User talk:FloraC

• User talk:FloraC/Archive 2020
• User talk:FloraC/Archive 2021

Normalized mapping vs minimum generator

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

• [⟨1 0 -4 -13], ⟨0 1 4 10]] (generator: ~3 = 1896.5 cents) vs [⟨1 2 4 7], ⟨0 -1 -4 -10]] (generator: ~4/3 = 503.5 cents) in the meantone temperament (12&19)
• [⟨1 0 -4 2], ⟨0 2 8 1]] (generator: ~7/4 = 947.4 cents) vs [⟨1 2 4 3], ⟨0 -2 -8 -1]] (generator: ~7/6 = 252.6 cents) in the godzilla temperament (5&14c)
• [⟨1 0 -13 -3], ⟨0 3 29 11]] (generator: ~81/56 = 634.0 cents) vs [⟨1 3 16 8], ⟨0 -3 -29 -11]] (generator: ~112/81 = 566.0 cents) in the tricot temperament (53&70)
• [⟨1 7 3 15], ⟨0 -8 -1 -18]] (generator: ~8/5 = 812.6 cents) vs [⟨1 -1 2 -3], ⟨0 8 1 18]] (generator: ~5/4 = 387.4 cents) in the würschmidt temperament (31&96)
• [⟨1 12 56 -2], ⟨0 -13 -67 6]] (generator: ~256/147 = 961.4 cents) vs [⟨1 -1 -11 4], ⟨0 13 67 -6]] (generator: ~147/128 = 238.6 cents) in the tokko temperament (5&166)
• [⟨1 16 32 -15], ⟨0 -17 -35 21]] (generator: ~9/5 = 1017.5 cents) vs [⟨1 -1 -3 6], ⟨0 17 35 -21]] (generator: ~10/9 = 182.5 cents) in the mitonic temperament (46&125)
• [⟨1 25 -31 -8], ⟨0 -26 37 12]] (generator: ~28/15 = 1080.7 cents) vs [⟨1 -1 6 4], ⟨0 26 -37 -12]] (generator: ~15/14 = 119.3 cents) in the septidiasemi temperament (10&161)
• [⟨1 17 9 10], ⟨0 -30 -13 -14]] (generator: ~10/7 = 616.6 cents) vs [⟨1 -13 -4 -4], ⟨0 30 13 14]] (generator: ~7/5 = 583.4 cents) in the cotritone temperament (37&72)
• [⟨2 0 11 31], ⟨0 1 -2 -8]] (generator: ~3 = 1903.7 cents) vs [⟨2 3 5 7], ⟨0 1 -2 -8]] (generator: ~16/15 = 103.7 cents) in the diaschismic temperament (46&58)
• [⟨2 1 9 -2], ⟨0 2 -4 7]] (generator: ~35/24 = 652.8 cents) vs [⟨2 3 5 5], ⟨0 2 -4 7]] (generator: ~36/35 = 52.8 cents) in the shrutar temperament (22&46)
• [⟨3 0 7 18], ⟨0 1 0 -2]] (generator: ~3 = 1909.3 cents) vs [⟨3 5 7 8], ⟨0 -1 0 2]] (generator: ~16/15 = 90.7 cents) in augene temperament (12&15)
• [⟨9 1 1 12], ⟨0 2 3 2]] (generator: ~5/3 = 884.3 cents) vs [⟨9 15 22 26], ⟨0 -2 -3 -2]] (generator: ~36/35 = 49.0 cents) in the 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 [⟨a₁ a₂ a₃ …], ⟨0 b₂ b₃ …]] takes 0 ≤ a₂ < abs(b₂) if b₂ ≠ 0. The minimum generator form ("Reduced Mapping" in the 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? --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. 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 --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.

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? --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. 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.

--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. 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 TE (CTE) instead of 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 ... --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. FloraC (talk) 10:24, 3 May 2023 (UTC)

Temperament name revision for 99&166 and 166&198

Reviewing 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 → witcher) and 166&198 (semiwitch→semiwitcher). Deal? --Xenllium (talk) 07:29, 6 August 2023 (UTC)

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

Meantone tuning spectrum additions?

My thoughts behind the additions I made to the tuning spectrum table (both removed and remaining):

1. Add clarification about syntonic comma vs other commas -- quite a number of commas appear in the table, but syntonic comma has its adjective stripped (as is traditional, so I didn't think it right to change that), which could be confusing to new people, especially if they have also seen another tuning spectrum table that has a different primary comma.
2. Fractions of Pythagorean comma appear often in this table, but the endpoints 7EDO and 5EDO have different 3-limit commas, so I thought it would be good to put those in there in the relevant lines.
3. 3/4-comma (especially) and 2/3 comma Meantone are very close to 7EDO.
4. Some of the EDOs in the table are there only by way of non-patent vals, but this was not explicit before.
5. 12EDO is almost exactly 1 Schisma Meantone; also, somebody (probably copy/paste error) had 12EDO notated as as "virtually 1/12 Pythagorean comma" and not "virtually 1/11 (syntonic) comma".
6. Since 5EDO is in the table (come to think of it, should it be there?), I thought the addition of some of the more prominent negative Meantone (not sure what it should be called) tunings would be in order, especially Ptolemismic which is very close to 5EDO.

For (especially) the first last, I now understand from your edit comment that non-Septimal-Meantone 7-limit and all 11-limit entries should go somewhere else. I did see the tuning table for Flattone, so maybe the entries close to 7EDO should go there? And maybe the Flattone EDOs currently in this table should also be moved there? But then flatter-than-flattone (Flattertone) doesn't have its own tuning spectrum table, and given that it is a sub-entry of the Meantone family article, I thought a new table would look kind of funny there. Similarly, Dominant doesn't have its own tuning spectrum table, and given that it is a sub-entry of the Meantone family article, I thought a new table would look kind of funny there. Not sure yet whether all negative Meantones like 17c should all go in a hypothetical Dominant tuning spectrum table, although 17c itself is Dominant. I DID see (although I must confess temporarily forgot about) the multiple tuning tables in Meantone vs Meanpop, so maybe the Ptolemismic tuning (11-limit) should go there? Although I'm not sure which of the tables it would fit into. Of these tables, only Tridecimal Meantone and Meanpop (but not Tridecimal Meanpop) have a negative meantone entry at all, and those are all only very slightly sharpened. Although at least if a new tuning spectrum table was needed in there, it wouldn't seem out of place. On the other hand, maybe such a hypothetical table should be somewhere else entirely, since undecimal negative Meantone (probably -- haven't done the math yet) would be neither Undecimal Meantone nor Meanpop?

Anyway, when I made my edits, I didn't realize that I was stepping on an organizational convention in making the edits I thought of above, so until I learn it better, I will revert back to proposing such potentially organization-altering changes in the Talk pages associated with the pages I am considering, and sorry for the trouble.

Lucius Chiaraviglio (talk) 18:03, 30 July 2024 (UTC)

Thank you for sharing your thoughts. I appreciate your professionality regarding editing the wiki.

1. Since you clarified this in the first entry, I think it's good now. The syntonic comma is also special cuz the article is about meantone. In other temps you shouldn't see fractions of the syntonic comma.
2. The fractional Pythagorean-comma tunings are senseless enough – I've never seen anyone looking for them, nor are they technically compatible with RTT. If I were bolder I'd remove all the Pythagorean-comma and septimal-comma tunings alike, but I'd better consult the community first. The actual problem is, there's no point adding those information of fractional limmas or fractional apotomes cuz there's no other fractions. Also every edo has such an association: for 19edo it's a 1/19-(19-comma) tuning; for 31edo it's a 1/31-(31-comma) tuning.
3. I don't think closeness to an edo warrants an entry. Why would someone look for those instead of grabbing the exact edo tuning?
4. I appreciate the specification of vals you added. Thank you.
5. Thank you for correcting it.
6. You have a point here. I think 5edo should have a place there cuz it's a relatively low-numbered edo that defines the edge of a tuning range (5-odd-limit diamond monotone), making it significant. Some higher edos tho really just clutters the space, esp. those in the flattone or dominant range. Pls note that extensions like flattertone and dominant will eventually get their own pages and own tuning spectra. I can make this quickly happen, if someone asks. But I don't think a simple split of the spectrum is the best solution. For one thing, all the extensions are meantone extensions and all the 5-limit eigeninterval tunings still apply. I think it's a question of which range to put the focus on. For meantone it's prolly best to maintain a higher precision in the meantone range, for flattone higher precision in the flattone range, etc.

FloraC (talk) 08:53, 31 July 2024 (UTC)