Generator embedding optimization: Difference between revisions

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=== Advanced tie-breaking example: Setup ===

To help illustrate advanced tie-breaking, we're going to look at a minimax-C tuning of [[augmented]] temperament, with mapping {{rket|{{map|3 0 7}} {{map|0 1 0}}}}. In particular, we're going to use the somewhat arbitrary target-interval set <math>\{ \frac32, \frac52, \frac53, \frac83, \frac95, \frac{16}{5}, \frac{15}{8}, \frac{18}{5} \}</math>. As a rank-2 temperament, we're going to be searching 3D tuning damage space. This temperament divides the octave into three parts, so our ballpark <math>g_1</math> is 400 ¢, and our second generator <math>g_2</math> is a free generator for prime 3, so it's going to be ballpark its pure tuning of 1901.955 ¢.

To help illustrate advanced tie-breaking, we're going to look at a minimax-C tuning of [[augmented (temperament)|augmented]] temperament, with mapping {{rket|{{map|3 0 7}} {{map|0 1 0}}}}. In particular, we're going to use the somewhat arbitrary target-interval set <math>\{ \frac32, \frac52, \frac53, \frac83, \frac95, \frac{16}{5}, \frac{15}{8}, \frac{18}{5} \}</math>. As a rank-2 temperament, we're going to be searching 3D tuning damage space. This temperament divides the octave into three parts, so our ballpark <math>g_1</math> is 400 ¢, and our second generator <math>g_2</math> is a free generator for prime 3, so it's going to be ballpark its pure tuning of 1901.955 ¢.

Here's an aerial view on the tuning damage space, where we've "clipped" every damage graph hyper-V where it has gone out-of-bounds, above 150 ¢(C) damage; that is, we've colored it in grey and flattened it across the top of the box of our visualization. This lets us focus in clearly on the region of real interest, which is where all target-intervals' damages are less than this cap at the same time. This is the multicolored crater in the middle here:

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 === Advanced tie-breaking example: Setup ===
-To help illustrate advanced tie-breaking, we're going to look at a minimax-C tuning of [[augmented]] temperament, with mapping {{rket|{{map|3 0 7}} {{map|0 1 0}}}}. In particular, we're going to use the somewhat arbitrary target-interval set <math>\{ \frac32, \frac52, \frac53, \frac83, \frac95, \frac{16}{5}, \frac{15}{8}, \frac{18}{5} \}</math>. As a rank-2 temperament, we're going to be searching 3D tuning damage space. This temperament divides the octave into three parts, so our ballpark <math>g_1</math> is 400 ¢, and our second generator <math>g_2</math> is a free generator for prime 3, so it's going to be ballpark its pure tuning of 1901.955 ¢.
+To help illustrate advanced tie-breaking, we're going to look at a minimax-C tuning of [[augmented (temperament)|augmented]] temperament, with mapping {{rket|{{map|3 0 7}} {{map|0 1 0}}}}. In particular, we're going to use the somewhat arbitrary target-interval set <math>\{ \frac32, \frac52, \frac53, \frac83, \frac95, \frac{16}{5}, \frac{15}{8}, \frac{18}{5} \}</math>. As a rank-2 temperament, we're going to be searching 3D tuning damage space. This temperament divides the octave into three parts, so our ballpark <math>g_1</math> is 400 ¢, and our second generator <math>g_2</math> is a free generator for prime 3, so it's going to be ballpark its pure tuning of 1901.955 ¢.
 Here's an aerial view on the tuning damage space, where we've "clipped" every damage graph hyper-V where it has gone out-of-bounds, above 150 ¢(C) damage; that is, we've colored it in grey and flattened it across the top of the box of our visualization. This lets us focus in clearly on the region of real interest, which is where all target-intervals' damages are less than this cap at the same time. This is the multicolored crater in the middle here: