User:Frostburn/Music vs Math: Difference between revisions

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| Chord || A set of pitches often played simultaneously or arpeggiated || A straight line segment whose endpoints both lie on a circular arc

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| Root || The fundamental note of a chord || Of a function, an argument for which the function evaluates to zero

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| Harmonic analysis || Study of chord progressions || Study of Fourier Transforms

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| Set theory || Combinatorics and transformations of subsets of an edo || Study of infinite sets, usually based on ZFC axioms

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| Chromatic || ~~Child~~ MOS of a small MOS || Concerning colorings of vertices of a graph

| Chromatic || Using small steps to stray from the diatonic scale; child MOS of a small MOS || Concerning colorings of vertices of a graph

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| Sharp, flat || Alteration by 7 fifths − 3 octaves || Induced isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold

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| Scale || Collection of relative pitches, usually with a periodic step pattern || A type of infinite sequence of ordinal-valued functions on a subset of a Polish space

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| Consistent || Of an edo pval, mapping every interval in a set of odd harmonics to its best approximation|| Of an axiomatic theory, proving no contradiction

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| Limit || A collection of all prime or odd harmonics below a certain prime or odd || A value that is approached arbitrarily closely

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| Ring || A sub-edo of an edo generated by stacking its best fifth || An algebraic structure whose semigroup or monoid operation distributes over its abelian group operation

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| Augmented || An interval quality, being a semitone larger than major or perfect || Matrix formed by putting two matrices with the same number of rows side-by-side

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| Family || The set of all extensions of a temperament || A set of sets, also called a collection

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| Origin || Of a family, the temperament which generates a family || A fixed point of reference for the geometry of a space

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| Transpose || Change the pitch of a piece of music || Flip a matrix over its diagonal

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| Riemannian || Relating to the theory of chordal functions studied by Hugo Riemann || Relating to smooth manifolds with a particular metric structure, named after Bernhard Riemann

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| Minor || A diatonic mode, tonality, or (MOS or categorical) interval quality || A matrix made by removing one row and one column of a larger one; a smaller graph made from a larger one

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| Category || A region of similar musical intervals || A collection of mathematical objects of the same "type", related by morphisms aka arrows

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| Stack || To add two musical intervals || A 2-sheaf

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| Chain || A sequence (finite or not, closed or not) of consecutive stacked generators, e.g. a chain of fifths || A formal sum of oriented ''k''-simplices or ''k''-cells, certain equivalence classes of which form homology groups

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| Suspension || Non-chord tone on a strong beat resolved downwards on a weak beat || A cylinder <math>X \times [0,1]</math> made from the space ''X'' but with both ends collapsed to points, denoted <math>\Sigma X</math>

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| Mode || Specific rotation of a musical scale || The most frequently occurring number

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| Bridge || A contrasting section in a piece of music that prepares for the return of the original material section || An edge of a graph whose deletion increases the graph's number of connected components

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| Mediant || The third scale degree || Freshman sum

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| Circle || A star polygon that covers all steps in an equal temperament || A round geometric object with no self-intersections

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| Inversion || A variant of a root position chord with pitches transposed by octaves || Taking the multiplicative inverse or reflecting a space about a circle or a sphere

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| ~~#, b~~ || ~~Alteration by 7 fifths - 3 octaves~~ || ~~Isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold~~

| Neutral || Interval quality between major and minor || An identity element

|}

@@ Line 7: / Line 7: @@
 |-
 | Chord || A set of pitches often played simultaneously or arpeggiated || A straight line segment whose endpoints both lie on a circular arc
+|-
+| Root || The fundamental note of a chord || Of a function, an argument for which the function evaluates to zero
 |-
 | Harmonic analysis || Study of chord progressions || Study of Fourier Transforms
@@ Line 24: / Line 26: @@
 | Set theory || Combinatorics and transformations of subsets of an edo || Study of infinite sets, usually based on ZFC axioms
 |-
-| Chromatic || Child MOS of a small MOS || Concerning colorings of vertices of a graph
+| Chromatic || Using small steps to stray from the diatonic scale; child MOS of a small MOS || Concerning colorings of vertices of a graph
+|-
+| Sharp, flat || Alteration by 7 fifths &minus; 3 octaves || Induced isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold
+|-
+| Scale || Collection of relative pitches, usually with a periodic step pattern || A type of infinite sequence of ordinal-valued functions on a subset of a Polish space
+|-
+| Consistent || Of an edo pval, mapping every interval in a set of odd harmonics to its best approximation|| Of an axiomatic theory, proving no contradiction
+|-
+| Limit || A collection of all prime or odd harmonics below a certain prime or odd || A value that is approached arbitrarily closely
+|-
+| Ring || A sub-edo of an edo generated by stacking its best fifth || An algebraic structure whose semigroup or monoid operation distributes over its abelian group operation
+|-
+| Augmented || An interval quality, being a semitone larger than major or perfect || Matrix formed by putting two matrices with the same number of rows side-by-side
+|-
+| Family || The set of all extensions of a temperament || A set of sets, also called a collection
+|-
+| Origin || Of a family, the temperament which generates a family || A fixed point of reference for the geometry of a space
+|-
+| Transpose || Change the pitch of a piece of music || Flip a matrix over its diagonal
+|-
+| Riemannian || Relating to the theory of chordal functions studied by Hugo Riemann || Relating to smooth manifolds with a particular metric structure, named after Bernhard Riemann
+|-
+| Minor || A diatonic mode, tonality, or (MOS or categorical) interval quality || A matrix made by removing one row and one column of a larger one; a smaller graph made from a larger one
+|-
+| Category || A region of similar musical intervals || A collection of mathematical objects of the same "type", related by morphisms aka arrows
+|-
+| Stack || To add two musical intervals || A 2-sheaf
+|-
+| Chain || A sequence (finite or not, closed or not) of consecutive stacked generators, e.g. a chain of fifths || A formal sum of oriented ''k''-simplices or ''k''-cells, certain equivalence classes of which form homology groups
+|-
+| Suspension || Non-chord tone on a strong beat resolved downwards on a weak beat || A cylinder <math>X \times [0,1]</math> made from the space ''X'' but with both ends collapsed to points, denoted <math>\Sigma X</math>
+|-
+| Mode || Specific rotation of a musical scale || The most frequently occurring number
+|-
+| Bridge || A contrasting section in a piece of music that prepares for the return of the original material section || An edge of a graph whose deletion increases the graph's number of connected components
+|-
+| Mediant || The third scale degree || Freshman sum
+|-
+| Circle || A star polygon that covers all steps in an equal temperament || A round geometric object with no self-intersections
+|-
+| Inversion || A variant of a root position chord with pitches transposed by octaves || Taking the multiplicative inverse or reflecting a space about a circle or a sphere
 |-
-| #, b || Alteration by 7 fifths - 3 octaves || Isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold
+| Neutral || Interval quality between major and minor || An identity element
 |}