Our default values: don't let us be a black box

There is not one correct way to model music or music perception. Treating words/notes/chords as a sequence of “symbols” which are grouped into subsequences (“N-grams”) is one approach, but it is not the only approach or the “correct” approach. Modeling our expectations as probabilities, “information content,” or entropy is one approach, but it is not the only approach or the “correct” approach. Using a convenient corpus of musical scores as the “training dataset” to represent the past experience (enculturation) of a hypothetical listener is one approach, but it is not the only approach of the “correct” approach. The specific prediction by partial matching (PPM) is one specific approach to N-gram modeling, but it also has many specific variations, some of which are implemented as various arguments to ppidyom functions. None of these variations are obviously the “correct” approach for addressing any particular research question.

All of these approaches have been shown to be useful in lots of music research, but that doesn’t mean they are the only or correct way of doing research. They all make certain assumptions which are certainly wrong (or at least oversimplifications).

When we, as researchers, decide to make use of existing research methods that have been widely used before—like for example, PPM modeling of sequences of “symbols” in convenient musical datasets—, it can be easy to forget to regard the method critically—as an imperfect convenience, not an absolute truth. If we use a sophisticated system, like ppidyom or IDyOM, to model entropy in music, we can’t regard the model output as “the uncertainty of the music”—the calculation is based on particular assumptions, particular parameters, particular training data, etc. It is one particular estimate of the entropy, which itself (may) correlate with a listeners cognitive uncertainty while listening to the music.

Default values

When you go to use a software like ppidyom, you don’t necessarily want to have to do extensive background reading on different escape-probability and interpolation algorithms before you see some numbers. It is nice if the software just works out of the box, easy, and simple. ppidyom is no exception:

library(ppidyom)
library(humdrumR)

chorales <- readHumdrum(humdrumRroot, 'HumdrumData/BachChorales/*krn')


chorales |> solfa(simple = TRUE) |> ppidyom()

It worked! But, how exactly did it work?

One of the peeves that motivated the creation of ppidyom is that papers get published using, for example, IDyOM or ppm, without mentioning details of the implementation. Presumably, researchers are simply relying on the default values. What are those values? Are they optimal for the research you’re doing? We have done the work to suss out the default values of IDyOM and ppm. This is not to say that the developers of these systems have documented any of these details themselves—the point here is that researchers tend to use the default values, whether or not they are the right values for them.

Our defaults

Below are the default values used by ppidyom(). If you use ppidyom() without specifying your own parameter details, it would be appropriate to note the following details in your report. Some of these details are specific to the humdrumR implementation/usage.

• Maximum N-gram length: 10xxx
• Escape method:
• “Long-term”/“Short-term” training method:
  • “Leave-one-out” cross validation by Piece field in a humdrumR corpus.