Squib
Joined 25 April 2025
pretend i am good at formatting |
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The other way to approximate 5/4 is to indeed add more notes between the existing ones. The tuning we already have is called Pythagorean tuning because it uses only ratios of 2 and 3. We can take two sets of Pythagorean and put them together. There are an infinite number of ways to do this, but only 3 preserve isomorphism. (In fact, the number of equal tunings with N sets of pythagorean is exactly equal to the sum of the unique factors of N. Don't ask me why, although I suspect figuring it out will help me name them.) | The other way to approximate 5/4 is to indeed add more notes between the existing ones. The tuning we already have is called Pythagorean tuning because it uses only ratios of 2 and 3. We can take two sets of Pythagorean and put them together. There are an infinite number of ways to do this, but only 3 preserve isomorphism. (In fact, the number of equal tunings with N sets of pythagorean is exactly equal to the sum of the unique factors of N. Don't ask me why, although I suspect figuring it out will help me name them.) | ||
===Overview=== | |||
For now, this is just a list of the things I want to explain here. | |||
* philosophy | |||
** creating the theory based on experience and what actually works/is helpful | |||
** intentionally keeping it simple; this makes it more useful even if it's not what i would naturally gravitate to otherwise | |||
** as a result of this: models emerge! | |||
** models are abstractions, describing the important attributes of a complex phenomenon in a simple way. | |||
* what are notes? | |||
* 2d tunings | |||
* 3d tunings in a 2d space | |||