Talk:Archytas clan
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Rename to Archy family?
As I read in Subgroup temperament families, relationships, and genes#Families, Dominant belongs to Meantone family and "Archy family" and in the introduction of this article (Archytas clan), I see the Dominant temperament in the list. Any suggestions how to cope with it? --Xenwolf (talk) 12:47, 21 May 2021 (UTC)
- Clan was Gene's term for subgroup family. Yeah it's sometimes confusing and the use has never carried on in the community. Not all clan pages can be renamed tho, as some of the subgroup temperaments haven't got distinct names (example: Quince clan). FloraC (talk) 17:36, 21 May 2021 (UTC)
Alternate 13-limit superpyth?
In the canonical 13-limit extension to superpyth, prime 13 is tuned very flat unlike the other harmonics unless tunings close to 27edo are used, and 27e-edo is the only reasonable tuning of it (tunings flatter than it swap 13/12 and 14/13, and tunings sharper than it swap 11/8 and 7/5). I suggest adding the extension 22f&27e, mapping prime 13 to -14 generators, though one may be against that as this extension wouldn't be supported by any patent vals (at least not to my knowledge). One may even argue to make that extension canonical and decanonicalize the currently canonical extension, though I am personally against doing that.--Overthink (talk) 19:59, 5 October 2025 (UTC)
- In my opinion, superpyth shouldn't really have a 13-limit canonical extension. 22edo and 27edo don't support it well in the full 13-limit, and though 49edo is a patent val tuning, the 49edo 13-limit patent val is very inaccurate, with errors over 24 cents, as well as failing to be diamond monotone in the 13-odd-limit due to 13/12 being 5 steps while 14/13 is 6 steps. 13-limit superpyth is awkward because for 13/12 and 14/13 to not be swapped, we must have 13/8 be mapped no less than an octave minus half a fifth due to 64/63=(169/168)(512/507), and thus 16/13 mapped no greater than a hemififth. However, unless 16/13 is exactly a hemififth, then it must be mapped narrower, which cannot be done consistently unless the fifth is wider than 256/169=718.9 ¢, and thus no strong 13-limit extension of archy is supported by more than one patent val. A similar situation occurs with 11-limit meantone, where 11/9 must be mapped no less than a hemififth in order to map (11/10)/(12/11)=121/120=(81/80)/(243/242) nonnegatively, but 11/9 must be an exact hemififth to be consistent unless the fifth is narrower than 121/81=694.8 ¢. Note that 19edo and 26edo map 11/9 consistently despite not having a hemififth, due to their fifth being flatter than a just 121/81. In superpyth, however, the neutral third with this awkward situation is the 13th subharmonic, which is mapped consistently in any patent val, and only inconsistently mapped in non-patent vals.--Overthink (talk) 07:42, 2 December 2025 (UTC)