Talk:159edo/Notation: Difference between revisions

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== My Second Idea for a Notation System ==

Okay, after talking with Sam, I now think ~~while~~ we need to make another notation system. Truth be told, I've been trying to make a notation system that is accessible for people with a background in [[24edo]] like myself this whole time, and this is the main reason for my notation systems being as complicated as they are. Nevertheless, I'm hoping to make things as intuitive as possible as well. I'm thinking that this new system should keep the traditional symbols for naturals, sharps, flats, double sharps and double flats, and that we need to make two different versions of each of the quartertone accidentals to reflect how the rastma is not tempered out, and that some of these quartertone accidentals can only be lowered, while the others can only be raised.

Okay, after talking with Sam, I now think we need to make another notation system. Truth be told, I've been trying to make a notation system that is accessible for people with a background in [[24edo]] like myself this whole time, and this is the main reason for my notation systems being as complicated as they are. Nevertheless, I'm hoping to make things as intuitive as possible as well. I'm thinking that this new system should keep the traditional symbols for naturals, sharps, flats, double sharps and double flats, and that we need to make two different versions of each of the quartertone accidentals to reflect how the rastma is not tempered out, and that some of these quartertone accidentals can only be lowered, while the others can only be raised.

One set of quartertone accidentals has the two broad cross strokes of the traditional demisharp accidental set closer together than those of the sharp accidental while keeping the same traditional "demiflat" accidental, while the "sesquisharp" accidental and the "sesquiflat" accidental in this set are similarly redesigned, and modify the base tone by an interval consisting of an apotome and a 33/32 quartertone. The second set of quartertone accidentals are also based on the traditional quartertone accidentals, and the second "demisharp" and "sesquisharp" accidentals has the two broad cross strokes set further apart than those of the sharp accidental, while the corresponding "demiflat" and "sesquiflat" accidentals each have a narrow cross stroke on their stems- the "demisharp" and "demiflat" accidentals in this set modify the base tone by a 709/704 interval, while the "sesquisharp" and "sesquiflat" accidentals in this set modify the base tone by an interval consisting of an apotome and a 709/704 interval. Furthermore, since the rastma itself is a potential JI basis for the single step of 159edo, and since combined symbols need to be deciphered, I think we need to make two new sets of symbols- one set for modification by one or two syntonic commas based on the combining arrows from Helmholtz-Ellis notation, and another pair of symbols to represent modification by a rastma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:46, 10 October 2020 (UTC)

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:: At present, I'm thinking there should probably be two- one to hold both the classic and quartertone accidentals, and one to hold accidentals which modify by combinations of the syntonic comma and the rastma. With the syntonic comma modifiers being simultaneously separated from the classic and quartertone accidentals and combined with the rastmic modifiers to form single glyphs, that renders a total of 25 different glyphs as opposed to the 45 in the first system. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:13, 13 October 2020 (UTC)

::: So the glyphs for the first box are already there? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:17, 13 October 2020 (UTC)

:::: A number of them are indeed already there- the natural, the sharp, the flat, the double sharp and the double flat. We'd need to remake the quartertone accidentals as per my descriptions of them during the course of this conversation, with the end result being that instead of there being nine main accidentals in the first box, there would be thirteen accidentals total. Furthermore, we can derive at least four of the accidentals for the second box directly from the syntonic arrows of HEJI- albeit they need to be larger- so that's pretty simple. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:34, 13 October 2020 (UTC)

::::: Why exactly do we need different quartertone accidentals? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:57, 13 October 2020 (UTC)

:::::: The problem, according to what Kite has said, is that these quartertone accidentals by themselves don't add up intuitively- for instance, two modifications by [[File:HeQu1.svg|48x48px]] don't add up to a modification by [[File:Heji25.svg|48x48px]] but rather fall short of [[File:Heji25.svg|48x48px]] by a rastma. Don't get me wrong, we can keep all four of the quartertone accidentals, but we still need to create four more on account of the rastma not being tempered out- that is, we need a distinction between "wide" and "narrow" quartertones.

::::::: If I understand you correctly, for an EDO that subdivides a the [[apotome]] into 15 equal-sized parts, we need "quartertones" that are 7/15 of an aptome but with symbols can be distinguished from 50-cent symbols not being used here? Isn't ''this'' the problem: that you wish to include quartertone symbols to ease adapting the system to people familiar with [[24edo]]? But if this is the case, wouldn't it be better to tell them "the truth" about quartertones: that they aren't actually quarter tones? Remember: the semitones in this system aren't 100cents either but we decided to use the exact symbols of [[12edo]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:27, 13 October 2020 (UTC)

:::::::: I'm perfectly aware of the fact that two "semitones" add up to more than a "whole tone" in this system- the same problem on a different level, as they are ''still'' called "semitones" in spite of this- but we seem to have a way of getting around that in this and other systems by means of the double sharp and double flat accidentals... I guess you could say that I now want to come up with a similar solution for these "quartertones". Alternatively, we should not only mention that the "quartertones" aren't exactly "quartertones", but also that the "semitones" aren't exactly "semitones"... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:40, 13 October 2020 (UTC)

:::::::: Either way you look at it, and regardless of the option we choose, 33/32 is to the 11-limit what the apotome is to the 3-limit in terms of its importance for navigation. It is also true that I have now decided simply to include quartertone symbols to ease adapting the system to people familiar with 24edo. With this in mind, and in light of the fact that the precursor to the prefix "semi-" apparently had the meaning of "half" since [https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-European/s%C4%93mi before the days of Latin], what do you propose we do? (comment posted and heavily edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:28, 13 October 2020 (UTC))

:::::: Those quartertone symbols should only be used in systems that tempers out 243/242, which guarantees the split of apotome into two. Whereas 159edo (or "15eda", to be precise) is essentially different. However, the solution is clearly present: simply use [[HEJI]] symbols [[File:heji41.svg|48x48px]] [[File:heji40.svg|48x48px]] for 33/32 will suffice for all undecimal work. If another quartertone is ever needed, it may represent 1053/1024 or 27/26 but never to mess with 11-limit anymore. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:02, 14 October 2020 (UTC)

::::::: Flora, I'm afraid it's not that simple, as [[File:heji40.svg|48x48px]] and [[File:HeQd1.svg|48x48px]] are identical, resulting in confusion, while [[File:heji41.svg|48x48px]] does not suggest the close connection that exists between 33/32 and 1\24 to microtonalists who come from a 24edo background. Furthermore, what do you do when you take something already modified by the apotome and further modify it by 33/32? This is why I was suggesting new quartertone accidentals in the first place. I admit I'm not sure just what the solution is right now, but I do want to get this issue dealt with. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:50, 14 October 2020 (UTC)

Here's an idea of what I was talking about for this idea originally:

[[File:Possible_Quartertone_Accidentals.png]]

I hope this idea make sense... In rastmic systems only the set of quartertone accidentals in the middle are used, while when the rastma is not tempered out, a contrast exists between the top set and the bottom set. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 14 October 2020 (UTC)

In response to your comment [[User_talk:Xenwolf#Another_Comma|here]], Xenwolf, I'm glad you think this picture is clear. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:26, 14 October 2020 (UTC)

: Saw all this and thought I'd mention that the idea that there is only one type of semitone is a modern idea arising directly from 12-edo. In Pythagorean tunings, there are two types of semitone. The diatonic semitone is a minor 2nd 256/243, and the chromatic semitone is the augmented unison 2187/2048. The two add up to exactly a whole tone 9/8. The two semitones are obviously notated completely differently, since one is a 2nd and one isn't. Meantone tunings draw the same distinction, but of course the semitones are tuned differently.

: In 5-limit JI, both semitones can be altered by 81/80, making even more semitones, e.g. 135/128, 25/24, 16/15 and 27/25. Each of these is either diatonic or chromatic, and corresponding pairs add up to a whole tone.

: Once you make the distinction between chromatic and diatonic semitones, it becomes clear that the sharp sign that represents the chromatic semitone was never meant to denote exactly half a whole tone. It represents a whole tone minus a minor 2nd.

: BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.

:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are significant (which, after posting the initial version of this comment, I have confirmed through further investigation and [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|documented my findings on the matter]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval, as 33/32 and 8192/8019 add up to 256/243... However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma. As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]]. This on its face means that there are already multiple types of parachromatic quartertones. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)

:: If I take the logic of what I said in the previous comment, that means that a stack of two 33/32 quartertones, plus 8192/8019 plus 729/704 is a full 9/8 whole tone- that means that four quartertones equals a whole tone... If, on the other hand, the rastma is taken from 729/704 and added to 8192/8019, the result is a third 33/32 quartertone plus [[4096/3993]]- another paradiatonic quartertone. This would actually make the addition much more straightforward, as a stack of three 33/32 quartertones plus 4096/3993 is also 9/8. So yes, four quartertones *do* in fact add up to a whole tone. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 15 October 2020 (UTC)

::: Here is my draft of quartertone accidentals (in staff context):

::: [[File:Quarter-accidentals-narrow-rastmic-wide.png|300px]]

:::# top line: narrow

:::# middle line: rastmic

:::# bottom line: wide

::: Hope this helps. ---[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:02, 15 October 2020 (UTC)

:::: It does, but I should point out that the vertical lines on all three demisharp accidentals are actually supposed to be the same. The same thing is true of the vertical lines on all three sesquisharp accidentals, as well as the the stems of the various demiflat and sesquiflat accidentals. However, that's not to say that the vertical lines in the demisharp and sesquisharp accidentals all share a length for their vertical lines, however. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:06, 15 October 2020 (UTC)

:::: Still, despite the flaws, I actually like your work. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:11, 15 October 2020 (UTC)

::::: Glad you like it! It's actually just cut/copy & paste work, even if done in Inkscape. I was interested in the appearance within staff context and indeed: it seems to work! Also the horizontal and vertical positioning is done by hand and naked eye. A clean design would take a bit longer. BTW also the other glyphs I made are not really clean. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:20, 15 October 2020 (UTC)

:::::: Ah. That makes sense. In that light, this is actually a good rough draft! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 15 October 2020 (UTC)

: This proposal is basically equivalent to having one accidental for half-apotome and another for 33/32, so, yes, I see it works for most equal temperaments. Better if they appear more distinct glyph-wise. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:15, 16 October 2020 (UTC)

:: Thanks for your thoughts, Flora. Besides the minor flaws (lenghts of verticals) the sharps seem okay to me, but the flats are harder. I'm not sure if sticking with the b-shape isn't the fundamental problem here. But you are experienced with fonts maybe you are the right person for the details. Maybe having three lines is for 4 accidentals each is not ideal. I did a tiny improvement right now to set the single accidental glyphs apart from each other (maybe a browser refresh will be needed). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:50, 16 October 2020 (UTC)

::: For the record, if there are issues with the flat accidentals, I'd have to say that the thickness and angle of the extra strokes on the stems of the narrow and wide flat accidentals is most likely to be the problem. Perhaps those cross strokes ought to be thicker and should set at 60-degree angles from the vertical rather than 45-degree angles. The reason I say this is that those extra strokes are what make the extra flat accidentals stand out from one another, while the shape of the rest of the accidental is what makes them recognizable as flats in the first place. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 16 October 2020 (UTC)

:::: When you said "60-degree angles from the vertical" -- did you mean this [[File:Rect949.png|24x24px]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:44, 16 October 2020 (UTC)

::::: I think that works, but the question is whether or not the distinctions still work in the staff context. Also, the ends of the cross stroke need fixing, but we'll get to that later. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:21, 16 October 2020 (UTC)

::::: If 60-degree angles don't work as well, then we can reinstate the 45-degree angles, but regardless, the cross strokes still need to be thick like you have them now. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:25, 16 October 2020 (UTC)

:::::: Please have a look on the new version of [[:File:Quarter-accidentals-narrow-rastmic-wide.png]] (maybe a browser refresh is needed). I made the corresponding vertical lines the same length, the cross strokes are thicker with ends that reflect the vertical direction again. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:58, 16 October 2020 (UTC)

::::::: I like what I'm seeing. Still, I suppose it wouldn't hurt for the cross strokes to be even thicker, just to make sure people notice them while sight-reading. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:00, 16 October 2020 (UTC)

:::::::: As thick as the sharp's strokes are? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:20, 16 October 2020 (UTC)

::::::::: Yeah, I think that will work as long as the positioning is right. While you're at it, the strokes of all the demisharp and sesquisharp accidentals should also be fixed to have the same angle and thickness as those of the sharp symbol. Again, thank you very much for taking your time to help me do this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:33, 16 October 2020 (UTC)

:::::::::: Done (remember the browser refresh if you don't see any difference) :) the extraction of single glyphs in SVG format will follow tomorrow. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 16 October 2020 (UTC)

::::::::::: Right.

::::::: Oh, and I should have said this earlier, but thank you very much for your help in all of this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:05, 16 October 2020 (UTC)

::: Oh, and I should also point out that for EDOs where the rastma is not tempered out, but the half-apotome also exists, (think [[318edo]]) the rastmic accidentals would not be used because 33/32 takes priority, and... well... because the half-apotome is not formed by tempering out the rastma in such EDOs. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:24, 16 October 2020 (UTC)

Hey, Xenwolf, do you think we have time to work on this some more? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:33, 27 January 2021 (UTC)

I'm asking because if you do, perhaps we can consider adding these accidentals to the mix...

[[File:Possible_159edo_Accidentals.png]]

I hope this makes sense. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:47, 27 January 2021 (UTC)

: Currently I have not the time to work on that. One thing that just struck me: thin horizontal lines will be a problem between staff lines. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:20, 28 January 2021 (UTC)

:: I kind of figured you don't have the time to work on it. Still, I want to get this done at some point. The horizontal lines can be replaced with a slightly thicker curved marking, though I can't help but wonder what that would do... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:44, 28 January 2021 (UTC)

Okay, I updated the picture of the second group of accidentals to change the thin, straight horizontal lines to thicker, more curvy ones. Does this make a difference? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 06:17, 29 January 2021 (UTC)

: I think you should really give [https://inkscape.org/ Inkscape] a try, it's great for this kind of stuff, and there are a lot of tutorials around the web. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:09, 29 January 2021 (UTC)

:: Part of the problem is that it feels like I need constraints and grids and the ability to measure when drawing on the computer. So, do you like the changes I made or no? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:19, 29 January 2021 (UTC)

Okay Xenwolf and Flora, after talking on Discord with other people about possible accidentals, I think I've arrived at a solution for a different set of accidentals for 159edo...

[[File:Quartertone Accidentals.png|1400px]]

[[File:Syntonic Accidentals.png|700px]]

[[File:Rastmic Accidentals.png|700px]]

I hope you two like these. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 14 July 2021 (UTC)

@@ Line 131: / Line 131: @@
 == My Second Idea for a Notation System ==
-Okay, after talking with Sam, I now think while we need to make another notation system.  Truth be told, I've been trying to make a notation system that is accessible for people with a background in [[24edo]] like myself this whole time, and this is the main reason for my notation systems being as complicated as they are.  Nevertheless, I'm hoping to make things as intuitive as possible as well.  I'm thinking that this new system should keep the traditional symbols for naturals, sharps, flats, double sharps and double flats, and that we need to make two different versions of each of the quartertone accidentals to reflect how the rastma is not tempered out, and that some of these quartertone accidentals can only be lowered, while the others can only be raised.
+Okay, after talking with Sam, I now think we need to make another notation system.  Truth be told, I've been trying to make a notation system that is accessible for people with a background in [[24edo]] like myself this whole time, and this is the main reason for my notation systems being as complicated as they are.  Nevertheless, I'm hoping to make things as intuitive as possible as well.  I'm thinking that this new system should keep the traditional symbols for naturals, sharps, flats, double sharps and double flats, and that we need to make two different versions of each of the quartertone accidentals to reflect how the rastma is not tempered out, and that some of these quartertone accidentals can only be lowered, while the others can only be raised.
 One set of quartertone accidentals has the two broad cross strokes of the traditional demisharp accidental set closer together than those of the sharp accidental while keeping the same traditional "demiflat" accidental, while the "sesquisharp" accidental and the "sesquiflat" accidental in this set are similarly redesigned, and modify the base tone by an interval consisting of an apotome and a 33/32 quartertone.  The second set of quartertone accidentals are also based on the traditional quartertone accidentals, and the second "demisharp" and "sesquisharp" accidentals has the two broad cross strokes set further apart than those of the sharp accidental, while the corresponding "demiflat" and "sesquiflat" accidentals each have a narrow cross stroke on their stems- the "demisharp" and "demiflat" accidentals in this set modify the base tone by a 709/704 interval, while the "sesquisharp" and "sesquiflat" accidentals in this set modify the base tone by an interval consisting of an apotome and a 709/704 interval.  Furthermore, since the rastma itself is a potential JI basis for the single step of 159edo, and since combined symbols need to be deciphered, I think we need to make two new sets of symbols- one set for modification by one or two syntonic commas based on the combining arrows from Helmholtz-Ellis notation, and another pair of symbols to represent modification by a rastma. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:46, 10 October 2020 (UTC)
@@ Line 138: / Line 138: @@
 :: At present, I'm thinking there should probably be two- one to hold both the classic and quartertone accidentals, and one to hold accidentals which modify by combinations of the syntonic comma and the rastma.  With the syntonic comma modifiers being simultaneously separated from the classic and quartertone accidentals and combined with the rastmic modifiers to form single glyphs, that renders a total of 25 different glyphs as opposed to the 45 in the first system. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:13, 13 October 2020 (UTC)
+::: So the glyphs for the first box are already there? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:17, 13 October 2020 (UTC)
+:::: A number of them are indeed already there- the natural, the sharp, the flat, the double sharp and the double flat.  We'd need to remake the quartertone accidentals as per my descriptions of them during the course of this conversation, with the end result being that instead of there being nine main accidentals in the first box, there would be thirteen accidentals total.  Furthermore, we can derive at least four of the accidentals for the second box directly from the syntonic arrows of HEJI- albeit they need to be larger- so that's pretty simple. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:34, 13 October 2020 (UTC)
+::::: Why exactly do we need different quartertone accidentals? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:57, 13 October 2020 (UTC)
+::::: IOW: What's wrong with [[File:HeQd3.svg|48x48px]] [[File:HeQd1.svg|48x48px]] [[File:HeQu1.svg|48x48px]] [[File:HeQu3.svg|48x48px]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:59, 13 October 2020 (UTC)
+:::::: The problem, according to what Kite has said, is that these quartertone accidentals by themselves don't add up intuitively- for instance, two modifications by [[File:HeQu1.svg|48x48px]] don't add up to a modification by [[File:Heji25.svg|48x48px]] but rather fall short of [[File:Heji25.svg|48x48px]] by a rastma.  Don't get me wrong, we can keep all four of the quartertone accidentals, but we still need to create four more on account of the rastma not being tempered out- that is, we need a distinction between "wide" and "narrow" quartertones.
+::::::: If I understand you correctly, for an EDO that subdivides a the [[apotome]] into 15 equal-sized parts, we need "quartertones" that are 7/15 of an aptome but with symbols can be distinguished from 50-cent symbols not being used here? Isn't ''this'' the problem: that you wish to include quartertone symbols to ease adapting the system to people familiar with [[24edo]]? But if this is the case, wouldn't it be better to tell them "the truth" about quartertones: that they aren't actually quarter tones? Remember: the semitones in this system aren't 100cents either but we decided to use the exact symbols of [[12edo]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:27, 13 October 2020 (UTC)
+:::::::: I'm perfectly aware of the fact that two "semitones" add up to more than a "whole tone" in this system- the same problem on a different level, as they are ''still'' called "semitones" in spite of this- but we seem to have a way of getting around that in this and other systems by means of the double sharp and double flat accidentals...  I guess you could say that I now want to come up with a similar solution for these "quartertones".  Alternatively, we should not only mention that the "quartertones" aren't exactly "quartertones", but also that the "semitones" aren't exactly "semitones"... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:40, 13 October 2020 (UTC)
+:::::::: Either way you look at it, and regardless of the option we choose, 33/32 is to the 11-limit what the apotome is to the 3-limit in terms of its importance for navigation.  It is also true that I have now decided simply to include quartertone symbols to ease adapting the system to people familiar with 24edo.  With this in mind, and in light of the fact that the precursor to the prefix "semi-" apparently had the meaning of "half" since [https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-European/s%C4%93mi before the days of Latin], what do you propose we do? (comment posted and heavily edited by --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:28, 13 October 2020 (UTC))
+:::::: Those quartertone symbols should only be used in systems that tempers out 243/242, which guarantees the split of apotome into two. Whereas 159edo (or "15eda", to be precise) is essentially different. However, the solution is clearly present: simply use [[HEJI]] symbols [[File:heji41.svg|48x48px]] [[File:heji40.svg|48x48px]] for 33/32 will suffice for all undecimal work. If another quartertone is ever needed, it may represent 1053/1024 or 27/26 but never to mess with 11-limit anymore. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:02, 14 October 2020 (UTC)
+::::::: Flora, I'm afraid it's not that simple, as [[File:heji40.svg|48x48px]] and [[File:HeQd1.svg|48x48px]] are identical, resulting in confusion, while [[File:heji41.svg|48x48px]] does not suggest the close connection that exists between 33/32 and 1\24 to microtonalists who come from a 24edo background.  Furthermore, what do you do when you take something already modified by the apotome and further modify it by 33/32?  This is why I was suggesting new quartertone accidentals in the first place.  I admit I'm not sure just what the solution is right now, but I do want to get this issue dealt with. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:50, 14 October 2020 (UTC)
+Here's an idea of what I was talking about for this idea originally:
+[[File:Possible_Quartertone_Accidentals.png]]
+I hope this idea make sense...  In rastmic systems only the set of quartertone accidentals in the middle are used, while when the rastma is not tempered out, a contrast exists between the top set and the bottom set. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 14 October 2020 (UTC)
+In response to your comment [[User_talk:Xenwolf#Another_Comma|here]], Xenwolf, I'm glad you think this picture is clear. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:26, 14 October 2020 (UTC)
+: Saw all this and thought I'd mention that the idea that there is only one type of semitone is a modern idea arising directly from 12-edo. In Pythagorean tunings, there are two types of semitone. The diatonic semitone is a minor 2nd 256/243, and the chromatic semitone is the augmented unison 2187/2048. The two add up to exactly a whole tone 9/8. The two semitones are obviously notated completely differently, since one is a 2nd and one isn't. Meantone tunings draw the same distinction, but of course the semitones are tuned differently.
+: In 5-limit JI, both semitones can be altered by 81/80, making even more semitones, e.g. 135/128, 25/24, 16/15 and 27/25. Each of these is either diatonic or chromatic, and corresponding pairs add up to a whole tone.
+: Once you make the distinction between chromatic and diatonic semitones, it becomes clear that the sharp sign that represents the chromatic semitone was never meant to denote exactly half a whole tone. It represents a whole tone minus a minor 2nd.
+: BTW something similar happened to the term tritone. In modern times, it means exactly half an octave, but in the past it literally meant the aug 4th, which at the time was distinct from the dim 5th.
+:: Well Kite, applying this logic to quartertones, it's clear that 33/32 is a kind of parachroma, and, if you consider that [[256/243]] is a 3-limit diatonic semitone, while 33/32 is an 11-limit quartertone, and both the 3-limit and the 11-limit are significant (which, after posting the initial version of this comment, I have confirmed through further investigation and [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|documented my findings on the matter]]), it makes sense to think of [[8192/8019]] as being the corresponding paradiatonic interval, as 33/32 and 8192/8019 add up to 256/243...  However, it seems the relationships between chromas and parachromas is more complicated, as evidenced by the relationship between [[45/44]] and [[55/54]]- two other 11-limit parachromas which together add up to [[25/24]] while differing from each other by a ragisma.  As another example, 33/32 has a similar relationship to [[729/704]], with the two adding up to the [[2187/2048|apotome]].  This on its face means that there are already multiple types of parachromatic quartertones.  --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 15 October 2020 (UTC)
+:: If I take the logic of what I said in the previous comment, that means that a stack of two 33/32 quartertones, plus 8192/8019 plus 729/704 is a full 9/8 whole tone- that means that four quartertones equals a whole tone...  If, on the other hand, the rastma is taken from 729/704 and added to 8192/8019, the result is a third 33/32 quartertone plus [[4096/3993]]- another paradiatonic quartertone.  This would actually make the addition much more straightforward, as a stack of three 33/32 quartertones plus 4096/3993 is also 9/8.  So yes, four quartertones *do* in fact add up to a whole tone. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:45, 15 October 2020 (UTC)
+::: Here is my draft of quartertone accidentals (in staff context):
+::: [[File:Quarter-accidentals-narrow-rastmic-wide.png|300px]]
+:::# top line: narrow
+:::# middle line: rastmic
+:::# bottom line: wide
+::: Hope this helps. ---[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:02, 15 October 2020 (UTC)
+:::: It does, but I should point out that the vertical lines on all three demisharp accidentals are actually supposed to be the same.  The same thing is true of the vertical lines on all three sesquisharp accidentals, as well as the the stems of the various demiflat and sesquiflat accidentals.  However, that's not to say that the vertical lines in the demisharp and sesquisharp accidentals all share a length for their vertical lines, however. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:06, 15 October 2020 (UTC)
+:::: Still, despite the flaws, I actually like your work. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:11, 15 October 2020 (UTC)
+::::: Glad you like it! It's actually just cut/copy & paste work, even if done in Inkscape. I was interested in the appearance within staff context and indeed: it seems to work! Also the horizontal and vertical positioning is done by hand and naked eye. A clean design would take a bit longer. BTW also the other glyphs I made are not really clean. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:20, 15 October 2020 (UTC)
+:::::: Ah.  That makes sense.  In that light, this is actually a good rough draft! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:31, 15 October 2020 (UTC)
+: This proposal is basically equivalent to having one accidental for half-apotome and another for 33/32, so, yes, I see it works for most equal temperaments. Better if they appear more distinct glyph-wise. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 06:15, 16 October 2020 (UTC)
+:: Thanks for your thoughts, Flora. Besides the minor flaws (lenghts of verticals) the sharps seem okay to me, but the flats are harder. I'm not sure if sticking with the b-shape isn't the fundamental problem here. But you are experienced with fonts maybe you are the right person for the details. Maybe having three lines is for 4 accidentals each is not ideal. I did a tiny improvement right now to set the single accidental glyphs apart from each other (maybe a browser refresh will be needed). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:50, 16 October 2020 (UTC)
+::: For the record, if there are issues with the flat accidentals, I'd have to say that the thickness and angle of the extra strokes on the stems of the narrow and wide flat accidentals is most likely to be the problem.  Perhaps those cross strokes ought to be thicker and should set at 60-degree angles from the vertical rather than 45-degree angles.  The reason I say this is that those extra strokes are what make the extra flat accidentals stand out from one another, while the shape of the rest of the accidental is what makes them recognizable as flats in the first place. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:17, 16 October 2020 (UTC)
+:::: When you said "60-degree angles from the vertical" -- did you mean this [[File:Rect949.png|24x24px]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:44, 16 October 2020 (UTC)
+::::: I think that works, but the question is whether or not the distinctions still work in the staff context.  Also, the ends of the cross stroke need fixing, but we'll get to that later. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:21, 16 October 2020 (UTC)
+::::: If 60-degree angles don't work as well, then we can reinstate the 45-degree angles, but regardless, the cross strokes still need to be thick like you have them now. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:25, 16 October 2020 (UTC)
+:::::: Please have a look on the new version of [[:File:Quarter-accidentals-narrow-rastmic-wide.png]] (maybe a browser refresh is needed). I made the corresponding vertical lines the same length, the cross strokes are thicker with ends that reflect the vertical direction again. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:58, 16 October 2020 (UTC)
+::::::: I like what I'm seeing.  Still, I suppose it wouldn't hurt for the cross strokes to be even thicker, just to make sure people notice them while sight-reading. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:00, 16 October 2020 (UTC)
+:::::::: As thick as the sharp's strokes are? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:20, 16 October 2020 (UTC)
+::::::::: Yeah, I think that will work as long as the positioning is right.  While you're at it, the strokes of all the demisharp and sesquisharp accidentals should also be fixed to have the same angle and thickness as those of the sharp symbol.  Again, thank you very much for taking your time to help me do this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:33, 16 October 2020 (UTC)
+:::::::::: Done (remember the browser refresh if you don't see any difference) :) the extraction of single glyphs in SVG format will follow tomorrow. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:45, 16 October 2020 (UTC)
+::::::::::: Right.
+::::::: Oh, and I should have said this earlier, but thank you very much for your help in all of this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:05, 16 October 2020 (UTC)
+::: Oh, and I should also point out that for EDOs where the rastma is not tempered out, but the half-apotome also exists, (think [[318edo]]) the rastmic accidentals would not be used because 33/32 takes priority, and... well... because the half-apotome is not formed by tempering out the rastma in such EDOs. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:24, 16 October 2020 (UTC)
+Hey, Xenwolf, do you think we have time to work on this some more? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:33, 27 January 2021 (UTC)
+I'm asking because if you do, perhaps we can consider adding these accidentals to the mix...
+[[File:Possible_159edo_Accidentals.png]]
+I hope this makes sense. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:47, 27 January 2021 (UTC)
+: Currently I have not the time to work on that. One thing that just struck me: thin horizontal lines will be a problem between staff lines. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:20, 28 January 2021 (UTC)
+:: I kind of figured you don't have the time to work on it.  Still, I want to get this done at some point.  The horizontal lines can be replaced with a slightly thicker curved marking, though I can't help but wonder what that would do... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:44, 28 January 2021 (UTC)
+Okay, I updated the picture of the second group of accidentals to change the thin, straight horizontal lines to thicker, more curvy ones.  Does this make a difference? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 06:17, 29 January 2021 (UTC)
+: I think you should really give [https://inkscape.org/ Inkscape] a try, it's great for this kind of stuff, and there are a lot of tutorials around the web. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:09, 29 January 2021 (UTC)
+:: Part of the problem is that it feels like I need constraints and grids and the ability to measure when drawing on the computer.  So, do you like the changes I made or no? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:19, 29 January 2021 (UTC)
+Okay Xenwolf and Flora, after talking on Discord with other people about possible accidentals, I think I've arrived at a solution for a different set of accidentals for 159edo...
+[[File:Quartertone Accidentals.png|1400px]]
+[[File:Syntonic Accidentals.png|700px]]
+[[File:Rastmic Accidentals.png|700px]]
+I hope you two like these. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:52, 14 July 2021 (UTC)