User:Frostburn/Music vs Math: Difference between revisions

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! Term !! Musical meaning !! Mathematical meaning

|-

| 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

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| Periodic || Geometrically cumulative || Repeating (non-cumulative)

|-

| Prime || [[1/1 | Unison]] || Number with exactly two divisors; can be generalized to prime ideals in ring theory

|-

| Interval || A positive real number ratio of frequencies || A connected subset of <math>\mathbb{R}</math>

|-

| Variety || Number of distinct ''k''-step intervals in a scale || An algebraic variety, such as the solution set of a system of polynomial equations; ~~objects~~ of ~~study~~ in algebraic geometry

| Variety || Number of distinct ''k''-step intervals in a scale || An algebraic variety, such as the solution set of a system of polynomial equations

|-

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

|-

| 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 || 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

|-

| ~~Set theory~~ || ~~Combinatorics of edo (conventionally 12edo) subsets~~ || ~~Theory of infinite sets, usually based on ZFC axioms~~

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

|}

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=== The wrong solution ===

The words "first", "second" and "last" are perfectly good ordinals with no intrinsic numerical association. We should just change the numerical notation to 0st, 1nd, 2st, 3st, 4st, 5st, etc. pronounced "twost", "threest", "fourst" and "fivest" standing in for the old "third", "fourth", "fifth" and "sixth" respectively (a numeric shift of one).

The words "first", "second" and "last" are perfectly good ordinals with no intrinsic numerical association. We should just change the numerical notation to 0st, 1nd for "first" and "second" continuing with 2st, 3st, 4st, 5st, etc. pronounced "twost", "threest", "fourst" and "fivest" standing in for the old "third", "fourth", "fifth" and "sixth" respectively (a numeric shift of one).

Now we finally have that 1nd + 1nd is 2st.

@@ Line 5: / Line 5: @@
 |-
 ! Term !! Musical meaning !! Mathematical meaning
+|-
+| 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 13: / Line 17: @@
 |-
 | Periodic || Geometrically cumulative || Repeating (non-cumulative)
+|-
+| Prime || [[1/1 | Unison]] || Number with exactly two divisors; can be generalized to prime ideals in ring theory
 |-
 | Interval || A positive real number ratio of frequencies || A connected subset of <math>\mathbb{R}</math>
 |-
-| Variety || Number of distinct ''k''-step intervals in a scale || An algebraic variety, such as the solution set of a system of polynomial equations; objects of study in algebraic geometry
+| Variety || Number of distinct ''k''-step intervals in a scale || An algebraic variety, such as the solution set of a system of polynomial equations
+|-
+| Set theory || Combinatorics and transformations of subsets of an edo || Study of infinite sets, usually based on ZFC axioms
+|-
+| 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
 |-
-| Set theory || Combinatorics of edo (conventionally 12edo) subsets || Theory of infinite sets, usually based on ZFC axioms
+| Neutral || Interval quality between major and minor || An identity element
 |}
@@ Line 31: / Line 81: @@
 === The wrong solution ===
-The words "first", "second" and "last" are perfectly good ordinals with no intrinsic numerical association. We should just change the numerical notation to 0st, 1nd, 2st, 3st, 4st, 5st, etc. pronounced "twost", "threest", "fourst" and "fivest" standing in for the old "third", "fourth", "fifth" and "sixth" respectively (a numeric shift of one).
+The words "first", "second" and "last" are perfectly good ordinals with no intrinsic numerical association. We should just change the numerical notation to 0st, 1nd for "first" and "second" continuing with 2st, 3st, 4st, 5st, etc. pronounced "twost", "threest", "fourst" and "fivest" standing in for the old "third", "fourth", "fifth" and "sixth" respectively (a numeric shift of one).
 Now we finally have that 1nd + 1nd is 2st.