# User talk:IlL

## Contents

## 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)

## 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:

{{Special:PrefixIndex/{{FULLPAGENAME}}/}}

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

- Now I found an (in my opinion) better way to use this function:
`{{Special:Prefixindex|prefix={{FULLPAGENAME}}/|hideredirects=1|stripprefix=1}}`

- 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)

## 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)

- 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 2.3.7.11 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 2.3.7.11 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 2.3.7.11 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)

- 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 2.3.7.11 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)

- 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)

- 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

- 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)

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)

- 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)

- Ah. I'm also interested in how 159edo handles the 2.3.7.11 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)