I'm hoping to get seven commas named by the end of the year, and not only do I not see a name for this comma anywhere on this wiki, but I also don't see a name for this comma on the Huygens-Fokker interval list. Perhaps I should come up with a name for it. I hope I'm not sticking my foot in my mouth like I was with 625/624- that was embarrassing. --Aura (talk) 00:41, 27 December 2020 (UTC)
- In my opinion the importance of a comma/temperament/whatever should be obvious before we bind much energy in dedicated pages/names/etc. I sometimes have the impression that we are - in part - generating content from nothing here. --Xenwolf (talk) 19:25, 28 December 2020 (UTC)
- I'm already looking into what's going on with this comma, and so far I've found that tempering out this comma equates 18/17 with 55/52, 17/13 with 72/55, 24/17 with 55/39, 144/143 with 170/169, 44/39 with 96/85, and perhaps most interestingly for me- 117/64 with 935/512. The reason I find that lattermost instances of equated intervals interesting has more to do with cultural reference- particularly with regards to the Halo series of videogames as the Master Chief- the protagonist of the main series Halo games, is also known as "John-117". I'm still looking into this comma to see if I can find anything else of interest. --Aura (talk) 20:17, 28 December 2020 (UTC)
- After further investigation, it seems that by tempering out 936/935, we end up equating 289/288 with 221/220, 256/255 with 352/351, 375/374 with 625/624, 351/350 with 561/560, and- in another interesting twist- 385/384 (the keenanisma) with 273/272 (the tannisma). --Aura (talk) 21:44, 28 December 2020 (UTC)
- As for the idea of generating content from nothing, well, that sounds almost like a part of my job description as a pioneer in microtonal music theory- to explore intervals and temperaments where few have explored before, and to find the beauty in intervals that other music theorists have overlooked, ignored, or dismissed. --Aura (talk) 22:39, 28 December 2020 (UTC)
- > Perhaps most interestingly for me- 117/64 with 935/512.
- It's nothing special: any interval can be decomposed into a difference of two overtones.
- It maybe true that any interval can be decomposed into a difference of two overtones or two undertones, but the fact that one of the two overtones in this case was 117/64 is what I found interesting in light of the potential for cultural references. At any rate, it's good to know that this comma leads to essentially tempered chords. --Aura (talk) 08:38, 29 December 2020 (UTC)
- These are the triads:
- 1-17/16-13/11 with steps 17/16-10/9-22/13, and its inversions;
- 1-10/9-13/11 with steps 10/9-17/16-22/13, and its inversions;
- 1-13/11-24/17 with steps 13/11-6/5-24/17, and its inversions;
- 1-6/5-24/17 with steps 6/5-13/11-24/17, and its inversions;
- 1-18/17-5/4 with steps 18/17-13/11-8/5, and its inversions;
- 1-13/11-5/4 with steps 13/11-18/17-8/5, and its inversions.
- These are the triads:
- This list is good to have on hand. Perhaps I should make note of the the fact that this comma leads to essentially tempered chords- "ainic chords" in this case, and then make an article showing off some of these chords. Unfortunately, however I don't seem to have a good way of finding all the essentially tempered chords. --Aura (talk) 08:38, 29 December 2020 (UTC)
Forms of 17-limit Temperaments
- Note it's not that we don't know what a 17-limit temperament is; it's that we haven't got examples of such pages for temperaments of a 17-limit comma. Quoting:
If X is a 3- or 5-limit comma, "X family" is for rank-2 temperaments that temper it out. If X is a 7-limit comma, "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. If X is an 11-limit comma, "X family" is for rank-4 temperaments that temper it out, and "X temperaments" is for rank-3 temperaments that temper it out. 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. If X is an 13-limit comma, there are only three such pages: The Archipelago, The Biosphere, Marveltwin, which list temperaments of various ranks.