Having dealt with both the distribution of durations, duration ratios, and rests in the Skiptune database, the last item is the pitch differential: The difference between any note’s pitch and its neighbor on either side. Let’s start with the basic counts:
- 4,446,196 note-to-note transitions
- 92.7 percent of all transitions are between notes
- 7.3 percent involve rests
- 99.32 percent of intervals stay within an octave
- Only 0.68 percent exceed an octave
The 4.4 million is short of the full transition count of 4.8 million because it excludes rests, which we see later in the list involve 7 percent of the transitions.
Local
The last two bullets tell us that melodic motion in the corpus is overwhelmingly local, which simply quantifies the obvious: Composers generally do not stray too far from the previous note, and trips over an octave are rare. Most note-to-note transitions in the entire corpus are only a few semitones apart.
To quantify further, here’s the motion of pitch changes for no change, minor seconds (one semitone), and major seconds (two semitones):
|
Absolute interval |
Count |
Percent |
|
0 |
608,322 |
13.7 percent |
|
1 |
848,176 |
19.1 percent |
|
2 |
1,525,585 |
34.3 percent |
Adding up those percentages, we see that roughly two-thirds (67 percent) of all pitch changes move by a whole tone or less. That’s rather local. In language terms, it is analogous to discovering that a small handful of common words account for most word transitions.
Symmetry
The second finding is asymmetry with respect to increases and decreases in pitch. For instance, this pattern was found:
-2 = 18.5 percent
+2 = 15.8 percent
-1 = 9.7 percent
+1 = 9.4 percent
-3 = 6.4 percent
+3 = 4.8 percent
Descending motion is consistently more common than ascending motion. This is developed more fully on the Skiptune website, both descriptively and quantitatively, so we won’t duplicate that here. See https://horvathcampbell.com/intervals/ for that analysis.
It is well known that many folk-song collections show a mild descending bias because melodies tend to climb gradually, then resolve downward toward the tonic. The Skiptune corpus appears large enough to suggest that this bias survives aggregation across genres. When there’s time, it would be interesting to explore whether the asymmetry indeed holds across multiple genres, and if so, what if any differences there are.
Harmonic Outlining
The third finding is that thirds, fourths, and fifths form a secondary tier. After stepwise motion as demonstrated in the previous paragraphs, these intervals are the most prominent:
|
Interval |
Percent |
|
±3 |
11.2 + 4.8 percent |
|
±4 |
6.7 percent |
|
±5 |
6.5 percent |
|
±7 |
2.9 percent |
These are the intervals associated with triads, arpeggiation, tonic-dominant motion, and cadential gestures.
So the model is learning two different musical mechanisms: Melodic movement (mostly repeated notes or minor and major seconds) and harmonic outlining (thirds, fourths, fifths).
Octaves and More
We fall off a cliff once we hit an octave and especially beyond. Observe that while octaval jumps (+ or -12 semitones) are 1.35 percent, all jumps in either direction over an octave comprise just 0.68 percent of the intervals in the tunes.
Intervals of ±14, ±15, ±16, ±17 occur thousands of times. So large leaps are rare but not noise. The corpus genuinely contains them. Those intervals likely arise from:
- octave-displaced sequences
- instrumental virtuoso passages
- keyboard music
- military marches
- fiddle tunes
- baroque music
Our AI model architecture must be able to have enough capacity to learn these rare but legitimate long-distance jumps.
Next week we’ll apply what we learned about pitch differentials and their distribution to informing us about how to choose the correct AI model to train.