Setting up Wilsonic based pitch tables in Dorico

As far as I know this is not supported in Dorico 5.

I am always loth to suggest it on this forum, but you can do exotic things like that in Lilypond. [By using the word exotic, pardon me, I just mean outside the predominantly Western notation that Dorico is for (at the present time).]

In Dorico you don’t set the total EDO; you set the relative distances between the 7 white notes and the dialog shows the resulting total.

If Scala “knows” which notes should be the white notes in this scale, get the cents between them and set your intervals to those values. (Multiply them all by 2 for 2400 EDO.)

Hi Andro! Good to connect again with you! I will take a look at LilyPond, my thanks for your suggestion!

If these are supposed to be just intervals (the exact ratios), of the examples you posted, the Sagittal system looks the most informative. Certainly the SIMS accidentals aren’t appropriate because they are for 72-EDO. And it’s not clear to me what the others are indicating. These pitches are also very easy to write in Ben Johnston notation, requiring only a dozen different accidentals:

Ratio Cents Note
1:1 0 C
25:24 71 C♯
16:15 112 D♭-
27:25 133 D♭
625:576 141 C♯♯
10:9 182 D-
9:8 204 D♮
256:225 223 E♭♭-
144:125 245 E♭♭
75:64 275 D♯
6:5 316 E♭
100:81 365 E-
5:4 386 E♮
32:25 427 F♭
125:96 457 E♯
4:3 498 F
27:20 520 F+
25:18 569 F♯
45:32 590 F♯+
64:45 610 G♭-
36:25 631 G♭
40:27 680 G-
3:2 702 G♮
192:125 743 A♭♭
25:16 773 G♯
8:5 814 A♭
81:50 835 A♭+
5:3 884 A♮
128:75 925 B♭♭-
125:72 955 A♯
225:128 977 A♯+
16:9 996 B♭-
9:5 1018 B♭
1152:625 1059 C♭♭
50:27 1067 B-
15:8 1088 B♮
48:25 1129 C♭
2:1 1200 C
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Mark, Thank you! I will look into the Ben Johnston notation as well. I have not previously encountered this method. I appreciate this suggestion. I think I am realizing every challenge has a number of unique answers. There is perhaps not a universal “Best Practice” answer at least in this century. I have a friend that steers clears of standard notation and seems to deal with colors. I have yet to comprehend the method, but enjoy learning various methods of pitch perception. I will endeavor to post a template based on these ideas to seek further refinement. Best in music!

For my own curiosity I plotted these notes in a lattice of 5ths horizontally and 3rds vertically. It makes a lot more sense than the table in pitch order. You can see the symmetry. It’s interesting that it has more 5ths around C♯ and C♭ than around C♮, and that it goes all the way out to C♯♯ and C♭♭ vertically. As the ratios show, several of these notes are harmonically much farther from C than other notes not included.


Mark, this is beautiful work! I honestly would not have seen this previously but with your lattice, the values appears almost star shaped. I appreciate you illustrating how to map it in this way. I will apply this practice to other systems for the purpose of visualization. You have given me another idea to perhaps view chordal structures by means of a virtual Oscilloscope. I will try this and post anything of interest. Marcus has a wonderful function of his Wilsonic software which illustrates chordal relationships. I will post an image. I appreciate you expanding my thoughts.

Wow … I have studied Sagittal a little; not enough to recognize the meanings of these at sight. Also, you have definitely set a new record for the most screenshots in a single post (40). I thought the scroll might go on forever. (You can zoom them down while editing!)

SMuFL does include all the Sagittal symbols, but of course the actual tonality system must be built (or imported) by the user. I know they are certainly simpler to use than the Johnston symbols, as each is only one glyph. Best wishes, and let us know how it goes!

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I found the Sagittal-SMuFL Character Map
This is incredibly helpful information.

Yes, I’ve explored it, and even made my own spreadsheet-copy to work with.…
Also the SMuFL spec gives you more compact and direct access.

If I define each scale degree ascending from 1/1. Will the software know to insert the accidental beyond 2/1. Conversely would it be better to look at the distance between each scale degree and set the accidentals this way? IE. 1/1 to 70.6724 would obviously be sharp 25-s-diesis 70.672
looking at the next degree of 111.731 If I just found the closest it would be sharp 5:7-kleisma down 107.927.
or, as I posed should I take the 70.6724 and 111.731 calling it 41.0586 and calling this 23-S-diesis up 40.004
Capture last
I might pose this in the Sagittal Forum as well. Thanks for any thoughts.

No – AFAIK in custom tonality systems all accidentals must be added manually.

For J.I. you have to start from the 7 natural notes being defined in relation to each other, and then the accidentals modify them. In other words, you don’t get from one note in the cracks directly to another by accidentals. For example in Johnston notation, as I showed above, 25:24 is a kind of C and 16:15 is a kind of D. In other systems they can be defined differently.

A few days ago I got interested in Ben’s Suite for Microtonal Piano and started recopying it for my own study. Since he wrote only 12 pitches (all harmonics of C, and the same ones in every octave), Dorico handles this very easily. I enter the notes in 12-EDO, then change the key to the custom tonality, Select All, and filter to select one pitch in the whole flow, and apply the correct accidental to them all at once.

For a scale like yours with 37 tones, it’s going to be a much more manual process.

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Here’s how to do it in Johnston notation: Hexagonal 37.dorico (1013.9 KB)

I am trying to learn enough about Sagittal to do it in that notation too. But I need help understanding how to represent such abstruse ratios in Sagittal. So far I’ve got this; I don’t know how to go further vertically:

The essential difference between the two is how the natural notes (in bold in these lattices) are defined. Notice in Johnston, it’s J.I. in C, but in Sagittal they’re Pythagorean, all in the one horizontal row. (And therefore Sagittal A♮, E♮ and B♮ aren’t even in this scale.) So we can’t just take the BJ tonality system I made and change the symbols; we have to start over.

For e.g. Johnston A♯ 125:72, do I just pick an arrow that’s close enough? I’m looking at a “medium diesis up” from A such as 33/32 (U+E30A) or 36/35 (U+E306). Seeking advice. Once I know what symbols to use, making the tonality system is easy.

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Hi Mark, I will have a look at that template later this evening. Impressive work. I am reading through the “ Sagittal
A Microtonal Notation System“ from the website and will endeavor to be able to answer that question in regards to approximations. I think, though that is the idea it’s not so much of hard and fast thing, but best practice and usage. You gave me another idea from the previous system that you put together. I was thinking about perhaps trying to take this system, which I have mapped to a continuum and essentially starting from the 1/1 up to the 1200. Just going through the steps of Solfège and keeping in mind this as the nominals, analyzing whatever pitch that is, and then falling back to whatever the closest approximated value to the actual system is. At that point as you suggest, then dividing the accidentals from there. I’m not sure if that will work, but I’m also going to give that a try. I will also pose that question about approximate values on the sagittal forum. One other thought removed is trying to keep in mind what a performer would be thinking when they encounter music with this notation. It’s interesting how Sagittal allows for different precision values, I wonder what an actual performer would appreciate the most in regards to a composer, communicating the information to them but something that’s understandable. In performance notes one could define the cent values easily enough. I’m curious if there is a place that has outlined how traditional performers have experienced microtonal compositions, notations, and their impressions about performing that kind of music.

Quick Proof of concept.

Quite a good experience working with the Ben Johnston. I used this Labs VST but one could use anything. The setting was the Fragile Air.
Quieti Ventus.dorico (955.6 KB)

Nice. One awkward thing about BJ notation is that, since there are no enharmonic equivalents, and accidentals can get as big as you want, it is a little too easy for a note higher on the staff to sound lower in pitch – as happens a few times with this set of 37 pitches.

I noticed some unexpected results, but indeed that is par for the course. This notation system while having its eccentricities does provide a starting place. I am incredibly grateful for that. I will tell you something funny when using it, I felt like driving something that was both familiar and unfamiliar. Also, super fun which in my opinion is essential to the creative process as a whole. I tend to occasionally forget that.