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What are the correct orientation of fractional beams?
Is it true that they should always head to left except if it is the leftmost note of the outer beam (when they are forced to head to the right).
My question also applies to the straight and upside-down notes.
I heard a theory that the heading sometimes depends on the position of dotted 8th inside the beam if any. I am programming a song editor software and I would like to know the conventions.
Your example seems somewhat artifical, since 5/8 is a strange meter. Typically fractional beams occur in combination with dotted notes and in that case the beam extends towards the dotted note to make connection to this note visible, which adds up to a multiple of 1/8 notes.
I verified that in Elaine Goulds "Behind Bars". There an additional strange case is mentioned: in a 6/16 meter after a dotted eighth the following 16th would have its beam point towards the succeeding plain 8th. So the main criterion is: the fractional beam points to the note, where the one with the fractional beam belongs to - not too easy to program I'm afraid.
I follow the development of music notation software. (I'm not a developer myself; I'm a user.) To answer questions like this, people in every development project I've come across recently cite one particular reference book that was recently published:
Behind Bars: The Definitive Guide to Music Notation, by Elaine Gould, Alfred Music, 2011.
Perhaps you should consult that source.
The description of the book says:
In the most thorough and painstakingly researched book to be published since the 1980s, specialist music editor Elaine Gould provides a comprehensive grounding in notational principles.
Behind Bars covers everything from basic rules, conventions and themes to complex instrumental techniques, empowering the reader to prepare music with total clarity and precision. With the advent of computer technology, it has never been more important for musicians to have ready access to principles of best practice in this dynamic field, and this book will support the endeavors of software users and devotees of hand-copying alike.
This seminal and all-encompassing guide encourages new standards of excellence and accuracy and, at a weighty 704 pages, it is supported by 1,500 music examples of published scores from Bach to Xenakis.
The split beam goes on the same side as the blob part of the note. If the note is low on the stave, the tail is on the right, and the extra mini-beam is on the left. EXCEPT when it's the leftmost note joined by a beam, when it fits under the beam. This looks neater. The same happens with a high note with the blob on the right of the tail. The minibeam goes under the blob (head) UNLESS it's at the right hand end of the beam.
I would say it depends on the how the meter is logically subdivided. As written in your question, I would expect the subdivision to be: 3+2/16 1. If it were to the right, I would expect the subdivision to be 2+3/16 1.
What do you mean by fractional beams? Your example is fine as far as the beam orientation goes, despite the fact that the grouping of the beaming is incorrect and hard to read. To be clear, I'm assuming this particular example is in a slightly uncommon time signature which explains the odd grouping and probably makes it OK, as the beam groupings (most importantly) don't cross the middle of a bar divisionally (e.g. in 4/4, 2 + 2 = don't group beams across the middle).
Rule of thumb is that below the middle staff line, the beams go up (on the right of the note head) and on or above the middle staff line they go down (on the left of the note head).
