here, suitable for both mathematicians and musicians, see “A Geometry of Music” by Dmitri Tymoczko. The “Umbilic Torus” sculpture shown at the end of the video was created by Helaman Ferguson. (via Mathematical Impressions: Making Music with a Möbius Strip: Scientific American)

katherine-mansfield
I’d love to tearfully absorb you in every way and I’d love to play with your hair, read your eyes, feel disarmed in your presence. I’d love to experience a seizure of full-silenced tenderness with you and at the same time dwell on your Dionysian idiosyncrasy of red, slightly heated wine, constant passion and chaos; How can I even imprison this desire into mere letters structured together in order to form a coherent meaning? There is no meaning. Darling! Darling! You can flash “meaning” down the toilet if you wish. Still, I’d love to share a life full of richness with you: Richness not in terms of events, incidents, facts or experiences; but richness in terms of a colourful, adventurous, enthusiastically unraveling life. I’d love to lose all privileges of existence as long as I might have a small chance of walking on water with you.
Katherine Mansfield, Selected Letters (via violentwavesofemotion)
devidsketchbook

devidsketchbook:

HANGARBICOCCA BY THOMAS SARACENO

Argentinian artist Tomas Saraceno (born 1973) - installation view at HangarBicocca, Milan. (previously)

For On Space Time Foam, his new installation at the HangarBicocca, Saraceno conceived a large transparent membrane (which he amusingly calls la lasagna) that visitors can get into. Folded in three layers, it is suspended at 25-metres above the ground, providing a radical bodily experience. (An interview from Milan by Filipa Ramos)