User talk:FloraC: Difference between revisions

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There are an infinite of mappings of each temperaments including normalized form (left) and minimum generator form (right). In the normalized form, ''a2'' in the mapping [{{val|a1 a2 a3 …}}, {{val|0 b2 b3 …}}] takes 0 ≤ ''a2'' < abs(''b2'') if ''b2'' ≠ 0. The minimum generator form ("Reduced Mapping" in the [http://x31eq.com/temper Temperament finding scripts] by [[Graham Breed]], taking 0 ≤ ''g'' ≤ ''p''/2 where ''p'' is the period and ''g'' is the generator) can be yielded by Euclidean algorithm. Which form are you favor? --[[User:Xenllium|Xenllium]] ([[User talk:Xenllium|talk]]) 13:48, 29 January 2022 (UTC)

: I'm aware of all the normal forms. I participated in the rework on the ''Normal lists'' page, after all (see also the corresponding talk page). The positive generator form is what I prefer, and with ''mapping generators'' showing the corresponding ratios. Reasons? First, Gene has always chosen that form. Second, it makes sense in higher ranks, whereas the minimum generator form doesn't. That said, I'm less sure about the ''POTE generator'' line. This line is more practical and sometimes really used to tune things. I hope octave-reduced form for this line isn't a bad choice. We're used to meantone being generated by fifths, not fourths. We may also add minimum generator form in parentheses when appropriate. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:08, 29 January 2022 (UTC)

Revision as of 13:48, 29 January 2022 view source Xenllium (talk \| contribs) autopatrolled, emailconfirmed 5,032 edits →Normalized mapping vs minimum generator: new section ← Older edit		Revision as of 14:08, 29 January 2022 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,500 edits →Normalized mapping vs minimum generator: re Newer edit →
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	There are an infinite of mappings of each temperaments including normalized form (left) and minimum generator form (right). In the normalized form, ''a<sub>2</sub>'' in the mapping [{{val\|a<sub>1</sub> a<sub>2</sub> a<sub>3</sub> …}}, {{val\|0 b<sub>2</sub> b<sub>3</sub> …}}] takes 0 ≤ ''a<sub>2</sub>'' < abs(''b<sub>2</sub>'') if ''b<sub>2</sub>'' ≠ 0. The minimum generator form ("Reduced Mapping" in the [http://x31eq.com/temper Temperament finding scripts] by [[Graham Breed]], taking 0 ≤ ''g'' ≤ ''p''/2 where ''p'' is the period and ''g'' is the generator) can be yielded by Euclidean algorithm. Which form are you favor? --[[User:Xenllium\|Xenllium]] ([[User talk:Xenllium\|talk]]) 13:48, 29 January 2022 (UTC)		There are an infinite of mappings of each temperaments including normalized form (left) and minimum generator form (right). In the normalized form, ''a<sub>2</sub>'' in the mapping [{{val\|a<sub>1</sub> a<sub>2</sub> a<sub>3</sub> …}}, {{val\|0 b<sub>2</sub> b<sub>3</sub> …}}] takes 0 ≤ ''a<sub>2</sub>'' < abs(''b<sub>2</sub>'') if ''b<sub>2</sub>'' ≠ 0. The minimum generator form ("Reduced Mapping" in the [http://x31eq.com/temper Temperament finding scripts] by [[Graham Breed]], taking 0 ≤ ''g'' ≤ ''p''/2 where ''p'' is the period and ''g'' is the generator) can be yielded by Euclidean algorithm. Which form are you favor? --[[User:Xenllium\|Xenllium]] ([[User talk:Xenllium\|talk]]) 13:48, 29 January 2022 (UTC)

			: I'm aware of all the normal forms. I participated in the rework on the ''Normal lists'' page, after all (see also the corresponding talk page). The positive generator form is what I prefer, and with ''mapping generators'' showing the corresponding ratios. Reasons? First, Gene has always chosen that form. Second, it makes sense in higher ranks, whereas the minimum generator form doesn't. That said, I'm less sure about the ''POTE generator'' line. This line is more practical and sometimes really used to tune things. I hope octave-reduced form for this line isn't a bad choice. We're used to meantone being generated by fifths, not fourths. We may also add minimum generator form in parentheses when appropriate. [[User:FloraC\|FloraC]] ([[User talk:FloraC\|talk]]) 14:08, 29 January 2022 (UTC)