User:Frostburn/Music vs Math
I'm collecting a list of terms with different meanings in Xenharmonic Music Theory and Mathematics. These could be used to make a joke video in the future if we can come up with enough of them. Feel free to contribute to the table below.
| 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 |
| Harmonic analysis | Study of chord progressions | Study of Fourier Transforms |
| Harmonic series | Overtonal ratios i.e. natural numbers | A diverging sum of reciprocals |
| Perfect | Rank-2 generator and its inverse | Number that is the sum of its divisors |
| Periodic | Geometrically cumulative | Repeating (non-cumulative) |
| Prime | 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]\displaystyle{ \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 |
| 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 |
| #, b | Alteration by 7 fifths − 3 octaves | Isomorphisms between the tangent and cotangent bundles of a pseudo-Riemannian manifold; the isomorphisms are induced by its metric tensor |
Ordinal rant
We all know how ordinal notation is broken. The 2nd after 2nd is 3rd instead of 4th which you would expect from 2 + 2 = 4.
Mathematicians understood this and came up with a degree 0. The degree 1 polynomial is ax + b while the degree 2 polynomial is ax² + bx + c. Multiplying two degree 2 polynomials results in a degree 4 polynomial and everything makes sense numerically. Colloquially we use ordinals and say that two 2nd degree polynomials make up a 4th degree polynomial.
Musicians never got the memo and we're stuck with the fact that two perfect 4ths make up a minor 7th instead of an 8th of some kind.
Spoob bless TAMNAMS for using step span instead of ordinals.
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 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.