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. 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 z , if e and z are hyperbolic-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 hyperbolic-orthogonal to z.
External link
Simultaneity in Music (http://www.toysatellite.org/iolini/thesis2.html) by Robert Iolini. Extract from a Master of Arts thesis entitled Simultaneity in Music. Macquarie University. Sydney. Australia. February 1998.
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In mathematics, a system of equations or a set of simultaneousequations share variables; a solution is a set of variable values for which all these equations are satisfied simultaneously.
Concurrence or Simultaneity is a legal term, from Western jurisprudence, referring to the simultaneous occurrence of actus reus (bad action) and mens rea (bad mind), which must be present for a crime to have occurred; except in crimes of strict liability.
Note that this establishes the clock simultaneity of events distant from the observer, though the same determination of clock simultaneity of distant events with events of the observers world-line may be deduced from the description as outlined by Whitehead (PNK 51f.).
The simultaneity of the whole of nature comprising the discerned events is the special relation of that background of nature to the percipient event, which is itself part of the whole.
Hence simultaneity for Whitehead is the spatial spread of events in a given inertial frame as defined by a given duration, and is Newtonian in the sense that each instantaneous space in a frame provides a single present class of all events in nature relative to that frame.
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