Simultaneity

Simultaneity is the property of two events happening at the same time.

In mathematics, a system of equations or a set of simultaneous equations share variables; a solution is a set of variable values for which all these equations are satisfied simultaneously.

In music a simultaneity is more than one complete musical texture occurring at the same time, rather than in succession. This first appeared in the music of Charles Ives, and is common in the music of Conlon Nancarrow, and others. A pitch simultaneity is also more than one pitch or pitch class all of which occur at the same time, or simultaneously. Simultaneity is a more general term than chord: most chord progressions or harmonic progressions are then simultaneity successions, though not all simultaneity successions are harmonic progressions and not all simultaneities are chords.

In modern physics two events may be simultaneous with respect to a time event as follows:

A central event (0,0) is used to anchor a spacetime plane {(x,t) in RxR} = ST where x measures distance in units of 30 centimeters and t measures time in nanoseconds. The space events satisfy |x| > |t| and the time events satisfy |x| < |t|.
Now a space event e is simultaneous with the origin (0,0), with respect to a time event t , if e and t are hyperbolically-orthogonal points in ST.
Two events g and h in ST are simultaneous with respect to z if their difference g - h in ST is hyperbolically-orthogonal to z.

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Simultaneity in Music by Robert Iolini. Extract from a Master of Arts thesis entitled Simultaneity in Music. Macquarie University. Sydney. Australia. February 1998.

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