Simplified "Stoic" Sagittal for 13-limit tonality diamond use

[ndentonprotsack]

Hey Dave,

Thank you for your patience! Let's just say Feb. was a rough month, and March has been an attempt to catchup with everything. Don't worry; all is well now.

I can confirm right now that I am very much happy with the current outlines we have for the stoic symbols. I have been utilizing them, especially, and in my composing and can now officially say that stoic sagittal has appeared in works that have been performed in Christchurch (New Zealand), New York City, San Francisco, and Toronto. (The temperament I have been using is one I concocted myself, where we have a period of 12-edo, and a generator of 28 cents. 1 generator down from a minor seventh gives a 7th harmonic, 2 generators up from a perfect fourth gives the 11th harmonic, and 2 generators down from a major sixth gives the 13th harmonic. All are tuned around 4-5 cents sharp, so that they dull the almost 14 cent sharp major third of 12edo).

Regarding the JSON metadata, it was giving me a rough time. Last I tried (which was essentially a year ago now) I was able to get the symbols to appear in Dorico, but not as a new category called "Stoic Sagittal" that could be accessed from the dropdown menu. I will tinker with this this week, though, and see if I can get it to work. If you would like to take a stab at it, please be my guest.
Here https://www.dropbox.com/sh/2s5q29w68guy ... GPUma?dl=0 is a Dropbox folder containing all the most recent versions of Bravura-S and its metadata.

All the best,
Nick

[Dave Keenan]

@ndentonprotsack
Hi Nick,

That's great news.

<pedantry warning> I'm not sure what you mean when you say your temperament has a "period of 12-edo", since 12-edo is a tuning containing many intervals whereas a period is a single interval. Do you mean it has a period of 1/12th of an octave, 100 cents? And it wasn't clear initially, how you were defining minor seventh, perfect fourth and major sixth. Sometimes they are defined as stacks of (possibly tempered) fifths or fourths octave reduced — sometimes as ratios 16/9 (or 9/5), 4/3 and 5/3. But when you say that the 7th, 11th and 13th harmonic are tuned 4-5 cents sharp by offsets of respectively -1, 2 and -2 times 28 cents from those intervals, I can first see that you must be talking about octave-reductions of those harmonics, namely 7/4, 11/8, 13/8 and then, with the aid of a spreadsheet, I can work backwards to find that you must be defining minor seventh, perfect fourth and major sixth as in 12-edo. But I remain completely mystified by your phrase "so that they dull the almost 14 cent sharp major third of 12edo". I understand the major third of 12edo is almost 14 cents sharp of 5/4, but what can it mean to "dull" a sharp interval. I can only think it means to reduce its sharpness, and therefore make it nearer to pure. But I cannot see how a slightly sharp 7th, 11th and 13th harmonic (or the generator and mapping that produce them) can possibly have any effect on the tuning of the major third of 12edo as an approximation of 5/4, since this involves zero generators (but 4 periods). However, with further use of the spreadsheet, I see that a 28 cent generator is near optimal if your approximation of 5/4 is 3 generators up from the minor third of 12edo (3 periods).

I just learned of the existence of the free Dorico SE. I will install that and see what I can figure out about the JSON metadata.

[ndentonprotsack]

Hey Dave,

Yes, my language might have been a bit vague. I did indeed mean a period of 1/12th of an octave, and a generator of exactly 28 cents.
What I meant by "dull the almost 14 cent sharp 5/4" is this... With a generator of 28 cents, you achieve: 7/4 with +10 periods and -1 generator, 11/8 with +5 periods and +2 generators, and 13/8 with +9 periods and -2 generators. These are all tuned between 4 and 6 cents sharp, which in turn when used to form intervals such as 11/10, 7/5, 13/10, (etc.) interact with 12edo's very sharp 5/4 (aka +4p, 0g) such that they reduce its apparent sharpness. Basically, if these intervals are all tuned sharp relative to the tonic, then their intonation in relation to one another is better.

Please let me know what you manage to come up with in regard to Dorico SE.

[Dave Keenan]

@ndentonprotsack
I finally got Dorico SE 4 installed correctly. I screwed it up the first time thanks to Steinberg's outdated and misleading installation video.

The help has the following to say about Microtonal accidentals:

Microtonal accidentals indicate pitches beyond the standard accepted chromatic scale in Western tonality, such as a quarter sharp or quarter flat. Microtonal accidentals are only shown in Dorico SE if you open a project that already contains them. They are available for input only where the corresponding key signature and tonality system apply.

It is not possible, with Dorico SE 4, to specify any tonality system other than the default 12-EDO. Although the help says:

The term “tonality system” is used in Dorico SE to encompass three crucial elements that together make up the concept of tonality.

The three elements that make up tonality systems are:

A number of equal divisions of the octave, or EDO. For example, standard Western scales with half-step (semitone) steps have 12-EDO.

A set of accidentals. This allows you to notate how much a note is raised or lowered.

A key signature. In Dorico SE, you can use any traditional Western key signature.

Dorico SE provides the following tonality systems in each project by default:

Equal temperament (12-EDO): Contains twelve half-step (semitone) steps

Equal temperament (24-EDO, Gould arrows): Contains 24 quarter tone steps and uses Gould arrow quarter tone accidentals

Equal temperament (24-EDO, Stein-Zimmermann): Contains 24 quarter tone steps and uses Stein-Zimmermann quarter tone accidentals

You can find existing tonality systems in your project in the Tonality System section of the Key Signatures, Tonality Systems, and Accidentals panel.

In fact there is no Tonality System section. There is only a Key Signatures section and an Accidentals section which is limited to conventional naturals, sharps and flats, and multiples thereof.

It would be good if you could attach a project file that is set to use an alternative tonality system with Stoic accidentals, in case Dorico SE lets me see more of the user interface relating to inputting microtonal accidentals when I open it.