Although the combinations are finite. The number may be so large that it may be a hundred-thousand years before it happens. Here’s why I think so.
Available Notes-Are we sticking to the chromatic scale or can we use microtones?
Scales-What subset of notes are used to write the melody? Is another subset used for the harmony? Nicolas Slonimsky’s Thesaurus of Scales and Melodic Patterns is 356 pages long.
Key Signature-Horns playing in C will sound different than horns playing in F, because of the natural resonances of the instruments
Melody-How long can the melody be before it is impractical? In theory, a melody can be as long as you want.
Chords-How high do you stack the notes? At some point the notes become supersonic, so that is an upward limit. Subsonic is the downward limit.
Chord Voicing-What inversion is it? Is it open or closed? Open chords can have its notes stacked in any combination.
Harmony-In theory, a chord progression can be as long as we want. What is the practical limit?
Harmonic Rhythm-When do the chords change? Are some held for two bars? some for one bar? Are there bars with several chords in it?
Voice Leading-If a chord has a certain voicing, what voicing do you use for the next chord and the chord after that etc.?
Bass Line-How are the bass notes of the harmony connected? Are there passing tones? Are these passing tones diatonic or chromatic? Are there auxiliary tones? Are these tones diatonic or chromatic? Are there root bass notes preceded by the fifth of the chord? Are there bass notes preceded from a half step below?
Accompaniment-Is the harmony in block chords, arpeggios, Alberti bass, alternating bass note and chord? etc.
Time Signature-Are you in a duple meter or a triple meter? Is the meter simple, compound, complex or mixed?
Rhythm-There is melodic rhythm, harmonic rhythm and the rhythms played by the percussion instruments.
Texture-Is the piece monophonic, biphonic, polyphonic (counterpoint), homophonic, heterophonic or homorhythmic?
Articulation-Which notes are slurred? Which notes are legato? Which are portato? Which are staccato? Which are staccatissimo? Marcato? Tenuto? Pizzicato? Tremolo? Apagados? etc.
Dynamics-Which notes are played pianissimo? piano? mezzopiano? mezzoforte? forte? fortissimo? etc. Does the passage crescendo, diminuendo or stay at the same level? Are some notes accented?
Tempo-How fast is it played? This makes a huge effect on how it sounds. Are there tempo changes in the piece?
Form-Is the piece in sonata form? Rondo form? Scherzo form? Theme and variations? Is it a fugue? A canon? An invention? etc. Are the movements arranged in a symphony, a sonata or a concerto? etc.
Timbre and Orchestration-Is it written for a solo instrument, a small ensemble or a large group? How are the various parts assigned to each instrument?
Interpretation-The musician imbues the music with feel by varying the tempo and dynamics based on her interpretation. This is over and above the tempo and dynamic markings made by the composer.
I am sure that there are many more aspects to music I have overlooked when writing this. In short, I don’t think we have to worry about composers running out of ideas during our lifetimes.
©2016 Stephen L. Martin
Picture: music manuscript for a Gloria, all other details unknown.