User:Ganaram inukshuk/Notes/TAMNAMS: Difference between revisions

Line 1,442:

=== Names for other mos families (in-progress) ===

Mosses of the form xL (kx+y)s form an infinite linear family.

Mosses of the form xL (kx+y)s form an infinite linear family. The first member of this family is the mos such that k = 0 and y < x, or x = y = 1.

* The simplest mos family of this form, the '''monolarge''' family, includes all mosses of the form 1L ns~~, starting~~ at 1L 1s~~; all mosses of the form 1L ns belong to the same family~~.

* The simplest mos family of this form, the '''monolarge''' family, includes all mosses of the form 1L ns. This family starts at 1L 1s.

* The next simplest mos family, the '''bilarge''' family, includes all mosses of the form 2L (kx+1)s~~, starting~~ at 2L 1s~~; all mosses of the form 2L (kx+1)s belong to the same family~~.

* The next simplest mos family, the '''bilarge''' family, includes all mosses of the form 2L (kn+1)s. This family starts at 2L 1s.

* Mosses of the general form of xL (kx+y)s, the '''xL ys polylarge''' or '''(mos name) polylarge''' family, belong to the same family ~~and start at xL ys (k=0)~~.

* Mosses of the general form of xL (kx+y)s, the '''xL ys polylarge''' or '''(mos name) polylarge''' family, belong to the same family.

** For a mos of the form xL ys, descendant mosses of the form xL (kx+y)s are formed using a step ratio for xL ys that is around the pseudocollapesed range, and xL (kx+y)s is the kth mos descendant of this form.

** For a mos of the form xL ys, a similar linear family ~~starts at yL~~ (x+y)~~s, the sister of xL~~ (x+y)s. These mosses are formed using a step ratio for xL ys that is around the ~~pseduocollapsed~~ range.

** For a mos of the form xL ys, a similar linear family has the form (x+y)L (x+k(x+y))s. These descendant mosses are formed using a step ratio for xL ys that is around the pseduequalized range, and (x+y)L (x+k(x+y))s is the kth mos descendant of this form.

A similar family of mosses are of the form (x+ky)L ys. These do not form a family of related mosses in that their generators are different sizes, but serves as the sister of the form xL (kx+y)s. One noteworthy example is diatonic (5L 2s) and superdiatonic/armotonoc (7L 2s), a pair of indirectly related mosses where the structure of the mos is similar except for the number of large steps.

* The sister of the mos family 1L ns is nL 1s, and may be called monosmall.

* The sister of the mos family 2L (kn+1)s is (kn+1)L 2s, and may be call bismall.

* The sister of the mos family xL (kx+y)s is (x+ky)L ys, and may be called yL xs polysmall or (mos name) polysmall.

Another mos family corresponds to the golden ratio, and is commonly associated with golden temperaments, such as golden meantone. These mosses have the form (F(n)x+F(n-1)y)L (F(n-1)x+F(n-2)y)s, where F(n), F(n-1), and F(n-2) are the nth, (n-1)th, and (n-2)th Fibonacci numbers. Here, F(1) = 1 and F(0) = 0. These mosses are formed using a step ratio for xL ys that approximates or is equal to the golden ratio.

=== Reasoning for names ===

@@ Line 1,442: / Line 1,442: @@
 === Names for other mos families (in-progress) ===
-Mosses of the form xL (kx+y)s form an infinite linear family.
+Mosses of the form xL (kx+y)s form an infinite linear family. The first member of this family is the mos such that k = 0 and y < x, or x = y = 1.
-* The simplest mos family of this form, the '''monolarge''' family, includes all mosses of the form 1L ns, starting at 1L 1s; all mosses of the form 1L ns belong to the same family.
+* The simplest mos family of this form, the '''monolarge''' family, includes all mosses of the form 1L ns. This family starts at 1L 1s.
-* The next simplest mos family, the '''bilarge''' family, includes all mosses of the form 2L (kx+1)s, starting at 2L 1s; all mosses of the form 2L (kx+1)s belong to the same family.
+* The next simplest mos family, the '''bilarge''' family, includes all mosses of the form 2L (kn+1)s. This family starts at 2L 1s.
-* Mosses of the general form of xL (kx+y)s, the '''xL ys polylarge''' or '''(mos name) polylarge''' family, belong to the same family and start at xL ys (k=0).
+* Mosses of the general form of xL (kx+y)s, the '''xL ys polylarge''' or '''(mos name) polylarge''' family, belong to the same family.
 ** For a mos of the form xL ys, descendant mosses of the form xL (kx+y)s are formed using a step ratio for xL ys that is around the pseudocollapesed range, and xL (kx+y)s is the kth mos descendant of this form.
-** For a mos of the form xL ys, a similar linear family starts at yL (x+y)s, the sister of xL (x+y)s. These mosses are formed using a step ratio for xL ys that is around the pseduocollapsed range.
+** For a mos of the form xL ys, a similar linear family has the form (x+y)L (x+k(x+y))s. These descendant mosses are formed using a step ratio for xL ys that is around the pseduequalized range, and (x+y)L (x+k(x+y))s is the kth mos descendant of this form.
 A similar family of mosses are of the form (x+ky)L ys. These do not form a family of related mosses in that their generators are different sizes, but serves as the sister of the form xL (kx+y)s. One noteworthy example is diatonic (5L 2s) and superdiatonic/armotonoc (7L 2s), a pair of indirectly related mosses where the structure of the mos is similar except for the number of large steps.
+* The sister of the mos family 1L ns is nL 1s, and may be called monosmall.
+* The sister of the mos family 2L (kn+1)s is (kn+1)L 2s, and may be call bismall.
+* The sister of the mos family xL (kx+y)s is (x+ky)L ys, and may be called yL xs polysmall or (mos name) polysmall.
+Another mos family corresponds to the golden ratio, and is commonly associated with golden temperaments, such as golden meantone. These mosses have the form (F(n)x+F(n-1)y)L (F(n-1)x+F(n-2)y)s, where F(n), F(n-1), and F(n-2) are the nth, (n-1)th, and (n-2)th Fibonacci numbers. Here, F(1) = 1 and F(0) = 0. These mosses are formed using a step ratio for xL ys that approximates or is equal to the golden ratio.
 === Reasoning for names ===