Metallic MOS: Difference between revisions

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To know how to define this scale in terms of the present discussion, we recognize:

# √2 is the first isotope of the silver mean, δs - 1.

# <math>\sqrt{2}</math> is the first isotope of the silver mean, <math>δ_s - 1</math>.

# The fifth and the fourth sum to the period, so we can use one or the other as the generator; we’ll prefer the reduced one, the fourth.

So in our terms, this would be an isotopic generator, and again, by design, this was the isotopic generator chosen for examples in this discussion, ≈ 0.414214.

So in our terms, this would be an isotopic generator, and again, by design, this was the isotopic generator chosen for examples in this discussion, <math>≈ 0.414214</math>.

It may seem odd that the most popular use of the silver mean uses its isotope rather than the mean directly. However, if we consider the ratio of the generator to the period here, that ratio is the silver mean. In the golden case, there was no difference between these two conceptions; both splitting the period into two segments in the ratio of <math>φ</math> and having the generator to period ratio be <math>φ</math> produce the same result. So while in this discussion from the beginning we put things in terms of splitting intervals (in order to smoothly transition from the golden generator into noble generators), it is probably the case that those who first brought us the Fibonacci generator and Argent Temperament were thinking in terms of the ratio of the generator to the period.

Argent means “silver” in French, which explains the name (it has also been called Arguros, which is “silver” in Greek). Wilson called this generator 2-Zig/2-Zag, after the pattern of the lines in the Stern-Brocot tree that results as we traverse deeper into the tree searching for better approximations of it: we move twice to the right, then twice to the left, and repeat.

Argent means “silver” in French, which explains the name (it has also been called Arguros, which is “silver” in Greek). Wilson called this generator "2-Zig/2-Zag", after the pattern of the lines in the Stern-Brocot tree that results as we traverse deeper into the tree searching for better approximations of it: we move twice to the right, then twice to the left, and repeat.

== Imaginary ==

@@ Line 975: / Line 975: @@
 To know how to define this scale in terms of the present discussion, we recognize:
-# √2 is the first isotope of the silver mean, δs - 1.
+# <span><math>\sqrt{2}</math></span> is the first isotope of the silver mean, <span><math>δ_s - 1</math></span>.
 # The fifth and the fourth sum to the period, so we can use one or the other as the generator; we’ll prefer the reduced one, the fourth.
-So in our terms, this would be an isotopic generator, and again, by design, this was the isotopic generator chosen for examples in this discussion, ≈ 0.414214.
+So in our terms, this would be an isotopic generator, and again, by design, this was the isotopic generator chosen for examples in this discussion, <span><math>≈ 0.414214</math></span>.
 It may seem odd that the most popular use of the silver mean uses its isotope rather than the mean directly. However, if we consider the ratio of the generator to the period here, that ratio is the silver mean. In the golden case, there was no difference between these two conceptions; both splitting the period into two segments in the ratio of <span><math>φ</math></span> and having the generator to period ratio be <span><math>φ</math></span> produce the same result. So while in this discussion from the beginning we put things in terms of splitting intervals (in order to smoothly transition from the golden generator into noble generators), it is probably the case that those who first brought us the Fibonacci generator and Argent Temperament were thinking in terms of the ratio of the generator to the period.
-Argent means “silver” in French, which explains the name (it has also been called Arguros, which is “silver” in Greek). Wilson called this generator 2-Zig/2-Zag, after the pattern of the lines in the Stern-Brocot tree that results as we traverse deeper into the tree searching for better approximations of it: we move twice to the right, then twice to the left, and repeat.
+Argent means “silver” in French, which explains the name (it has also been called Arguros, which is “silver” in Greek). Wilson called this generator "2-Zig/2-Zag", after the pattern of the lines in the Stern-Brocot tree that results as we traverse deeper into the tree searching for better approximations of it: we move twice to the right, then twice to the left, and repeat.
 == Imaginary ==