User talk:FloraC: Difference between revisions

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* [[User talk:FloraC/Archive 2020]]

* [[User talk:FloraC/Archive 2021]]

* [[User talk:FloraC/Archive 2022]]

~~== Normalized mapping vs minimum generator ==~~

* [[User talk:FloraC/Archive 2023]]

~~Why is the generator wider than a half octave in some temperaments? Why did you edit mappings to normalize?~~

* [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}] (generator: ~3 = 1896.5 cents) vs [{{val|1 2 4 7}}, {{val|0 -1 -4 -10}}] (generator: ~4/3 = 503.5 cents) in the [[Meantone family|meantone temperament]] (12&19)

* [{{val|1 0 -4 2}}, {{val|0 2 8 1}}] (generator: ~7/4 = 947.4 cents) vs [{{val|1 2 4 3}}, {{val|0 -2 -8 -1}}] (generator: ~7/6 = 252.6 cents) in the [[Meantone temperament #Godzilla|godzilla temperament]] (5&14c)

* [{{val|1 0 -13 -3}}, {{val|0 3 29 11}}] (generator: ~81/56 = 634.0 cents) vs [{{val|1 3 16 8}}, {{val|0 -3 -29 -11}}] (generator: ~112/81 = 566.0 cents) in the [[Tricot family|tricot temperament]] (53&70)

* [{{val|1 7 3 15}}, {{val|0 -8 -1 -18}}] (generator: ~8/5 = 812.6 cents) vs [{{val|1 -1 2 -3}}, {{val|0 8 1 18}}] (generator: ~5/4 = 387.4 cents) in the [[Würschmidt family|würschmidt temperament]] (31&96)

* [{{val|1 12 56 -2}}, {{val|0 -13 -67 6}}] (generator: ~256/147 = 961.4 cents) vs [{{val|1 -1 -11 4}}, {{val|0 13 67 -6}}] (generator: ~147/128 = 238.6 cents) in the [[Wizmic microtemperaments #Tokko|tokko temperament]] (5&166)

* [{{val|1 16 32 -15}}, {{val|0 -17 -35 21}}] (generator: ~9/5 = 1017.5 cents) vs [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}] (generator: ~10/9 = 182.5 cents) in the [[Minortonic family #Mitonic|mitonic temperament]] (46&125)

* [{{val|1 25 -31 -8}}, {{val|0 -26 37 12}}] (generator: ~28/15 = 1080.7 cents) vs [{{val|1 -1 6 4}}, {{val|0 26 -37 -12}}] (generator: ~15/14 = 119.3 cents) in the [[Breedsmic temperaments #Septidiasemi|septidiasemi temperament]] (10&161)

* [{{val|1 17 9 10}}, {{val|0 -30 -13 -14}}] (generator: ~10/7 = 616.6 cents) vs [{{val|1 -13 -4 -4}}, {{val|0 30 13 14}}] (generator: ~7/5 = 583.4 cents) in the [[Breedsmic temperaments #Cotritone|cotritone temperament]] (37&72)

* [{{val|2 0 11 31}}, {{val|0 1 -2 -8}}] (generator: ~3 = 1903.7 cents) vs [{{val|2 3 5 7}}, {{val|0 1 -2 -8}}] (generator: ~16/15 = 103.7 cents) in the [[Diaschismic family #Diaschismic|diaschismic temperament]] (46&58)

* [{{val|2 1 9 -2}}, {{val|0 2 -4 7}}] (generator: ~35/24 = 652.8 cents) vs [{{val|2 3 5 5}}, {{val|0 2 -4 7}}] (generator: ~36/35 = 52.8 cents) in the [[Diaschismic family #Shrutar|shrutar temperament]] (22&46)

* [{{val|3 0 7 18}}, {{val|0 1 0 -2}}] (generator: ~3 = 1909.3 cents) vs [{{val|3 5 7 8}}, {{val|0 -1 0 2}}] (generator: ~16/15 = 90.7 cents) in [[Augmented family #Augene|augene temperament]] (12&15)

* [{{val|9 1 1 12}}, {{val|0 2 3 2}}] (generator: ~5/3 = 884.3 cents) vs [{{val|9 15 22 26}}, {{val|0 -2 -3 -2}}] (generator: ~36/35 = 49.0 cents) in the [[Ragismic microtemperaments #Ennealimmal|ennealimmic temperament]] (27&45)

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)

~~== Reasonable commas extension ==~~

~~Hi there,~~

~~I recently stumbled upon your "reasonable commas" page, and I wanted to know a few things:~~

~~- What are/were your motivations for this page?~~

~~- What is the difference between the two definitions on that page?~~

~~- What is the algorithm you used? (as to extend to higher limits)~~

~~Thank you --[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 07:27, 28 September 2022 (UTC)~~

~~:> What are/were your motivations for this page?~~

~~: It seems like a good criterion for whether a comma is an efficient one.~~

~~:> What is the difference between the two definitions on that page?~~

: My redefinition is more strict. For example, 135/128 would be a reasonable comma in the original definition cuz none of 129, 130, 131, 132, 133, 134 is 5-limit. In my redefinition 135/128 isn't one since 135/128 = (25/24)(81/80), factored into two simpler commas.

~~:> What is the algorithm you used? (as to extend to higher limits)~~

~~: Dead Shaman somehow generated the lists of commas according to his original definition. I simply checked each comma manually. So unfortunately I don't have an algorithm to share.~~

~~: [[User:FloraC|FloraC]] (~~[[User talk:FloraC~~|talk]]) 05:50, 29 September 2022 (UTC)~~

~~== Optimal GPV sequence template~~/~~module ==~~

Is there a way to actually implement your temperament evaluator python files to find a temperament's optimal GPV sequence into a template on this site for better ease of use? Or for all of your temperament evaluator files? --[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 04:28, 12 October 2022 (UTC)

~~: I have no idea how to implement it in lua. That said, I might make a separate python script for this particular functionality. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:37, 12 October~~ 2022 ~~(UTC)~~

~~== Equivalence continua: fractional n's ==~~

~~How exactly do you get a rational number from using a fractional exponent? This is mostly for the diaschismic-porcupine continuum page I'm making.~~

~~--[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 02:52, 30 April 2023 (UTC)~~

: You can get the fractional monzos by adding or subtracting fractional multiples of the ''n'' = infinity monzo from the ''n'' = 0 3-limit base monzo, and then eliminate fractions by lcm-ing it. Btw I have some important comments and plz make sure you read the talk page of that particular page you mentioned. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:47, 30 April 2023 (UTC)

~~== Constrained tuning vs. POTE tuning ==~~

I wondered that optimal tunings of some temperaments are indicated by [[Constrained tuning|constrained TE]] (CTE) instead of [[POTE tuning|octave-destretched TE]] (POTE). Why did you update to replace generators POTE to CTE?

~~Temperament generators indicated by CTE tuning:~~

* [[Meantone family]]

* [[Porcupine family]]

* [[Augmented family]]

* ~~[[Hemifamity temperaments]]~~

~~and so on ... --[[User:Xenllium|Xenllium]] (~~[[User talk:~~Xenllium|talk]]) 08:36, 3 May 2023 (UTC)~~

~~: The community (at least the part from Discord) have generally agreed that CTE is a more logical tuning. It's planned that most of the RTT pages will be eventually updated to CTE. [[User:FloraC|~~FloraC~~]] ([[User talk:FloraC|talk]]) 10:24, 3 May 2023 (UTC)~~

~~== Temperament name revision for 99&166 and 166&198 ==~~

~~Reviewing [http://www.tonalsoft.com/enc/m/magic.aspx magic] in ''Encyclopedia of Microtonal Music Theory'', Tonalsoft, a low-accuacy temperament which tempers out 36/35 and 1875~~/1792 is given a name ''witch'', so I revised the temperament names for 99&166 (''witch'' → ''[[Wizmic microtemperaments #Witcher|witcher]]'') and 166&198 (''semiwitch''→''[[Wizmic microtemperaments #Witcher|semiwitcher]]''). Deal? --[[User:Xenllium|Xenllium]] ([[User talk:Xenllium|talk]]) 07:29, 6 August 2023 ~~(UTC)~~

~~: Sure, since you named them in the first place. [[User:FloraC|FloraC~~]] ~~([[User talk:FloraC|talk]]) 09:54, 6 August 2023 (UTC)~~

== Meantone tuning spectrum additions? ==

@@ Line 1: / Line 1: @@
 * [[User talk:FloraC/Archive 2020]]
 * [[User talk:FloraC/Archive 2021]]
+* [[User talk:FloraC/Archive 2022]]
-== Normalized mapping vs minimum generator ==
+* [[User talk:FloraC/Archive 2023]]
-Why is the generator wider than a half octave in some temperaments? Why did you edit mappings to normalize?
-* [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}] (generator: ~3 = 1896.5 cents) vs [{{val|1 2 4 7}}, {{val|0 -1 -4 -10}}] (generator: ~4/3 = 503.5 cents) in the [[Meantone family|meantone temperament]] (12&amp;19)
-* [{{val|1 0 -4 2}}, {{val|0 2 8 1}}] (generator: ~7/4 = 947.4 cents) vs [{{val|1 2 4 3}}, {{val|0 -2 -8 -1}}] (generator: ~7/6 = 252.6 cents) in the [[Meantone temperament #Godzilla|godzilla temperament]] (5&amp;14c)
-* [{{val|1 0 -13 -3}}, {{val|0 3 29 11}}] (generator: ~81/56 = 634.0 cents) vs [{{val|1 3 16 8}}, {{val|0 -3 -29 -11}}] (generator: ~112/81 = 566.0 cents) in the [[Tricot family|tricot temperament]] (53&amp;70)
-* [{{val|1 7 3 15}}, {{val|0 -8 -1 -18}}] (generator: ~8/5 = 812.6 cents) vs [{{val|1 -1 2 -3}}, {{val|0 8 1 18}}] (generator: ~5/4 = 387.4 cents) in the [[Würschmidt family|würschmidt temperament]] (31&amp;96)
-* [{{val|1 12 56 -2}}, {{val|0 -13 -67 6}}] (generator: ~256/147 = 961.4 cents) vs [{{val|1 -1 -11 4}}, {{val|0 13 67 -6}}] (generator: ~147/128 = 238.6 cents) in the [[Wizmic microtemperaments #Tokko|tokko temperament]] (5&amp;166)
-* [{{val|1 16 32 -15}}, {{val|0 -17 -35 21}}] (generator: ~9/5 = 1017.5 cents) vs [{{val|1 -1 -3 6}}, {{val|0 17 35 -21}}] (generator: ~10/9 = 182.5 cents) in the [[Minortonic family #Mitonic|mitonic temperament]] (46&amp;125)
-* [{{val|1 25 -31 -8}}, {{val|0 -26 37 12}}] (generator: ~28/15 = 1080.7 cents) vs [{{val|1 -1 6 4}}, {{val|0 26 -37 -12}}] (generator: ~15/14 = 119.3 cents) in the [[Breedsmic temperaments #Septidiasemi|septidiasemi temperament]] (10&amp;161)
-* [{{val|1 17 9 10}}, {{val|0 -30 -13 -14}}] (generator: ~10/7 = 616.6 cents) vs [{{val|1 -13 -4 -4}}, {{val|0 30 13 14}}] (generator: ~7/5 = 583.4 cents) in the [[Breedsmic temperaments #Cotritone|cotritone temperament]] (37&amp;72)
-* [{{val|2 0 11 31}}, {{val|0 1 -2 -8}}] (generator: ~3 = 1903.7 cents) vs [{{val|2 3 5 7}}, {{val|0 1 -2 -8}}] (generator: ~16/15 = 103.7 cents) in the [[Diaschismic family #Diaschismic|diaschismic temperament]] (46&amp;58)
-* [{{val|2 1 9 -2}}, {{val|0 2 -4 7}}] (generator: ~35/24 = 652.8 cents) vs [{{val|2 3 5 5}}, {{val|0 2 -4 7}}] (generator: ~36/35 = 52.8 cents) in the [[Diaschismic family #Shrutar|shrutar temperament]] (22&amp;46)
-* [{{val|3 0 7 18}}, {{val|0 1 0 -2}}] (generator: ~3 = 1909.3 cents) vs [{{val|3 5 7 8}}, {{val|0 -1 0 2}}] (generator: ~16/15 = 90.7 cents) in [[Augmented family #Augene|augene temperament]] (12&amp;15)
-* [{{val|9 1 1 12}}, {{val|0 2 3 2}}] (generator: ~5/3 = 884.3 cents) vs [{{val|9 15 22 26}}, {{val|0 -2 -3 -2}}] (generator: ~36/35 = 49.0 cents) in the [[Ragismic microtemperaments #Ennealimmal|ennealimmic temperament]] (27&amp;45)
-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 &le; ''a<sub>2</sub>'' &lt; abs(''b<sub>2</sub>'') if ''b<sub>2</sub>'' &ne; 0. The minimum generator form ("Reduced Mapping" in the [http://x31eq.com/temper Temperament finding scripts] by [[Graham Breed]], taking 0 &le; ''g'' &le; ''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)
-== Reasonable commas extension ==
-Hi there,
-I recently stumbled upon your "reasonable commas" page, and I wanted to know a few things:
- - What are/were your motivations for this page?
- - What is the difference between the two definitions on that page?
- - What is the algorithm you used? (as to extend to higher limits)
-Thank you --[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 07:27, 28 September 2022 (UTC)
-:> What are/were your motivations for this page?
-: It seems like a good criterion for whether a comma is an efficient one.
-:> What is the difference between the two definitions on that page?
-: My redefinition is more strict. For example, 135/128 would be a reasonable comma in the original definition cuz none of 129, 130, 131, 132, 133, 134 is 5-limit. In my redefinition 135/128 isn't one since 135/128 = (25/24)(81/80), factored into two simpler commas.
-:> What is the algorithm you used? (as to extend to higher limits)
-: Dead Shaman somehow generated the lists of commas according to his original definition. I simply checked each comma manually. So unfortunately I don't have an algorithm to share.
-: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:50, 29 September 2022 (UTC)
-== Optimal GPV sequence template/module ==
-Is there a way to actually implement your temperament evaluator python files to find a temperament's optimal GPV sequence into a template on this site for better ease of use? Or for all of your temperament evaluator files? --[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 04:28, 12 October 2022 (UTC)
-: I have no idea how to implement it in lua. That said, I might make a separate python script for this particular functionality. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:37, 12 October 2022 (UTC)
-== Equivalence continua: fractional n's ==
-How exactly do you get a rational number from using a fractional exponent? This is mostly for the diaschismic-porcupine continuum page I'm making.
---[[User:Royalmilktea|Royalmilktea]] ([[User talk:Royalmilktea|talk]]) 02:52, 30 April 2023 (UTC)
-: You can get the fractional monzos by adding or subtracting fractional multiples of the ''n'' = infinity monzo from the ''n'' = 0 3-limit base monzo, and then eliminate fractions by lcm-ing it. Btw I have some important comments and plz make sure you read the talk page of that particular page you mentioned. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:47, 30 April 2023 (UTC)
-== Constrained tuning vs. POTE tuning ==
-I wondered that optimal tunings of some temperaments are indicated by [[Constrained tuning|constrained TE]] (CTE) instead of [[POTE tuning|octave-destretched TE]] (POTE). Why did you update to replace generators POTE to CTE?
-Temperament generators indicated by CTE tuning:
-* [[Meantone family]]
-* [[Porcupine family]]
-* [[Augmented family]]
-* [[Hemifamity temperaments]]
-and so on ... --[[User:Xenllium|Xenllium]] ([[User talk:Xenllium|talk]]) 08:36, 3 May 2023 (UTC)
-: The community (at least the part from Discord) have generally agreed that CTE is a more logical tuning. It's planned that most of the RTT pages will be eventually updated to CTE. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 10:24, 3 May 2023 (UTC)
-== Temperament name revision for 99&166 and 166&198 ==
-Reviewing [http://www.tonalsoft.com/enc/m/magic.aspx magic] in ''Encyclopedia of Microtonal Music Theory'', Tonalsoft, a low-accuacy temperament which tempers out 36/35 and 1875/1792 is given a name ''witch'', so I revised the temperament names for 99&amp;166 (''witch'' → ''[[Wizmic microtemperaments #Witcher|witcher]]'') and 166&amp;198 (''semiwitch''→''[[Wizmic microtemperaments #Witcher|semiwitcher]]''). Deal? --[[User:Xenllium|Xenllium]] ([[User talk:Xenllium|talk]]) 07:29, 6 August 2023 (UTC)
-: Sure, since you named them in the first place. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:54, 6 August 2023 (UTC)
 == Meantone tuning spectrum additions? ==