notational specificity cont'd

Hi Dave. Thanks for your patience. Cound one say that "comma inflected" is a fairly accurate way to describe the notation? I've seen the uploaded samples of the notation, and seen posts referring to assignments of letter names and staff placements of notes... I wonder: how many notes of various inflections - or, said another way, how many discrete pitches - may conceivably occupy the same position on a five line staff? Is it simply a matter of symbol combinatorics? How are positional boundaries determined?

best regards,
Aaron

Aaron wrote:

>Hi Dave. Thanks for your patience. Could one say that "comma inflected" >is a fairly accurate way to describe the notation?

Yes! But of course it only describes one aspect of the notation.

> I've seen the uploaded samples of the notation, and seen posts > referring to assignments of letter names and staff placements of > notes... I wonder: how many notes of various inflections - or, said > another way, how many discrete pitches - may conceivably occupy the same > position on a five line staff?

We haven't counted them yet, and the more obscure ones using schisma accents are still in flux. But assuming the single or double symbol versions of the notation (considering any schisma accent marks to be part of a single symbol) we can go from double-flat to double-sharp in steps which are not more than 2 cents wide relative to just fifths, therefore we can do _at_least_ 233 discrete pitches, but I believe the actual figure is more like 400.

However most of what anyone will ever want to do with the notation can be done with only 12 symbols (and their inversions) in conjunction with existing sharp and flat symbols.

> Is it simply a matter of symbol combinatorics?

In the single-symbol version (using the multi-shaft and X-shaft arrows) there are no combinations of symbols required. In the double-symbol version one uses only the single-shaft arrows in combination with conventional sharps and flats and their doubles. So the answer to your question is "No" for these versions of the notation. It's simply a matter of the number of discrete symbols (including any which appear as an arrow with a schisma accent mark).

The symbols themselves have been derived as combinations of 8 flags or half arrowheads (at most two at a time), 2 accent marks (at most one used), 4 shafts (exactly one used) and 2 directions (up or down). But not all combinations are necessary or valid.

There is also the possibility of using multiple symbols against a single note in a one-symbol-per-prime manner. This is what I've called the multi-symbol version of the notation. We would discourage this as being _much_ harder to read. This could involve up to 10 symbols to determine a single pitch! And would give 98,415 (= 5*3^9) discrete pitches on a single staff line! About 98,000 of which would be utterly indistinguishable from their neighbours by even the most expert listener.

> How are positional boundaries determined?

Again, I'm not sure what you mean, but I'll assume you mean how does one determine which staff line or space to place a note on. This is really not much different from the situation _without_ comma inflection, and is often referred to as the issue of "correct spelling". This is usually based on the structure of the scale or the structure of any chords the note might be part of. But in the absence of such context the default solution would be to use the position that requires the least pitch deviation from the natural note (in which case double-flats or sharps would not be used).

-- Dave Keenan
Brisbane, Australia
http://dkeenan.com