# Talk:Extended meantone notation

## Notation

We require good notation. y, z, Y and Z are placeholders.

It should be in ASCII, so that it can easily be typed on a keyboard. ASCII includes:

!"#$%&'()*+,-./ 0123456789:;<=>? @ABCDEFGHIJKLMNO PQRSTUVWXYZ[\]^_ `abcdefghijklmno pqrstuvwxyz{|}~

PiotrGrochowski (talk) 06:03, 22 September 2018 (UTC)

The symbols should also only consist of one character. This is for convenience in certain situations, such as a music editor which has a compact view of the notes with 3 characters (base letter, modifier, octave number). PiotrGrochowski (talk) 18:27, 23 September 2018 (UTC)

- (+,-) , (^,v) , (/,\) have all been used as up/down inflections in various notation systems, and are easy to type. Some people have very strong opinions about notation, but I think it's fine to use any symbols you like, as long as you define them clearly and use them consistently! Spt3125 (talk) 19:30, 23 September 2018 (UTC)

Well, right now, you can get a diesis by just going from E# to F. But I like ^ and v for quarter tones (used in HEWM notation), and wouldn't mind using them for the diesis as well. So you would have Fv = E#. I don't like / and \ because I always forget which is which.

Then if you want the thing I was calling a kleisma (sometimes called a "lesser diesis"), I think that would be interval between E and E#v, right? Mike Battaglia (talk) 06:46, 24 September 2018 (UTC)

- Yes. A sharp is 7 fifths up, a diesis down is 12 fifths up, and a kleisma up is 19 fifths up. A diesis and kleisma added together are a sharp. PiotrGrochowski (talk) 07:06, 24 September 2018 (UTC)
- I really think it may be best to simply notate the diesis as C-Dbb, rather than C-C^ or anything else. For two reasons: first, from a "tonal" standpoint, that that's what this interval really is: a double diminished second. Consider the chord progression Cmaj -> Am -> Emaj -> C#m -> G#maj -> E#m -> B#maj -- you have now modulated and are a diesis lower than you started. But this interval may be different sizes in different tunings, and flatter than 19-EDO, the diesis is larger than the chromatic semitone! But even though it is larger, you can still "feel" that you have modulated to the "same place" on the chain of fifths, so there is an interesting perceptual effect there. This is true even if you do the above chord progression in a flattone tuning like 26-EDO for instance, where it's 92 cents, or in a superpyth tuning like 17-EDO, where it's -70 cents! So while the diesis may change in size - it always "feels" like a diesis - much like a chromatic semitone always "feels" like a chromatic semitone whether it's 19-EDO or 17-EDO. But, just my thought... Mike Battaglia (talk) 07:26, 24 September 2018 (UTC)
- Removing the diesis from the notation is a modification and the resulting notation is no longer Extended meantone notation. So you just proposed not to use Extended meantone notation, which is off-topic. PiotrGrochowski (talk) 15:59, 24 September 2018 (UTC)

- I really think it may be best to simply notate the diesis as C-Dbb, rather than C-C^ or anything else. For two reasons: first, from a "tonal" standpoint, that that's what this interval really is: a double diminished second. Consider the chord progression Cmaj -> Am -> Emaj -> C#m -> G#maj -> E#m -> B#maj -- you have now modulated and are a diesis lower than you started. But this interval may be different sizes in different tunings, and flatter than 19-EDO, the diesis is larger than the chromatic semitone! But even though it is larger, you can still "feel" that you have modulated to the "same place" on the chain of fifths, so there is an interesting perceptual effect there. This is true even if you do the above chord progression in a flattone tuning like 26-EDO for instance, where it's 92 cents, or in a superpyth tuning like 17-EDO, where it's -70 cents! So while the diesis may change in size - it always "feels" like a diesis - much like a chromatic semitone always "feels" like a chromatic semitone whether it's 19-EDO or 17-EDO. But, just my thought... Mike Battaglia (talk) 07:26, 24 September 2018 (UTC)

- ok, i changed Y/Z (diesis) to ^/v, and y/z (kleisma) to +/-, just to make the page less 'under construction'. i'm not attached to these, so change them if you want... Spt3125 (talk) 00:14, 2 December 2018 (UTC)

## under construction

Hello Piotr,

There's an obvious contradiction in:

`Do not read this page while it is under construction of notation.`

... why should the change being made when no one should see it? Please elaborate the change in your user name space (I moved the exact content to User:PiotrGrochowski/Extended meantone notation) and, if ready (meaning someone should read it), replace the content of the article Extended meantone notation. Don't misunderstand me: it's absolutely okay to change pages in-place, but not to bring a page into a limbo state or a quasi locked state (for two weeks now). I really hope you work it out, I'm looking forward to see the change.

Thanks for your understanding.

Best regards --Xenwolf (talk) 09:13, 15 October 2018 (UTC)

## Kite's critique

- Why does the title say meantone, since all of the content applies to or could be applied to non-meantone edos? More on the title later.
- "In some tunings, such as 24-tone... sharps can be split in half." More informative to say "In any edo of even sharpness..."
- "Note that the base note letters alternate. Using semisharps and semiflats, this can be re-written as: C Ct C#..." Using semisharps and semiflats puts the notes back in order, and it's implied that any time you can split the sharp, it will serve to do this. The confusion lies in the previous "In some tunings". Is the article talking about sharp-2 edos only? Or about all even-sharpness edos?
- "The generalized chain of fifths, however, does not have a single semisharp or semiflat." Confusing, especially "single". Perhaps what is meant is, semisharps and semiflats don't always occur?
- "In a general meantone tuning, a sharp is split into 2 different parts, the diesis and the kleisma." Finally meantone becomes relevant, because it equates the diesis to a 3-limit diminished 2nd, d2. Likewise the kleisma is equated to a descending dd2. But why talk about 5-limit commas in an article about 3-limit notation? Replacing diesis with d2 and kleisma with -dd2 makes the article clearer, simpler, and lets it apply to all edos, not just the meantone ones. The sentence would become "A sharp can always be split into 2 different parts, a d2 and a descending dd2." True because -12 fifths plus 19 fifths must equal 7 fifths. Likewise, "An octave is made up of 19 d2's and 12 descending dd2's." True because 19 * -12 fifths plus 12 * 19 fifths must equal 0 fifths.
- In the 2nd table, the "Syntonic comma fraction" column would be more accurately called "Approximate syntonic comma fraction".
- "True half-sharps and half-flats" The overall point of this entire section seems to be that in this notation, sometimes the up-arrow-with-shaft and the plus-sign are equated. But this isn't mentioned anywhere in this section. The article rambles, especially about equating 7/6 to a half-dim 3rd.
- "If true half-sharps and true half-flats are desired, which exactly bisect the chromatic semitone, the meantone fifth is split in half." This is a quibble, but IMO better as "Splitting the fifth in half creates true half-sharps and half-flats which exactly bisect the chromatic semitone."
- "While real-world Arabic and Persian music..." This article is about notating rank-1 (and rank-2?) tunings. Why bring up a very complex subject outside the scope of the article and then dismiss it after a very brief discussion?
- "adjacent sharps and flats, such as C♯ and D♭" Clearer as "two notes a dim 2nd apart, such as C♯ and D♭,"
- "The chain-of-neutral-thirds tuning system is not a true "temperament," because it is contorted" Confusing and unnecessary. The 5-limit meantone mapping is [(1 1 0) (0 1 4)]. A chain-of-neutral-thirds temperament will have the 5th number be 2 not 1. The sentence seems to be saying that getting that 2 there by simply doubling the 2nd row of this mapping, making [(1 1 0) (0 2 8)], is contorted. This is true, but besides the point. Obviously, simply doubling one row will cause contorsion. To avoid that, obviously one must add a column to the mapping by increasing the prime limit, and the last number in the new column must be odd. But we can talk about e.g. 31edo's half-sharps without discussing why they are there, i.e. without discussing mappings or commas.
- "the neutral third does not have any just interval mapping to it in the 7-limit." False, consider 49/40 in the Bizozogu temperament.
- "[If] 11/10 and 12/11 [are equated], we obtain mohajira" This assumes meantone. More general to equate 11/9 and 27/22.
- It's not clear if the article is about edos only, or includes rank-2 temperaments too. It could even be applied to 3-limit just intonation.
- Most of the first section discusses half-sharps. This needlessly delays the introduction of the actual notation. Better to move this entire discussion from the 1st section to the 3rd section.
- There needs to be a lead-in sentence conveying the general idea, something like "This notation extends conventional music notation by adding 2 new accidental pairs." Otherwise the reader must read too far to understand what it is.
- There should be a second lead-in sentence that discusses the advantages of this notation, since obviously conventional notation can suffice, and the two new accidental pairs are mathematically redundant. Then somewhere in the article, there should be comparisons of this notation with conventional notation, explicitly demonstrating the advantage of it. Otherwise the reader will wonder, why bother with a more complex notation when a simpler one would do? An example of such a comparison is in the color notation article. See the discussion of trills using po and qu. (which seem to be equivalent to the vertical-arrows-with-shafts here?).
- Finally, I have no idea what the title of the article, or the name of the notation, should actually be. It's an extension of 3-limit notation that doesn't extend the rank of the notation. It's not really about splitting the sharp into two unequal halves, because often one of the halves is negative, and the other is larger than a sharp, and that's hardly a "half".