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On “Crystal Growth” in Harmonic Space (1993/2003)
by
Tenney, James
in
Abstract spaces
/ Acoustical properties
/ Acoustics
/ Ancient philosophy
/ Applied mathematics
/ Applied statistics
/ Arts
/ composition
/ Condensed matter physics
/ Consonant intervals
/ crystal growth
/ Crystal lattices
/ Crystal morphology
/ Crystal structure
/ Crystallography
/ Dimensional analysis
/ Dimensionality
/ Formal logic
/ harmonic distance
/ harmonic lattice
/ harmonic space
/ harmonic syntax
/ Historical methodology
/ Historiography
/ History
/ History of philosophy
/ James Tenney
/ Lattice theory
/ Logic
/ Logical topics
/ Mathematical lattices
/ Mathematical logic
/ Mathematical set theory
/ Mathematics
/ Music
/ Music theory
/ Music Theory and Analysis
/ Musical intervals
/ Musical pitch
/ Musical register
/ Octaves
/ Perfect intervals
/ Performing arts
/ Philosophy
/ Physical sciences
/ Physics
/ pitch
/ Presocratic philosophy
/ Pythagorean pentatonic scale
/ Pythagoreanism
/ Sound pitch
/ Statistical physics
/ Statistics
/ tonal expansion
2015
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On “Crystal Growth” in Harmonic Space (1993/2003)
by
Tenney, James
in
Abstract spaces
/ Acoustical properties
/ Acoustics
/ Ancient philosophy
/ Applied mathematics
/ Applied statistics
/ Arts
/ composition
/ Condensed matter physics
/ Consonant intervals
/ crystal growth
/ Crystal lattices
/ Crystal morphology
/ Crystal structure
/ Crystallography
/ Dimensional analysis
/ Dimensionality
/ Formal logic
/ harmonic distance
/ harmonic lattice
/ harmonic space
/ harmonic syntax
/ Historical methodology
/ Historiography
/ History
/ History of philosophy
/ James Tenney
/ Lattice theory
/ Logic
/ Logical topics
/ Mathematical lattices
/ Mathematical logic
/ Mathematical set theory
/ Mathematics
/ Music
/ Music theory
/ Music Theory and Analysis
/ Musical intervals
/ Musical pitch
/ Musical register
/ Octaves
/ Perfect intervals
/ Performing arts
/ Philosophy
/ Physical sciences
/ Physics
/ pitch
/ Presocratic philosophy
/ Pythagorean pentatonic scale
/ Pythagoreanism
/ Sound pitch
/ Statistical physics
/ Statistics
/ tonal expansion
2015
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Do you wish to request the book?
On “Crystal Growth” in Harmonic Space (1993/2003)
by
Tenney, James
in
Abstract spaces
/ Acoustical properties
/ Acoustics
/ Ancient philosophy
/ Applied mathematics
/ Applied statistics
/ Arts
/ composition
/ Condensed matter physics
/ Consonant intervals
/ crystal growth
/ Crystal lattices
/ Crystal morphology
/ Crystal structure
/ Crystallography
/ Dimensional analysis
/ Dimensionality
/ Formal logic
/ harmonic distance
/ harmonic lattice
/ harmonic space
/ harmonic syntax
/ Historical methodology
/ Historiography
/ History
/ History of philosophy
/ James Tenney
/ Lattice theory
/ Logic
/ Logical topics
/ Mathematical lattices
/ Mathematical logic
/ Mathematical set theory
/ Mathematics
/ Music
/ Music theory
/ Music Theory and Analysis
/ Musical intervals
/ Musical pitch
/ Musical register
/ Octaves
/ Perfect intervals
/ Performing arts
/ Philosophy
/ Physical sciences
/ Physics
/ pitch
/ Presocratic philosophy
/ Pythagorean pentatonic scale
/ Pythagoreanism
/ Sound pitch
/ Statistical physics
/ Statistics
/ tonal expansion
2015
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Book Chapter
On “Crystal Growth” in Harmonic Space (1993/2003)
2015
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Overview
It seems clear, intuitively, that a concern for harmonic coherence would lead to the use of relatively compact, connected sets of points in harmonic space, where “connected” simply means that every element is adjacent to at least one other element in the set. How might such compactness be defined more precisely? I have been investigating an interesting algorithm in which sets of points are chosen, one by one, in somen-dimensional harmonic space, under the condition that each new point must have the smallest possible sum of harmonic distances to all points already in the set. That is, at each
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