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| == 13-Limit,17-Limit and 19-Limit Comma Pages == | | == 13-Limit, 17-Limit and 19-Limit Comma Pages == |
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| Hey, I was thinking we ought to start reorganizing the 11-limit and 13-limit temperaments, as well as figuring out how to deal with 17-limit temperaments, so far, just leaning on the preview that Flora provided me in a brief discussion on this matter, I'm thinking it should go something like this:
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| <pre>
| | A project to reorganize 11-limit and 13-limit temperaments. That is still discussed. |
| If X is a 3-limit or 5-limit comma,
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| "X family" is for rank-2 temperaments that temper it out.
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| If X is a 7-limit comma,
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| "X family" is for rank-3 temperaments that temper it out, and "X temperaments" is for rank-2 temperaments that temper it out ("X clan" if the comma is a subgroup comma). See: Marvel family, Marvel temperaments.
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| If X is an 11-limit comma,
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| "X family" is for rank-4 temperaments that temper it out, and "X temperaments" is for rank-3 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 13-limit branches), in "X temperaments" there is a brief of the rank-4 temperaments. See: Keenanismic family, Valinorsmic temperaments, Kalismic temperaments. We need to figure out how to handle pages like Quartismic family.
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| If X is an 13-limit comma,
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| "X family" is for rank-5 temperaments that temper it out, and "X temperaments" is for rank-4 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 17-limit branches), in "X temperaments" there is a brief of the rank-5 temperaments. We need to figure out how to handle pages like the Archipelago, the Biosphere and Marveltwin, which list temperaments of various ranks, as such pages will likely be more common going forward.
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| If X is a 17-limit comma,
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| "X family" is for rank 6-temperaments that temper it out, and "X temperaments" is for rank-5 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there (as it doesn't have many 19-limit branches), in "X temperaments" there is a brief of the rank-6 temperaments.
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| If X is a 19-limit comma,
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| "X family" is for rank 7-temperaments that temper it out, and "X temperaments" is for rank-6 temperaments that temper it out ("X clan" if the comma is a subgroup comma). If the "X family" page isn't there, in "X temperaments" there is a brief of the rank-7 temperaments.
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| </pre>
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| I hope this idea is at least the start of something feasible. The reason I'm stopping with the 19-limit is because aside from 94edo, none of the EDOs between 1edo and 171edo deal with the 23-limit consistently- at least to my knowledge. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:08, 31 December 2020 (UTC)
| | Join the discussion [[Xenharmonic Wiki talk:Things to do#13-Limit, 17-Limit and 19-Limit Comma Pages]]! |
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| I'm hoping for further discussion on how to deal with pages listing temperaments of various ranks that are all connected by the tempering if a single comma, such as the Archipelago, and even the Quartismic family page. Is it possible that these could be analyzed as types of "X family" or "X clan" pages depending on the nature of the comma? From the looks of things, how we handle the page on the Biosphere page in particular will determine how we handle the the current "Quartismic family" page going forward as there seem to be a lot of structural parallels. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:46, 31 December 2020 (UTC)
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| <br/>'''[ Start of suggestion/reply by''' [[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:06, 15 January 2021 (UTC)'''. ]'''<br/>
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| Re: the convention you are proposing, I do not think this is a good way to go about it. Superfamilies of temperaments formed by tempering only a single comma should be described on the page for that comma. Temperaments should get their own page separate from commas only if they temper ''at least'' 2 commas, but in higher-rank situations, that restriction should be 3 commas. High-rank temperaments tempering 2 or 3 commas should be listed on the page for a certain comma, with the page for that comma being the ultimate "super-family" of those temperaments. This could be justified further by that the temperaments listed for comma X should be ones which prioritise accuracy/idealness of tempering X, and that only temperaments involving at most 3 commas (including X) should be listed, but usually only listing X and 1 other comma. I also think that temperaments should be named based on increasing rank rather than decreasing rank, as it seems unlikely to me (from the perspective of practicality as opposed to theory, and due to various reasons) that someone would want to use (for example) a rank-5 or rank-6 temperament without tempering out any further commas, except as an exercise in exploring the temperings of specific commas or pairs of commas (hence the moving of that information to the main comma being tempered along with 1 or maybe 2 others). On the contrary, there is lots of motivation for using a rank 2 or 3 temperament. I think higher ranks usually serve to contextualise or conceptualise lower ranks, rather than vice versa, hence the lowest ranks should be the "centre of focus" for the most part, except when focusing on specific commas.
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| <br/>Another reason to avoid "single-comma superfamilies" on separate pages is it reduces redundancy/repeated information and it reduces the chaos caused by the fact that reasonably complex temperaments are defined by multiple commas, thus meaning that the position of a comma in a hierarchy of 'super-families' is generally not a necessarily well-defined concept, leading to a mess.
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| <br/>
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| <br/>"Temperaments" should therefore refer to rank 2 temperaments, and also rank 3 if the term is interpreted to include "planar temperaments". "Temperament families" should thus be rank 3, and "temperament superfamilies" should be rank 4. (Note that whether a rank 3 temperament is called a "planar temperament" or a "temperament family" should depend on its use in a discussion. If it is being considered as defining a "plane" of tones to choose from, generated by 2 generators with respect to some period, then it is a "planar temperament", but if it is being considered as a larger family uniting multiple rank 2 temperaments (and thus also rank 1 temperaments), it is a "temperament family".)
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| <br/>
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| <br/>With that said, here is my alternate proposal which I think would make things less chaotic if applied consistently and broadly. (Note that this is for higher limits/more complex cases, so as the 5- and 7-prime-limits are relatively trivial cases, I will skip past naming them and more generally all temperaments derived from a 3 or 4 dimensional untempered subgroup.)
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| <pre>
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| First, assume that we are dealing with an initial untempered subgroup of at least rank 5. (Lower ranks I'm not too concerned about how they're organised as they're generally pretty simple in comparison.) I'll call this initial untempered subgroup "IUS" for short.
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| Tempering 1 comma leads to a comma-specific temperament, described on the page for the comma.
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| If the IUS is rank 5, tempering 2 commas leads to a family or clan and tempering 3 leads to a temperament.
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| If the IUS is rank 6, tempering 2 commas leads to a superfamily, tempering 3 leads to a family or clan and tempering 4 leads to a temperament.
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| More generally, if the IUS is tempered from rank n to rank k < n through tempering (n - k) commas, then:
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| If the tempered result is rank 1, it is an equal temperament.
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| If the tempered result is rank 2, it is just a temperament.
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| If it is rank 3, it is a clan or family, alternatively named a planar temperament if using or considering it with no further tempering is desired.
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| If it is rank 4, it is a superfamily.
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| If it is rank 5, my proposed name is that it is an ultrafamily.
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| Meanwhile, for comma pages, the comma should be described in terms of its arithmetic and musical significance and in terms of the temperaments resulting from tempering it and up to 2 other commas, but generally prioritising the tuning of the comma in question, and providing a spectrum of possible tunings for that comma while showing ranges of possible tunings for other commas to temper with that comma, giving reasons as to why you might want to do so. Furthermore, if the tempering of this comma with 2 other commas results in a temperament of rank 6 or greater, I think the 3 comma combination - if considered significant - should get its own page corresponding to a type of family that I propose to be called a "metafamily". The existence of this "metafamily" should be mentioned on the page for all 3 commas, but no further information should be given (to avoid repetition of information on the page for the metafamily). In the case of tempering 2 commas resulting in rank 6 or greater, the temperament can easily just be named as the combination of the names of the commas, hence it should in that case ''definitely'' be part of the page for the comma(s) in question.
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| If we follow all of these rules, we have a very broad system for dealing with higher rank situations, as:
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| Temperaments of ranks 1 through 5 are given consistent names. (1 through 5 are covered.)
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| Tempering 1 comma is always associated with that comma. Adding only 1 more comma does not change this if the temperament is rank 6 or greater. (+2 ranks covered.)
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| In the extreme case where tempering 3 commas results in a temperament of interest that is rank 6 or greater, this is named a "metafamily", and there can be described derived temperaments of lower ranks. (+2 ranks covered.)
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| This takes us to a complete classification of up to as high as rank 9 temperaments (implying up to a rank 10 IUS, taking us to the 29-prime-limit), and I think this is a very reasonable place to draw a limit.
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| For aiding understanding of what I've stated so far, I'll provide a couple of examples of how the resulting ranks of temperaments would be classified for a couple of different rank IUS's. Rank 9 and lower temperaments would be classified in the following hierarchy (assuming an implied rank 10 IUS):
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| Rank 1 - Equal temperament.
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| Rank 2 - Temperament.
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| Rank 3 - Planar temperament. (Alternatively clan or family.)
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| Rank 4 - Superfamily AKA "[Ultrafamily] temperaments".
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| Rank 5 - Ultrafamily.
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| Rank 6 - Metafamily temperaments. Named as "[Metafamily name] + [comma name] temperaments". As a collective, derived temperaments of a Metafamily are named "[Metafamily name] temperaments".
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| Rank 7 - Metafamily.
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| Rank 8 - 2 comma temperament, derived from a 'main' comma. Named as "[main comma name] + [secondary comma name] temperament".
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| Rank 9 - 1 comma temperament. Named as just "the [comma name] temperament".
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| Rank 10 - the IUS (initial untempered subgroup).
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| If we assume a rank 8 IUS (corresponding to the 19-prime-limit) then the hierarchy looks almost the same except for rank 4 and onwards:
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| Rank 4 - Superfamily AKA an instance of a "[Metafamily] temperament".
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| Rank 5 - Ultrafamily or Metafamily. Which term is preferred depends on if you are looking at it from the perspective of a large (Ultra)family of low rank temperaments or from the perspective of a unique combination of 3 commas being tempered out of the full IUS (thus defining a Metafamily of temperaments).
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| Rank 6 - 2 comma temperament, derived from a 'main' comma. Named as "[main comma name] + [secondary comma name] temperament".
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| Rank 7 - 1 comma temperament. Named as just "the [comma name] temperament".
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| Rank 8 - the IUS (initial untempered subgroup).
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| </pre>
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| Note: A partial reason I chose "Metafamilies" to correspond to 3 commas (and thus "Metafamily temperaments" to 4) is to suggest focusing on tempering at least 3 or 4 commas in high rank situations so that we don't just get a whole bunch of 1 or 2 comma temperaments which are comparatively uninteresting and of which, at that scale, there will inevitably be (perhaps far too) many. This also has the neat property of meaning that Metafamily temperaments in the 19-prime-limit are "cubic" in analogy to how rank 3 temperaments are "planar", ad that Metafamily temperaments in the 17-prime-limit are "planar temperaments". Plus I like the fact that "Metafamily temperaments" are either equated or closely connected to Superfamilies and/or Ultrafamilies depending on how high of a rank your IUS is, further justifying the aesthetic choice of "meta" (at least IMO).<br/>
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| '''[ End of suggestion/reply by''' [[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:06, 15 January 2021 (UTC)'''. ]'''<br/><br/>
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| == Comma tables in EDO pages == | | == Comma tables in EDO pages == |