Musical Conlangs: Some Observations and Suggestions (Part I)

Many musical conlangs fail to take into account the different modality of music contra language. The most common "template" for musical languages is one where tone straightforwardly replaces phoneme. So instead of /p t k b d g ... i e a u o ... / you get /A B C D E F G/ or some other set of pitches - possibly over more than one octave, possibly with length distinctions and such thrown in for good measure.

This, to me, seems like rather too simple a way of using music for language. It sells music short. This is the first post in a series that will look a bit into the structure of music in order to suggest more interesting

Most humans do not have perfect pitch. Thus, in isolation, the sequence A C sounds much the same as any out of the sequences E G, B D or D F. Lots of similar groups of two notes, where the two notes cannot be distinguished by just hearing the two notes themselves exist. Let us restrict ourselves to the diatonic scale for now.

In fact, we can identify some subsets within the diatonic scale that are not "unique", i.e. there will be other subsets with the same structure to them.

CDE=^{modulo pitch} GAB

In fact, we find several similar structures where any melodic segment that only moves in that subset can be transposed with its structure intact into some other subset. We take a look at the structure of the thing:

F (5) - C (0) - G (7) - D (2) - A (9) - E (4) - B (11)

This is the cycle of fifths, a notion that might be familiar to musicians. The number gives an index - we simply index the tones by the chromatic scale. Simply put, the tones of the C major scale can be obtained by starting at F and ascending by 7 semitones repeatedly until you reach B. Now, this can be used to identify subsets with identical structures within them!

Any two structures that can be transposed one to the other will cover the same length of the cycle. Consider CDE and GAB:

F C G D A E B
F C G D A E B

Basically, we can form a metric for this! If we strip the melody of its melodic structure and only represent it as a set of tones, and then take the range from the leftmost to the rightmost tone as our metric, we have away of identifying whether a melodic snippet could have occurred elsewhere in the same key. The "width" of a melody in this metric is the difference of the leftmost and the rightmost tone present in it as per the following:

0 1  2  3 4 5  6
F C G D A E B

Thus a melody which jumps around G, D, A, E and B goes from 6-2 = 4, and same goes for one that moves around F, C, G, D and A – 4-0 = 4.

And it turns out the only "unique" span is that of F to B (however, looking at the chromatic side of things, it turns out B to F is exactly the same distance, and thus B to F is not distinguishable from F to B ... in isolation, that is.)

However, whenever F and B and a third note are involved, the resulting set can only happen on "one side" of the F-B endpoint. What can we do with this knowledge? Well, we could use 'structures' as lexemes instead of notes; thus, say, "F C D C" is a surface form of "0 1 3 1", where we simply add this to whichever starting point we use: if we were starting from G, we'd get "G D E D", if we were starting from D, we'd get "D A B A".

We could also try to do something that would ensure that a certain pitch is firmly etched as the "root" in the minds of the listener. Maybe we generate the vocabulary so that, say, forty percent of the phonemes in the dictionary are C, fifteen percent G, and each other tone something like 11%. In such a thing, it should be possible to orient oneself tonally fairly solidly.

Other possibilities include having some kind of cadenzas that introduce a statement (or appear somewhat regularly), grammatical prefixes or suffixes that occur in a limited subset (and therefore are easy to identify with regards to the scale structure). Finally, we could go for a different scale altogether, one where no structural similarities exist between any subsets. This makes for a very limited scale - if we permit similar structures between two-note subsets but not between three-note or larger subsets, we get more possible scales to chose from. Here's an example:

CDb Eb F#G [big gap] c

C-Eb and Eb-F# are identical, as are C-Db and F#-G, as are C-F#, F#-C, but other than that no other subset's structure recurs in another subset of this scale. However, we might want to stick to the diatonic scale due to its great melodic properties.

Of course, there's more to music than melody as well, and we'll get on that in the next installment.