Wednesday, September 9, 2015

Onwards with Ideas for a Musical Language

Music is not just pitches ordered in time. There are a number of other things: duration, rhythmic patterns, tempo, tonality, harmony, counterpoint, timbre, intensity, consonance, dissonance, resolution - and for all of these, sustained values, quick shifts and slow transitions are possible.



I previously described some properties of the diatonic scale with regards to "relatively identifiable" subsets. However, if we go beyond monophonic music (i.e. beyond music where one note is played at a time, no more than that) some of those problems can be resolved without all too many problems.

One easy solution would be to keep a single drone constantly throbbing along:

C - - -
c d c e
The c d c e melody snippet is now distinguishable from f g f a or g a g b on account of the constant C drone. The others would be audibly different, e.g.:
C - - -
f g f a
Music with this kind of structure does exist, most famously perhaps in the tradition of the Scottish bagpipe, but also elsewhere - in traditional musics all around the world. Since we have an established tone that frames the entire thing, we always know what tone we're hearing (or at least, after a while of practising, we are likely to be able to identify the intervals in all but the noisiest of circumstances, for at least those timbres we've been practising with)


A rather central thing to western music (and conspicuously absent in all traditional non-western music) are chords and their progressions. These have some fairly interesting properties as well, which might simplify the 'identification' issue; since each traditional chord contains at least three notes from the scale, and these are quite evenly distributed:


F C G D A E B
Chord tones of the C major chord as per the cycle of fifths.

C D E F G A B
Chord tones of the C major chord as per the major scale.
There's only two relationships between major chords within a major key that are ambiguous: F to C is identical to C to G; mistaking G to F for either G to C or C to F is unlikely with some practice. Beyond these, we get minor chords:
F C G D A E B
A minor
C D E F G A B (c d e ...)
A minor
Now, the same holds true with regards to minor-to-minor transitions as what held true with regards to major-to-major transitions. The minor-major (and vice versa) transitions contains some more ambiguities, though:
Fmaj Cmaj Gmaj Dmin Amin Emin (Bdim*)
Cmaj Dmin Emin Fmaj Gmaj Amin (Bdim)
Dmin → Fmaj = Amin → Cmaj = Emin → Gmaj. Beyond this, however, we also have:
Dmin → Cmaj = Amin → Gmaj, as well as Emin → Cmaj = Amin → Fmaj.

It does seem we may have some chance of identifying them correctly even in isolation, but there's a significant probability that people without perfect pitch will misidentify these in isolation.

Chords have rather nice properties in general: they do sound like their member tones together form a "supertone" of some kind. They have functions in keys. They can easily be split into melodic snippets that also hint at the "supertone" just by playing them in sequence instead of simultaneously.

We could take that and run with it, though! Let's first introduce another chord concept: inversions. Basically, the C major chord is a C major chord regardless of which pitch is lowest and highest. In the following set, pitches are ordered so that low-to-high corresponds to left-to-right:
    E1     C2 E2 G2 C3
        G1 C2            C3 E3
C1    G1       E2
All these lines are C major chords. However, we can describe the different forms using the term 'inversion'. We have three inversions of triads: root position, first inversion and second inversion. Root inversion is, say, CEG, first inversion is EGc, second inversion is Gce. Modern theorists generally don't distinguish the function of these, although some baroque theorists did. However, and this is a funny thing: trained musicians are less likely to hear inversions as different chords than amateurs are. So apparently there's a thing there we might be able to use!

Let us use a different notation now, where r, f, s stand for root, first and second. A letter normally codes for "major chord", and a letter followed by an m stands for a minor chord. We could now maybe start doing some kind of Semitic-inspired thing. Most words are three chords, except we permit a few two-chord words where the chords may be any two chords that form the right relation.

We could add two other things: order of arpeggiation. An arpeggio is any way of playing a chord in sequence rather than as a simultaneous block. Since we only deal with three tones for now, we can pick six different ways - one starting tone out of three, one next tone out of two, and there's one remainder. 3!, in other words. We simply number the tones from top to bottom, and write the order as 123, 132, 213, 231, 312, 321.

So, we have 18 possible arpeggios per root - three different inversions, six different orders. 6 (or 7) * {r,f,s} * {123, ...}.

 So, about 100-120 different building blocks. If a word consists of at least three chords, normally, we get about a million different 'words' (we do end up with less than that, due to some reasons, but still we're in the hundreds of thousands). That should be sufficient, although our words are somewhat longish: about nine tones each. Of course, it's possible that background noise and such might cover a tone or so, and you'll end up being misaligned among those chords.

Thus, we can have words like:
[CEG][DAF][B'EG]
[cEG][CAF][GBd]
...
If we restricted ourselves a bit, we could of course limit the onset to patterns where the first note is the lowest of the set: CEG, DAF, etc. We could restrict the types of inversion in the middle bit, and we could have some other restriction on the final bit. And now we could start doing something a bit "triconsonantal root"-inspired; maybe root voicings in the first element mark first person, first inversions mark second person, and second inversions mark third person; if it's ascending all the way it's plural, if the middle tone is higher than the last tone, it's singular. We might add that some "not quite chords" at the onset encode non-verbs, maybe any sequence of seconds at the onset encodes 'nouns'. For whatever reason, though, we prefer to retain the same starting note as the verb usually would have if we've derived the noun from a verb; [CEG][DAF][B'EG] inflected into a verbal form would either be [CDE][DAF][B'EG] or [CB'A'][DAF][B'EG]. We might derive participles or whatever by some other not-quite-chord: maybe fifths along this line: [CGC][DAF][B'EG]


Another thing we could use to encode different things, of course, is rhythm, as well as other things such as staccato vs. legato or somesuch.




We could also introduce some sound symbolism kinds of things: a very fast and high minor second motif like cc#c could encode "small", a slow similar thing over an octave could encode large. A segment of the chromatic scale could encode "all", whereas a pentatonic scale could encode "some". A trill could indicate 'many', glissandos '-ish'.

Imagination is all that limits us here.

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