User talk:Inthar/Archive 1

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This page is an archive of past discussions. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

Minimalist user page

Hi IlL,

It would really help others to understand your edits with a few words of background on your user page. As I see in 13edo/Inthar, your user name "IlL" has a relation to "Inthar"? Best regards --Xenwolf (talk) 08:38, 25 May 2020 (UTC)

I usually go by Inthar now. (IlL is my username on Linguifex (it used to stand for a name) and I retconned it later using a different conlang.) IlL (talk) 17:19, 25 May 2020 (UTC)

I see, thanks for adding the information. --Xenwolf (talk) 21:17, 25 May 2020 (UTC)

Difference between clan and family

Hi Inthar,
I have difficulties to understand the relationship between family and clan. At first I thought it's basically the same, but now I see that there ia a Sensamagic clan and a Sensamagic family. Since you write very actively in all parts of the wiki, I was hoping you might be able to help me in this matter. Thanks in advance!
--Xenwolf (talk) 17:25, 9 June 2020 (UTC)

I don't really know either, since these terms aren't formally defined anywhere on the wiki. But from what I understand they look like synonyms ("the set of rank 2 temperaments that temper out a given comma"). IlL (talk) 17:33, 9 June 2020 (UTC)

Thanks so far. It seems to me that it would help to establish a place in the wiki where such questions could be asked and answered. --Xenwolf (talk) 18:03, 9 June 2020 (UTC)

Do you know the preview function?

Hi Inthar,
Looking on the massive amount of relatively small changes you are doing (for instance on User:IlL/13edo), I was wondering if you maybe don't know about the preview function. This function is faster than a complete save and gives you a good feedback (as I know, there is no quality difference in the rendering between the saved version and the preview). But maybe you already know this function and there is an issue with your mobile device that makes it inaccessible to you. If this is the case, I say sorry for bothering.
have a great day --Xenwolf (talk) 21:40, 15 June 2020 (UTC)

Managing subpages

Hi Inthar,
Managing subpage links can be tedious. There is a wiki function that creates lists of pages with a specific prefix, it can be used to enumerate subpages.
The following snippet extracts the pagename from the page it's places in, so this could be used on your user page as well:


Best regards --Xenwolf (talk) 07:55, 19 June 2020 (UTC)

Now I found an (in my opinion) better way to use this function:
it provides the prefix as an argument and has two optional switches. Maybe this can be helpful for you as well.
--Xenwolf (talk) 08:48, 19 June 2020 (UTC)
PS: when looking on User:IlL/Best edos for a given subgroup, I found that we maybe have to few links to Graham Breed's temp finder in the wiki. 😉

bolded harmonics

Hi Inthar,
I just removed bolded rations that not only me led to confusion (the intention wasn't visible), now I see what the idea is. I'm not arguing pro or con "bolding harmonics" but if you bolded harmonics why didn't you write its meaning in the page as well. You will admit that nobody wants to read the history as to understand the contents. Thanks in advance for considering this in future typographic improvements.
Best regards --Xenwolf (talk) 11:06, 21 June 2020 (UTC)

Degree question

If/when you have the time: would you please have a look on Talk:17edo neutral scale? Thanks --Xenwolf (talk) 11:36, 10 July 2020 (UTC)

I'm sorry, nothing changed from my POV. --Xenwolf (talk) 15:31, 10 July 2020 (UTC)
Finally got it. Please have another look on the page to ensure I explained it correctly. --Xenwolf (talk) 15:41, 10 July 2020 (UTC)

Quartismic EDOs

Okay, Inthar, now that I know that EDOs that temper out the quartisma have to be a sum of various multiples of 24, 46, and 159, I think the first possible quartismic EDO on the list after 159edo is 229edo, the next would be 253edo, and after that would be 275edo and 277edo, then 321edo and 325edo... Wow... I hope we can confirm all this... --Aura (talk) 04:42, 7 September 2020 (UTC)

BTW, 22 also seems to be a quartismic edo. (It's 46 - 24.) IlL (talk) 04:45, 7 September 2020 (UTC)
So you can use differences between the defining EDOs for this as well... What's more, the patent vals of 22edo confirm your finding... Nice... --Aura (talk) 04:54, 7 September 2020 (UTC)
With that in mind, I'm guessing that we can expect 48edo, 50edo, 70edo, 72edo, 92edo and 96edo to also be quartismic EDOs, right? --Aura (talk) 05:06, 7 September 2020 (UTC)
Wait... 50edo doesn't temper out the quartisma in its patent vals despite being (4*24 - 46), I just checked... --Aura (talk) 05:06, 7 September 2020 (UTC)
However, I do notice that 46 is 22 + 24, so maybe 22edo is actually the independent value we should be using instead of 46... --Aura (talk) 05:11, 7 September 2020 (UTC)
I see that 70 is 48 + 22, and from the looks of things, 70edo seems to work... Hmm... if 22 is actually the independent number rather than 46, then that means that 68edo should also work as it is 2*22 + 24... --Aura (talk) 05:14, 7 September 2020 (UTC)
I can confirm from my calculation that 68edo is a very good quartismic EDO... This means that the quartismic EDOs are actually all of the form 22A + 24B + 159C... --Aura (talk) 05:20, 7 September 2020 (UTC)
Wait... something isn't right... One of the predictions of the 22A + 24B + 159C model for quartismic temperaments is that 94edo would be quartismic- but it isn't... --Aura (talk) 05:49, 7 September 2020 (UTC)
Hello. I can help you find all the edos with computer. Here's a sequence of edos that temper out [24 -6 0 1 -5 with progressively lower 11-limit TE error:
21, 22, 43, 46, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395 (6790), 7060, 7554.
Here's another sequence with progressively lower TE error:
21, 22, 24, 43, 46, 89, 135 (270), 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518 (5036), 7419.
BTW I suppose this would be a rank-4 family or a rank-3 clan. Unfortunately Graham's temperament finder recently went down (or I'm blocked) so I can't provide further insights. FloraC (talk) 06:00, 7 September 2020 (UTC)
Perhaps it would help if I gave you the rest of the information I know so far... The ratio of the quartisma is 117440512/117406179. If Inthar is correct, the quartisma is a rank-4 comma. I do know that 159edo tempers out this comma based on patent vals. Similarly, between Inthar and I, we have confirmed that 22edo, 24edo, 44edo, 46edo, 66edo, 68edo, 70edo, 88edo, and 90edo by examining and or calculating their patent vals. The quartisma is the difference between five 33/32 quartertones and a 7/6 subminor third, as well as the difference between six 33/32 quartertones and a 77/64 minor third. --Aura (talk) 06:35, 7 September 2020 (UTC)
The fact that patent val + patent val isn't necessarily a patent val might explain why 94edo doesn't work. IlL (talk) 13:50, 7 September 2020 (UTC)
The JI subgroup is rank (dimension) 4, and the temperament that tempers out the quartisma from JI (and only the quartisma or its multiples) is rank 3. IlL (talk) 13:54, 7 September 2020 (UTC)
Okay, I now have the val for 159edo up to the 19-limit. It is 159 252 369 446 550 588 650 675]. Using this, and checking against the quartisma's monzo, which, as Flora mentioned, is [24 -6 0 1 -5. I did the calculations as per the procedure documented on monzo and got "0" as my result- this is hard confirmation that 159edo tempers out the quartisma. Now we need to do the same thing for other EDOs... --Aura (talk) 14:27, 7 September 2020 (UTC)
Aura, I found the problem with 94edo: 3*<24 38 67 83] + <22 35 62 76] = <94 149 263 325] is not the patent val of 94edo which is <94 149 264 325] (I left out prime 5). You have to be careful when adding up edos to get other edos of the same temperament. The val resulting from adding two vals a and b will temper out all commas of a&b temperament (i.e. all commas tempered out by both a and b), but is not guaranteed to be patent. IlL (talk) 14:29, 7 September 2020 (UTC)
That does explain a lot. Do you think we ought to make pages on both the quartisma and its temperament family? --Aura (talk) 14:47, 7 September 2020 (UTC)

Hey Inthar, remember how we we initially included 46edo in the list of quartismic EDOs? Well, I did the math about a half an , and 46edo failed the monzo test- instead of getting a result of "0" like you would if 46edo tempered out the quartisma, I ended up getting a result of "-1"... and Flora's computer calculations didn't catch this until now... Looks like we all screwed up on this one. --Aura (talk) 21:17, 8 September 2020 (UTC)

Funny... I get 0 from that calculation (The vector on the left is 46edo's patent val, the one on the right is the monzo.) IlL (talk) 22:14, 8 September 2020 (UTC)
Ah, I see... I was looking at the wrong number of steps for the harmonic seventh on the chart to make my calculation. After doing the calculation again, I got "0". I'll fix the page then. While we're at this, do you mind running the calculation for 44edo? I want to make sure I didn't mess up the numbers for that one... --Aura (talk) 00:44, 9 September 2020 (UTC)
Oh, and thanks for providing me with the link. I think I'll go ahead and use the site to perform my calculations on various EDOs, but still, after that mistake on my part, I don't think we can be too careful. --Aura (talk) 00:55, 9 September 2020 (UTC)
44edo does temper it out, but it's contorted 22edo in the subgroup (the patent val is 44, 70, 124, 152] which is twice 22edo's patent val) so it's redundant. IlL (talk) 16:55, 9 September 2020 (UTC)
Okay, I didn't know that 44edo was contorted, as the entry on the wiki didn't say so. However, I don't think EDOs that are multiples of other established EDOs are necessarily redundant examples as because of their additional notes, they may yet offer additional possibilities. --Aura (talk) 17:12, 9 September 2020 (UTC)
Right now, I'm interested in the data on a series of four consecutive EDOs that temper out the quartisma- 89edo, 90edo, 91edo, and 92edo. If you know anything about the EDOs in this group, I'd like to hear it. --Aura (talk) 17:15, 9 September 2020 (UTC)
I'm sorry to say that I do not. IlL (talk) 19:05, 9 September 2020 (UTC)
Ah. I'm also interested in how 159edo handles the subgroup, for even though 159edo tempers out the quartisma mathematically, the fact that it also tempers out the keenanisma means that the best approximation of 49/32 is disconnected from the best approximation of 7/4. However, the best approximation of 49/32 can be reached in the 11-limit by means of 135/88, which, in JI, differs from 49/32 by 540/539- the swetisma. What do you make of this? --Aura (talk) 19:16, 9 September 2020 (UTC)
Dunno. The inconsistency could result in two different approximations or flavors for 7/4 and you could use different progressions to reach them. Otherwise... I don't think it's very easy to musically use the 49th harmonic qua the 49th harmonic (not thinking of it as 7*7) in the first place, unless you do what Zhea does and think of the 49th harmonic over a harmonic other than a power of two, say 37 or 46. If there's a prime (under 49) which 159edo approximates especially well, then a subset of 159edo could be used to approximate a primodal scale... IlL (talk) 00:25, 10 September 2020 (UTC)
To be frank, I've had a similar problem with 94edo in the 5-limit where the tempering of the marvel comma resulted in the best approximation of 25th harmonic being disconnected from the best approximation of the 5th harmonic, which, in some ways, works out worse for me in light of the fact that the 5-limit is kind of the bread and butter of most of my harmonic progressions and the 25th harmonic is useful in augmented chords. I know that one thing I'm doing as I'm mapping out the intervals of 159edo- especially now- is omitting the inconsistent intervals and their multiples, which enables me to effectively map out which portions of the harmonic lattice are actually usable in 159edo. So far, only a single instance of a 7 in the prime factorization in the numerator or denominator of any given ratio can work without putting the relative error above 50%. However, since 159edo is stated to be an excellent tuning for the guiron and tritikleismic temperaments- which are basically members of a 2.3.7 subgroup- even in light of the issues with the 49th harmonic, I have to wonder if that means that 159edo could also be considered a good candidate for a quartismic temperament. --Aura (talk) 01:04, 10 September 2020 (UTC)

Hey, Inthar, I'm thinking of the name "Altierran" for a quartismic temperament that also tempers out 10985/10976. Do you like this concept? --Aura (talk) 16:56, 10 September 2020 (UTC)

Another possibility is that the name "Altierran" could also refer to a quartismic temperament that tempers out 32805/32768... In fact, I think I like this concept better... We can choose another name for quartismic temperaments that also temper out 10985/10976. --Aura (talk) 19:10, 10 September 2020 (UTC)

Okay. IlL (talk) 20:47, 10 September 2020 (UTC)

Okay Inthar, I realize you worked hard to put data onto the page about quartismic temperaments. Unfortunately, since I found this site this site things have gotten very complicated very quickly. I now feel that there is a serious need for us to go through and improve definitions, get more complete data and stuff such. All I know is that the Altierran temperaments are a specific type of quartismic temperament that tempers out the schisma as well as the quartisma, however, judging from what the site in question says, doing this involves at minimum tempering out two other commas- 161280/161051 and 10333575/10307264- as this page shows. Judging from this, it looks like the Altierran temperaments require the tempering of at least all four of these commas... I've also seen this rank-4 temperament which tempers out nothing but the quartisma. So, in light of all this new info, how shall we proceed? --Aura (talk) 03:12, 11 September 2020 (UTC)

For the record, I'm thinking that the data you put on the page before can be re-entered once we've gotten things straightened out. --Aura (talk) 03:19, 11 September 2020 (UTC)

I'm very sorry, but this whole area isn't something I really have time for. We can resume this discussion later. IlL (talk) 04:13, 11 September 2020 (UTC)
Okay then. Let me know when we can resume the discussion. --Aura (talk) 04:21, 11 September 2020 (UTC)

Music Theory Review

Hello Inthar, it's been a while. I've recently began posting all of my stuff here on the wiki and trying to go through the underpinnings of my own music theory. Since I see you have recently stated on your user page that microtonal music theory is one of your main interests, I figured you might like to review what I have written down on tonality, consonance, and diatonic scales... I'd like to hear your thoughts on all this. --Aura (talk) 18:02, 21 October 2020 (UTC)

Harmonize categories of interval pages

Hi IlL, we are interested in your opinion about Categories of interval pages, thanks in advance for taking the time. --Xenwolf (talk) 21:20, 8 November 2020 (UTC)

Template:Infobox ET

Hi Inthar, you built Template:Infobox ET onbviously without noticing that we already started a project Xenharmonic Wiki:Things to do#Infobox for EDO pages discussed on Xenharmonic Wiki talk:Things to do#Infobox for EDO pages. It would be good if you take part in the discussion here: Template talk:Infobox ET. Thanks --Xenwolf (talk) 09:08, 3 December 2020 (UTC)

File:13edo 1MC.mp3

File:13edo 1MC.mp3 is quite impressive. Sadly it has not catchy name. How did you achieve the quite natural timbres? --Xenwolf (talk) 23:51, 3 December 2020 (UTC)

I've always been bad at naming my pieces. :) For the timbre I just found violin and cello soundfonts which I felt were satisfactory, (though getting the nuances I really wanted would have been even more time-consuming.) Is it ok to leave it up in the infobox for now? IlL (talk) 01:01, 4 December 2020 (UTC)
You mean in the infobox in 13edo? Sure, for now (I'll re-uncomment it soon), I find it an interesting by-product that your initiative has sparked the idea of a composition competition. --Xenwolf (talk) 07:56, 4 December 2020 (UTC)

A Moment of Respite

Is the File:A Moment of Respite.mp3 the same as the A Moment Of Respite (WIP) on SoundCloud? I'm impressed of the harmony, the semblance of normality in such a strange EDO! Hoping not to offend you: your composition reminds me a little of Tchaikovsky; it is amazing with what elegance the voices "sneak around" each other. Please share more of that! --Xenwolf (talk) 20:55, 5 December 2020 (UTC) PS: the Category:Edo was renamed into Category:Equal divisions of the octave; in the now outdated category are only two pages, one is in your user space. Maybe this branch is abandoned meanwhile? --Xenwolf (talk) 20:55, 5 December 2020 (UTC)

Oh, yeah, before I forget: the name A Moment of Respite contradicts your claim concerning "13edo 1MC". --Xenwolf (talk) 21:01, 5 December 2020 (UTC)
Thanks, I'm glad that you enjoyed the piece. I don't think 13edo's actually that strange anymore, but maybe I've only used less weird ways of using it. I moved my 13edo draft to the right category. IlL (talk) 22:14, 5 December 2020 (UTC)

A Near-Perfect Approximation of 159edo

Hey Inthar, I recently finished a piece called "Space Tour" in a near-perfect approximation of 159edo- "Space Tour". I know we haven't talked in a while, but since you seem to be interested in microtonal music theory, I'd like to hear how you attempt to analyze this piece. --Aura (talk) 04:58, 6 December 2020 (UTC)

Hi! On first listen it's interesting to have the basic colors of those different edos side by side, interesting how 159 isn't too bad even tho intervals sometimes are noticeably different. IlL (talk) 06:38, 6 December 2020 (UTC)
So, how would you describe the noticeable differences? Do those differences make some of the retempered EDOs sound more expressive in some ways? I have to admit that whenever a step of a smaller EDO fell halfway between the steps of 159edo, I picked the approximation that best fit the JI ratio and or the function of the specific note. One example is how 200 cents is approximated to 27\159 due to both intervals approximating 9/8, and another example is how the flat-five tritones that pervade much of "Space Tour" are always approximated by steps of 159edo that fall on the far side of 600 cents. --Aura (talk) 16:22, 6 December 2020 (UTC)
Oh, one more thing- approximations of the 40/27 grave fifth are deliberately used in the chord built on the sixth scale degree of G major in the final section- reflecting a characteristic of my microtonal compositions using familiar keys. This is because the grave fifth actually brings out the function of a deceptive cadence, and because it creates subtle tension that is best followed up by either an increase in tension with a either a tritone or a 16/11 minor fifth, or else, a decrease in tension with a regular perfect fifth. --Aura (talk) 16:22, 6 December 2020 (UTC)
Interesting. I've tried various diatonic tunings to make some modes have different degrees of consonances. I think 17edo and 39edo are great for Locrian and other minor modes (or 46edo if you need the major third to be less grating). Those tunings make the diminished fifth and minor seventh sound more restful and consonant and major thirds more dissonant; the small steps are also nice. A side effect is that secondary dominants on a major key tonicizes that major key a bit less, so it retains that element of familiarity while also being dynamic, which is useful for writing in those modes. It's the opposite for Lydian, for which 26edo is ideal for consonance. IlL (talk) 17:31, 6 December 2020 (UTC)
Actually, Space Tour uses Locrian mode in in the following portions of the song:
  • 0:14-1:12
  • 7:30-8:30
  • 14:52-17:04
Furthermore, my approach to Locrian is a bit different, as detailed on my relevant comment on the Space Tour page on reddit, I even give examples of how Locrian chord progressions operate, and it seems the flat-five best carries out the function I mention in that comment when it's set to something in the vicinity of 64/45. What I didn't mention on reddit is that Locrian is even capable of circle progressions with just a fixed set of pitches if you play your cards right. --Aura (talk) 17:41, 6 December 2020 (UTC)

Composer Name

For pieces, normally the composers are referenced by real name. I added you user name to Locrian Suite Gigue. What do you think? I mean, a short neutral page about you as person with links to SoundCloud - would you be okay with that? --Xenwolf (talk) 07:32, 6 December 2020 (UTC)

Yeah, that's fine. IlL (talk) 07:44, 6 December 2020 (UTC)
I don't fully understand, so I sent you a wiki email. --Xenwolf (talk) 09:52, 6 December 2020 (UTC)


I have to admit I had no reason to suspect that you were also on discord. I'm DaffodilAura218#7768 there. --Aura (talk) 18:41, 8 December 2020 (UTC)

It seems Arseniiv is also on Discord, so perhaps we can get the server set up when Arseniiv has time. --Aura (talk) 18:45, 8 December 2020 (UTC)

Okay, so SAKryukov has created the Microtonal Server on Discord. It's currently not very active, but I figured I'd let you know so that you can join. --Aura (talk) 06:58, 21 January 2021 (UTC)

Tuning by ear

Thanks for bringing that up. In my opinion these section are a great addition. I like to see more of practical help in the wiki (and less content that requires higher math skills to understand). --Xenwolf (talk) 11:15, 10 December 2020 (UTC)


Your File:Locrian Suite Gavotte.mp3 is fantastic! Congratulations! --Xenwolf (talk) 23:16, 18 December 2020 (UTC)

Well, the very end is ... well, ... --Xenwolf (talk) 23:17, 18 December 2020 (UTC)
Is the new ending better? Inthar (talk) 23:57, 18 December 2020 (UTC)
I think it's an articulation problem, I'd try without the pause before the very last chord (or at least with making it much shorter). --Xenwolf (talk) 00:13, 19 December 2020 (UTC)
Thanks. Inthar (talk) 01:48, 19 December 2020 (UTC)
Much better. I believe it could be even better but I have to figure out how ... --Xenwolf (talk) 12:00, 19 December 2020 (UTC)

Sarabande versions cleanup

In File:Locrian Suite Sarabande Score.pdf, which revisions should be deleted? All but the most recent one? --Xenwolf (talk) 12:22, 30 December 2020 (UTC)

Yes, thanks. Inthar (talk) 14:19, 30 December 2020 (UTC)

Done. --Xenwolf (talk) 15:10, 30 December 2020 (UTC)

Neji question

Hi Inthar, can you please take a look at User talk:IlL/Building JI scales #Neji? Thanks --Xenwolf (talk) 14:35, 8 January 2021 (UTC)

Reduce comma tables on EDO pages

Please have a look at Xenharmonic Wiki: Things to do #Comma tables in EDO_pages. Thanks --Xenwolf (talk) 09:09, 11 January 2021 (UTC)

Introduction to RTT

Hi Inthar, I really like what I see so far on User:IlL/Introduction to RTT. Just one question: Does RTT stand for Regular Temperament Terminology? --Xenwolf (talk) 06:41, 12 January 2021 (UTC)

Thanks, any feedback on my roadmap is welcome. The initialism stands for Regular Temperament Theory. Inthar (talk) 07:29, 12 January 2021 (UTC)
A great, even better! This is very exciting news. I really hope you get this done some day. I'll be your first reader: I regularly feel stopped by math terminology (especially if silently assumed as precondition). --Xenwolf (talk) 09:04, 12 January 2021 (UTC)
I'd like to suggest another title: "Regular temperaments in practice" (in short RTP). --Xenwolf (talk) 10:33, 17 January 2021 (UTC)

Telicity and the Classification of EDOs as Subgroup Temperaments

Hey, Inthar, I've been trying to work on a concept called telicity, and I'm starting to think that this concept is something that may be useful as a parameter for classifying EDOs as subgroup temperaments, as well as for evaluating concepts. Of course, there's more to it, and the concept of telicity itself still needs to have all the kinks ironed out, but still. --Aura (talk) 16:17, 20 January 2021 (UTC)

The reason I'm bringing up my concept of telicity is that given what your proposals concerning the definitions of "consistency", I think we can work together to refine our concepts. --Aura (talk) 18:23, 20 January 2021 (UTC)

Do you think we have time to talk this over? --Aura (talk) 18:41, 20 January 2021 (UTC)

I've been growing more skeptical of the idea of regular temperaments and limiting oneself to prime-limits or subgroups over time, but maybe subgroups or telicity could still be useful if you're accurate enough. I'm also skeptical of why one would limit oneself to a chain of 11/8's when a chain of 12/11's say, is also valid, or when you could take a less "straight" path in the lattice, so I don't really see the use of telicity for me personally I'd be interested in hearing how you would use telicity musically (though my replies might be more intermittent). Inthar (talk) 07:14, 21 January 2021 (UTC)
I'll admit, part of the reason I'm limiting myself to chains of prime intervals at the moment is because judging from my own exploration of Alpharabian tuning, pure prime chains seem to have a way of acting as the borders for the tuning space of the various combinations of the primes in question. When two primes come together via telicity, the tuning space for combinations of those two primes seems to be finite, and thus, more manageable- on one corner is the unison, and on the other corner is the place where the two primes come together. Aside from this, the other part of the reason I'm limiting myself to pure prime chains is that in some respects, I haven't gotten around to those combinations yet- after all, I need to start with the basics of the concept first.
It is true that there are less-straight paths available in the lattice, but when you want to return to the initial Tonic, as I myself often do, those less-straight paths are often more difficult to navigate, especially when you're dealing with higher primes in higher EDOs- I know this from experience, as I really like working in 159edo. Telicity gives easier-to-navigate paths for modulation, and sometimes, those paths are quite unexpected. For example, suppose you want to modulate down by a 32/27 minor third from your initial Tonic, but you know that the most expected way to get there is by chains of 3/2 fifths- well, it turns out that the nexus comma, which is unnoticeable and thus has a pretty high telicity range, joins the 11/8 prime chain together with the 3/2 prime chain at just that particular point, thus, going up by a chain of six 11/8 intervals allows you to reach the note at 32/27 below your original tonic by unexpected means. From there, you can simply modulate by a chain of perfect 3/2 fifths back to your original Tonic.
Does this all make sense? --Aura (talk) 19:17, 21 January 2021 (UTC)


Hello Inthar,
To understand what I am talking about, please first have a look at the history of "5L 3s".

I would like to ask you to reconsider your editing style. To do this, it might help to think of saving a change as publishing (which it actually is) rather than as a step to save an intermediate state. There are people (like me) who review every single edit on this wiki, for whom such mass micro-edits are a real burden. There is also the preview function to make sure that something technically new is reflected as intended on the finished page. Personally, it always helps me a lot to think about how I would describe what I plan to do, then make the change, and then review the change(s) to write a summary that comprehensively describes my action(s). This leads (mostly, except for trivial formal adjustments, ... and apart from occasional accidents) to a frequency of changes that is acceptable to my peers.

Please do not be angry with me about my criticism! And if there is a compelling reason for you to work this way, please let me know so I can understand. Thanks in advance! --Xenwolf (talk) 08:39, 2 February 2021 (UTC)

Hello. I've been stuck on editing on a mobile phone for the past couple days, until I get my hotspot working. I'm sorry that I normally have the tendency you described and this situation made my usual editing style a lot worse, and this will be fixed soon. Thanks for understanding. Inthar (talk) 08:53, 2 February 2021 (UTC)
I see, thanks for your explanations. Good luck fixing the hotspot! --Xenwolf (talk) 09:07, 2 February 2021 (UTC)


Hi Inthar, I have a somewhat uncomfortable feeling about results like these, what do you think? And, BTW: you also fell back into the #microediting habit, but there are also others who do this. Of course it's valuable to review what we write, but it also helps to take some time for this. Also the Preview function can help to avoid too much intermediate versions. A great help are the access keys E, P, V, S, (which in Firefox on Windows translates to Alt+Shift+E etc.):

View changes

My edit cycle looks like this (in regex) E(P|V)+S, maybe you fall in love with it too? --Xenwolf (talk) 08:22, 18 March 2021 (UTC)

Lygic and obsidic were my names but I now prefer semifourth and semitwelfth. And yes, I will try to get into this edit cycle. Inthar (talk) 16:26, 18 March 2021 (UTC)
I see. And thanks for your understanding. :-) --Xenwolf (talk) 17:16, 18 March 2021 (UTC)

On the semiwolf

I noticed you created this page for a fifth equivalent MOS pattern. I was just doing some stuff for 8EDF, preparing to publish (a framework here)

Specifically, I'm proposing naming the modes of this scale after the major uranian moons (since there are 5 of them), and it would make sense to then call the pentatonic MOS itself uranian rather than semiwolf.

And I was thinking of reusing semiwolf by helenising it into hemilycan, as a temperament name in the 7 and 11 limit. I suppose, gencom [3/2 7/6; 245/243 (2401/2376)], and maybe a more complex hemihendrix (half a hendrix fourth) gencom [3/2 7/6; 343/342 2401/2376]

What do you think? Ayceman (talk) 20:17, 22 April 2021 (UTC)

Hi. The bulk of the semiwolf page was written by User:SupahstarSaga. I simply created the page by adding the MOS infobox. The temperament names sound good, but Supahstar Saga and I found that there are two 11-limit extensions, one that equates LL to 11/9 (thus tempering out 100/99) and one that equates sLs to 11/9 (thus tempering out 441/440). Saga thinks LL = 11/9 is better because he considers 4:10:11 more important than 4:7:11 (and 8edf is special because it's the unique tuning that has both 4:7:11 and 4:10:11). Saga suggests semiwolf = the MOS and semilupine and hemilycan for the two 11-limit extensions (100/99 and 441/440 respectively). Inthar (talk) 02:03, 23 April 2021 (UTC)
The main reason for going with uranian for the MOS specifically was to match it up with the mode names that I came up with a while ago for this pentatonic scale. It also to divorces it from any temperament interpretations (it's not half a wolf fourth in the supersoft/hard range), but I do like how semiwolf sounds.
I was only originally considering commas made by stacking the generator itself. Anyway, the base 7-limit temperament needs a name as well, so I have a few options:
1. MOS - Uranian (with original mode names); 7-limit temperament - semiwolf; 11-limit temperament #1 - semilupine; 11-limit temperament #2 - hemilycan
2. MOS - Semiwolf (with new mode names based on mythological wolves); 7-limit temperament - 7-limit semilupine; 11-limit temperament #1 - 11-limit semilupine; 11-limit temperament #2 - hemilycan
+ the 19-limit subgroup temperament hemihendrix
EDIT: For semiwolf as MOS, I've come up with these mode names: Skollic > Fenriric > Asenic > Garmic > Hatic
Any preferences? Ayceman (talk) 21:16, 23 April 2021 (UTC)
Hi, after a discussion with SupahstarSaga I think 1 is better. It gives every temperament a different name, and it makes more sense for extensions to be Latin and Greek calques of a basic temperament name rather than a MOS name. Inthar (talk) 18:41, 1 May 2021 (UTC)

Double redirects to empty pages

Hi Inthar,
Looking on Special:DoubleRedirects, we see a number of redirects that ultimately lead to the empty pages User:Inthar/Template:RTT modularization and User:Inthar/13edo). Should the pages be deleted (with the redirects)? --Xenwolf (talk) 11:38, 5 June 2021 (UTC)

Yes, you should delete these. Inthar (talk) 16:05, 5 June 2021 (UTC)
Done. (there is template:delete for requesting a delete) --Xenwolf (talk) 21:02, 5 June 2021 (UTC)


Hi again Inthar,
I saw these 3 pages in Special:LonelyPages:

The wiki pages are orphaned, you can see from where linking to them is useful. Maybe you'd rather move them to your user namespace anyway? There is no built-in feature to link subpages, in fact, subpages don't exist in the article namespace (the option has been kept disabled to allow / in page titles).
--Xenwolf (talk) 21:45, 5 June 2021 (UTC)

I linked the edo approach pages from the main edo articles. Please delete the primodal page. Inthar (talk) 22:09, 5 June 2021 (UTC)
Thanks for the quick response. --Xenwolf (talk) 06:19, 7 June 2021 (UTC)


Hi Inthar,
Do you know that there is a category:user on SoundCloud?
BTW: Do you think the delete template now works correctly? (that is why I have not yet deleted the page) --Xenwolf (talk) 11:29, 4 July 2021 (UTC)

I deleted my soundcloud. Yes, the template works correctly now. Inthar (talk) 15:58, 4 July 2021 (UTC)

Broken redirects

Hi Inthar, there are some broken redirects in your older user namespace that seem to point to now deleted pages, can these be deleted as well? --Xenwolf (talk) 19:50, 1 March 2022 (UTC)

Of course, go ahead. Inthar (talk) 02:15, 3 March 2022 (UTC)

Oneirotonic Question

What would you recommend as the basic consonant chords for 31edo oneirotonic, delta rational or otherwise? The 0-387-658 doesn’t have the same cohesive sound as in 13, but at least to my ears, 0-271-735-929 still sounds reasonable. KingHyperio (talk) 00:48, 28 June 2022 (UTC)

I haven't used 31edo oneiro much, but I agree that 0-271-735-929 is still a good minor chord (in fact imo it sounds good anywhere from 21edo to 18edo). For 0-387-658 you could try 0-387-929 or 0-387-929-194 instead; maybe the 658 is too spicy for you? One interesting chord with 658 is 0-465-658 which is close to 13:17:19; 0-194-658 is also an alright sus chord, and when the tonic consonant chord has the sharp fifth (as in 0-271-735-929) the flat fifth on this less resolved chord can be used to voice lead to it. Though this is by no means an exhaustive list, hope this helps! Inthar (talk) 01:02, 29 June 2022 (UTC)

Thanks for your help! Love your work with oneiro, honestly adds a really interesting new way to use 31 that I hadn’t known much about. KingHyperio (talk) 01:49, 29 June 2022 (UTC)