Generator form manipulation: Difference between revisions

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== mingen form ==

=== ~~what is mingen form~~ ===

=== definition ===

A number of generator size targets have been described, such as [[UDP#Generalizing_to_Arbitrary_MOS.27s:_Bright_and_Dark_Generators_.28Chroma-Positive_and_Chroma-Negative.29|chroma-positive generators]], and probably more will be described in the future. The generator size target we'll be demonstrating here may not have been rigorously described elsewhere, or named<ref>It is the form used by [[Graham Breed]]'s regular temperament finding scripts hosted here: http://x31eq.com/temper/net.html, at least for rank-2 temperaments.</ref>, but these purposes, we'll be calling it minimum-generator, or mingen, for short. Mingen form is when each successive generator is less than half the size of the previous generator.<ref>Like octave reduction combined with octave inversion, since you can't just add or subtract half octaves until it's between 0 and 600 cents. You have to add or subtract octaves until it's between -600 and +600 cents, then multiply by -1 if it's negative.</ref>

A number of generator size targets have been described, such as [[UDP#Generalizing_to_Arbitrary_MOS.27s:_Bright_and_Dark_Generators_.28Chroma-Positive_and_Chroma-Negative.29|chroma-positive generators]], "musician's form", and probably more will be described in the future. The generator size target we'll be demonstrating here may not have been rigorously described elsewhere, or named<ref>It is the form used by [[Graham Breed]]'s regular temperament finding scripts hosted here: http://x31eq.com/temper/net.html, at least for rank-2 temperaments.</ref>, but these purposes, we'll be calling it minimum-generator, or mingen, for short. Mingen form is when each successive generator is less than half the size of the previous generator.<ref>Like octave reduction combined with octave inversion, since you can't just add or subtract half octaves until it's between 0 and 600 cents. You have to add or subtract octaves until it's between -600 and +600 cents, then multiply by -1 if it's negative.</ref>

In order to define the size of the generators, you need to specify a tuning strategy. Though if you have two generators that are close enough that their size ranking depends on the tuning, then you probably have other problems. In any case, the tuning strategy that we'll be using here is T2, because it's decent enough and easy to compute.

@@ Line 101: / Line 101: @@
 == mingen form ==
-=== what is mingen form ===
+=== definition ===
-A number of generator size targets have been described, such as [[UDP#Generalizing_to_Arbitrary_MOS.27s:_Bright_and_Dark_Generators_.28Chroma-Positive_and_Chroma-Negative.29|chroma-positive generators]], and probably more will be described in the future. The generator size target we'll be demonstrating here may not have been rigorously described elsewhere, or named<ref>It is the form used by [[Graham Breed]]'s regular temperament finding scripts hosted here: http://x31eq.com/temper/net.html, at least for rank-2 temperaments.</ref>, but these purposes, we'll be calling it minimum-generator, or mingen, for short. Mingen form is when each successive generator is less than half the size of the previous generator.<ref>Like octave reduction combined with octave inversion, since you can't just add or subtract half octaves until it's between 0 and 600 cents. You have to add or subtract octaves until it's between -600 and +600 cents, then multiply by -1 if it's negative.</ref>
+A number of generator size targets have been described, such as [[UDP#Generalizing_to_Arbitrary_MOS.27s:_Bright_and_Dark_Generators_.28Chroma-Positive_and_Chroma-Negative.29|chroma-positive generators]], "musician's form", and probably more will be described in the future. The generator size target we'll be demonstrating here may not have been rigorously described elsewhere, or named<ref>It is the form used by [[Graham Breed]]'s regular temperament finding scripts hosted here: http://x31eq.com/temper/net.html, at least for rank-2 temperaments.</ref>, but these purposes, we'll be calling it minimum-generator, or mingen, for short. Mingen form is when each successive generator is less than half the size of the previous generator.<ref>Like octave reduction combined with octave inversion, since you can't just add or subtract half octaves until it's between 0 and 600 cents. You have to add or subtract octaves until it's between -600 and +600 cents, then multiply by -1 if it's negative.</ref>
 In order to define the size of the generators, you need to specify a tuning strategy. Though if you have two generators that are close enough that their size ranking depends on the tuning, then you probably have other problems. In any case, the tuning strategy that we'll be using here is T2, because it's decent enough and easy to compute.