User:Frostburn/Music vs Math: Difference between revisions

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| 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 − 3 octaves || ~~Isomorphisms~~ between the tangent and cotangent bundles of a pseudo-Riemannian manifold~~; the isomorphisms are induced by the manifold's metric tensor~~

| Sharp, flat || Alteration by 7 fifths − 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

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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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| ~~Notation~~ || A ~~symbolic scheme for~~ ''~~denoting~~'' ~~mathematical objects~~ || A ~~scheme for~~ ''~~notating~~'' a piece of music

| 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>

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

|}

@@ Line 26: / 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 || Isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold; the isomorphisms are induced by the manifold's metric tensor
+| 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
@@ Line 50: / Line 50: @@
 | 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
 |-
-| Notation || A symbolic scheme for ''denoting'' mathematical objects || A scheme for ''notating'' a piece of music
+| 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
+|-
+| Neutral || Interval quality between major and minor || An identity element
 |}