Abstract timelines (was ""absolute" note pitches (was "The OMRAS2 Chord Ontology, first draft")")

[Yves Raimond]

Hello John!

Certainly there is a need for MIDI or some equivalent numbering of notes. Alternatives would include pitch class + octave which can always be calculated from the MIDI number. Another numbering system (which relies on the correct naming of a note) is Hewlett's base 40 numbering system see http://www.ccarh.org/publications/reprints/base40/ which allows correct intervals to be assigned between two notes. The example used in the paper is C#/Db to Bb. The same number of semitones exist between the notes, but C# to Bb is a diminished 7th whereas Db to Bb is a major sixth. It is fairly trivial to write inferencing rules to correctly name intervals using Jena to correctly name intervals given the correct base-40 numbers.

[I'll give it a read]

 

Regarding the comments on timelines, I used Allen's paper (Allen, J. F. (1983). "Maintaining knowledge about temporal intervals." Communications of the ACM 26(11): 832 - 843) as a starting point for the proof of concept idea I presented the other week. This gives a set of temporal relationships between events that can be applied to musical keys, chords and notes

Relation            Symbol    Symbol         Pictoral
X before Y        <        >                XXX   YYY
X equal Y        =        =                XXX
                                                                        YYY
X meets Y        M        Mi                XXXYYY
X overlaps Y        O        Oi                    XXX
                                                                          YYY
X during Y        D        Di                            XXX
                                                                        YYYYYYY
X starts Y        S        Si                   XXX
                                                                       YYYYY
X finishes Y        F        Fi                                 XXX
                                                                                 YYYY

Actually, the timeline + owl-time ontology already express Allen's relationships between time intervals. So it is already possible to express things such as "this chord is before this chord, which meets this chord, etc." or "the first verse is before the second chorus".

I think the tricky point, here, is to express the relative timing of such intervals ("the first verse is before the second chorus, and twice as long"), still on an abstract timeline (MusicXML-like information?). One solution maybe to use a coordinate system which captures such relationships (but in this case, we assume some reasoning to be done to get back to the actual relationships)? Or perhaps it would  be better to explicit the relationships constituting such information (in this case, it may be *really* verbose :-) )?
 

Cheers!
y

[seventy...@googlemail.com]

There is quite a lot of literature on axiomatic theories of time which build up
from the bare minimum of what it means to have 'time'. (See, eg Patrick
Hayes' 'A Catalogue of Temporal Theories') For example, you
can have a linearly ordered discrete time domain where the only relation
between time points is that they must be before or after each other, but
there doesn't have to be any concept of 'duration'. Other features or
alternatives can be added one by one, for example, dense time (for
any two time points there is always another time point between them),
continuous time, durations, multiple timelines, nonlinear, eg branching
time and so on. One can also abandon time points altogether and
work only with intervals. It all depends on what is appropriate for the
problem at hand.

For music, it might be quite useful to have a concept of discrete, linear
'score' time even without any concept of durations.  Even better, it
might be possible to have a kind  of 'metrical' time, where the time
points (or intervals) are arranged in structure which makes explicit
the metrical hierarchy, ie with weak, strong, and stronger beats recurring
in a certain pattern. Points and intervals could be addressed relative
to the hierarchy, eg the second third of the 4th beat of the 3rd measure of
the 2nd 'hypermeasure'.. etc, and there would be an accompanying
algebra of time that might include operations such as transposition
of metrical level. A performance of a score on a metrical time domain
would involve a mapping from events with metrical time coordinates
to events on the real time line, and this mapping could include subtleties
like swing timing or the lengthening of the 3rd beat in a waltz.
I've thought about this on an off for the past couple of years but it's
never really gelled into a really compelling whole.


- samer.