Talk:Porcupine family

But porkypine is the canonical extension?

I see no reason why the page should not start with 2.3.5, then go to 2.3.5.11, and then proceed to extensions to 7 and 13.

2.3.5.11-subgroup porcupine ("porkypine") is a canonical extension, so is 7- and 11-limit porcupine. Since porcupine is a full 11-limit temp, there's no reason to pick the subgroups within it instead of simply going 5-, 7-, and 11-limit. FloraC (talk) 10:28, 10 May 2025 (UTC)

Sure, but like, it makes no musical sense to restrict porcupine to 2.3.5.7. Does 7 somehow have some inherent priority over 11? --VectorGraphics (talk) 20:08, 10 May 2025 (UTC)

Yes it does. FloraC (talk) 11:30, 11 May 2025 (UTC)

How so, given porcupine extensions agree on the mapping for 11 more than they do for 7? --VectorGraphics (talk) 16:01, 11 May 2025 (UTC)

That's irrelevant. One gets 7-limit porcupine by tempering 7-limit JI, which makes perfectly valid musical sense. FloraC (talk) 09:30, 12 May 2025 (UTC)

Personally, I feel like it's reasonable to categorize that as "11-limit porcupine, but you don't use the intervals of 11". It's more reasonable to start with 11-limit porcupine and remove 11 (Which doesn't require any extra temp data) than to start with 7-limit porcupine and add 11. --VectorGraphics (talk) 02:08, 13 May 2025 (UTC)

Draft of revision

I have a revision draft at User:VectorGraphics/Porcupine_family/Draft_1 -- VectorGraphics (talk) 02:08, 13 May 2025 (UTC)

I haven't studied the whole draft in detail, but on a high level I agree this looks like a better way to organize the extensions. – Sintel🎏 (talk) 11:49, 13 May 2025 (UTC)

I strongly disagree. This makes it difficult to compare porcupine with other temps. Basically I'm saying the 7-limit, 11-limit, etc. are flatlands where all the systems can be studied and compared. This idea of defining temps on 2.3.5.11 and then adding 7 makes the scene opaque and hard to sort out. FloraC (talk) 12:19, 13 May 2025 (UTC)

Why obscure the idea that different systems more naturally support different primes? This seems like a crucial piece of info about any given temperament. Meantone works best in 2.3.5.7, mintra works best in 3.5.7.11, kleismic works best in 2.3.5.13, and porcupine works best in 2.3.5.11.

2.3.5.7 porcupine is simply unnatural. It is not a convergence of 2.3.5.7.11 porcupine and any other reasonable porcupine mapping, because strong porcupine has no other reasonable mapping of 11 than the porkypine version. Therefore, there is no reason to talk about it on its own. --VectorGraphics (talk) 23:02, 13 May 2025 (UTC)

2.3.5.11-subgroup porcupine has been documented. No one's saying it should be removed, so it's not being "obscured". Septimal porcupine is very natural: it extends 5-limit porcupine without changing the complexity, accuracy, or optimal tuning much. Thus, it is canon. "Porcupine has no other reasonable mapping of 11" is true but is besides the point cuz not everyone has to be interested in the 11-limit. FloraC (talk) 09:01, 14 May 2025 (UTC)

My point is why consider 2.3.5.7.11 porcupine a different temperament than 2.3.5.7 porcupine? -- 19:30, 14 May 2025 (UTC)

Not sure what exactly is meant by "different temperament" but generally speaking 11-limit porcupine is to 7-limit porcupine what 7-limit porcupine is to 5-limit porcupine. FloraC (talk) 13:16, 15 May 2025 (UTC)

but could the same not be said for 2.3.5.7.11 -> 2.3.5.11 -> 2.3.5? --VectorGraphics (talk) 20:20, 15 May 2025 (UTC)

One should be able to compare porcupine with e.g. septimal meantone, magic, or sensi. Not adopting the 7-limit makes that difficult. FloraC (talk) 14:56, 16 May 2025 (UTC)

How is it difficult to compare 2.3.5.11 porcupine to 2.3.5.7 meantone?

Similarities:

* Porcupine and meantone are both mildly inaccurate

* Both porcupine and meantone tend to tune 5/4 sharp

* Porcupine and meantone both equate a pair of adjacent superparticular whole-tones

* Porcupine and meantone both generate 7-note MOSes

* Both porcupine and meantone have a badness of around 0.01.

Differences:

* Porcupine is generated by 11/10, while meantone is diatonic

* Porcupine exaggerates the syntonic comma to a chromatic semitone, while meantone tempers it out

* Porcupine naturally extends to 2.3.5.11, while meantone naturally extends to 2.3.5.7

* Porcupine's three odd primes are found adjacent to each other and near +0 gens, while meantone's require significant stacking to reach (especially 7) -- VectorGraphics (talk) 02:34, 17 May 2025 (UTC)

The similarities and differences you listed are from properties of 5-limit porcupine and 5-limit meantone. "Porcupine is generated by 11/10, while meantone is diatonic" is pointless, cuz of course two temps are in general generated by different gens, and you can write 11/10 as 10/9.

"Both porcupine and meantone have a badness of around 0.01" makes absolutely no sense. It's a mistake to use Smith's badness metric across subgroups. Sintel's Dirichlet badness is the first true attempt of inter-subgroup badness comparison, but even that isn't perfect. 7 and 11 are inherently different primes, so they have different utilities and tendencies. That's why I said to meaningful compare temps they need to be tempering of the same subgroup.

FloraC (talk) 09:50, 17 May 2025 (UTC)

Okay, but why is "comparing temperaments" in that manner the chief purpose for this? Porcupine and meantone are different systems, and one likely chooses porcupine and then proceeds to work in 2.3.5.11, or chooses meantone and then proceeds to work in 2.3.5.7. -- VectorGraphics (talk) 17:10, 17 May 2025 (UTC)

Rename of tridecimal porcupine

I've suggested some of these names in the wiki channel on Discord, but it got buried under other discussion:

- porcupinefowl (the opposite of fish, from "neither fish nor fowl")

- equisuperparticular porcupine (from equating 13/12 through 10/9 equally)

- s-porcupine or sporcupine (from tempering out consecutive s-expressions) --hkm (talk) 06:26, 19 May 2025 (UTC)