Sagittal legend

[cmloegcmluin]

Again, apologies for posting this while I know Dave is preoccupied. But there's no particular rush on this.

I'd like to get a conversation started around something like a key that we could have a standardized format for at the top of scores notated in Sagittal.

I brought it up a couple of times on a private thread between @Dave Keenan and I (viewtopic.php?p=910#p910, if it ever goes public), but these were really early days in our correspondence and I was bombarding him with mountains of big picture questions. Here's the relevant snippet:

Since the Sagittal notation symbolizes intervals that are allowed to vary in size to accommodate many different tunings, it is necessary that sufficient information be provided in a score to specify the particular tuning that is intended, along with a pitch reference. It is expected that this information could be displayed in a standard format that will eventually be defined as a part of the formal specifications of this notation.

Please let me know if such a standard format has been described yet.

I think it could be quite helpful to define a standard format for describing the Sagittal notation used for a piece. At least I think it'd be a good recommendation to state whether you're using an EDO, a JI, or a prime factor notation. For a JI notation it could be nice to give a key for the diacritics you're dropping. For an EDO it might be nice to list the various EDOs the notation supports. Etc.

The deepest nested quote is from the original Xenharmonikon article. The other two quotes are both from me.

Other things I now think might be really handy to mention in such a key:

• size of the fifth (CG) (perhaps if using a non-native fifth for an EDO, you'd want to provide both sizes somehow)
• size of the apotome ( or  )
• size of the limma (BC, or do we prefer EF as in the Periodic Table?)
• size of the whole tone (CD)

Of course we want to keep such a key as compact as possible while still making Sagittal notation as powerful and approachable as possible.

[Dave Keenan]

Good ideas. I chose EF over BC, because it was easier to distinguish EF visually from CD and CG, and because in German music notation B means what we call B .

It could also show, e.g. for 72-edo = 1, = 2, = 3
or at a minimum, list the accidentals for consecutive numbers of steps in order, as in the periodic table.


Perhaps better to call this a "legend" rather than a key. The word "key" is already overloaded in music. As in keyboard and key signature.

[cmloegcmluin]

111% for renaming to legend. Already changed the topic.

Those are good reasons for preferring EF as the limma representation.

Alternatively we could use as the limma symbol in Pure (Revo) or in Mixed (Evo). That would make the whole tone or  , respectively.

I have come to appreciate the extreme economy of expression in the periodic table, but in this context, I would like to see the symbol sequence of one pair of nominals separated by a whole-tone (e.g. C to D) and another pair of nominals separated by a limma (e.g. from E to F). I think this may in particular assist folks using Revo.

Re: using the = sign, we may want to reserve that for reassigning values, as you suggested elsewhere:

But if you want to, you can drop the diacritics in cases where it doesn't cause any ambiguity. Effectively redefining the value of the accented symbol for the purpose of your work. If you felt bad about such redefinitions you could put a note at the top of your score, e.g. → .

[Dave Keenan]

I like to notate the range from D to F as covering all cases. You mentioned elsewhere having used B to D. It's a minor third either way. D is the point of symmetry (FCGDAEB), so yours would be the mirror image of mine.

[cmloegcmluin]

Oy, I did use B to D as my cover-all-cases. I think a case-sensitive global find-and-replace will do the trick for conforming to your D to F convention, though. I think I have a preference for yours as it gives the apotome first, followed by two limmas, and apotome is the more "important" interval in Sagittal.

[cmloegcmluin]

I reviewed the concept of smart defaults as linked from here. I'll admit I didn't really get this idea before, but I do now.

Previously @Dave Keenan and I had discussed the difference between "primary comma" and "default value" and I thought we settled on them being equivalent.

But I'm seeing now that a sagittal would have a default primary comma — irrespective of its nominal pairing — when smart defaults are "off", and then when smart defaults are "on" a sagittal potentially has a different primary comma for each nominal.

Or rather, a different primary comma for each node on the chain of fifths, since the smart defaults table gives different stats for nominals altered by sharps and flats.

What does it mean for smart defaults to be "on" for a human performer reading Sagittal notation?

It makes enough sense to me that a computer, such as the JI Notation Calculator, armed with smart defaults, would generate the same symbols as it did before, since the capture zone boundaries wouldn't have changed, but it associate them with different ratios than before, returning an error of 0 cents more often.

But what about for people? Maybe smart defaults could manifest for humans exchanging sheet music in this sense: the Sagittal legend could, with a single distinct indicator, call for the bundle of smart defaults, avoiding the need to provide a potentially lengthy map of symbol-and-chain-node-combinations to ratios which would otherwise have been secondary commas.

Perhaps there's a better name than "smart defaults" that would feel like a directive to a human rather than a machine... something more specific to the "per-chain-node" nature of the effect. I bring up the name just because a solid name for the effect could help determine what its indicator would look like.