I'm intrigued by your pitch histograms. Do you weight by note length? i.e., would a whole note count for as much as a 16th note?
Also the histograms don't have a concept of ordering for notes, so I think the following two tunes would have the same pitch histogram, despite sounding extremely different to the ear (I rearranged the notes in each measure, but didn't changes pitches or lengths)
Very insightful questions and comments! Due, I think, to my background in physics, I always try to go first for the classic physics approach of "assume the cow is a sphere", i.e. evaluate first how well the simplest model works and iterate from there. Hence, the pitch histograms with no regard for order or note length at this time. I went back and forth on note length, because it's hard to say with certainty how they affect how similar tunes sound to each other.
I think a good sanity check for the pitch histograms is that tunes of the same mode generally group together: dorian and minor tunes are close, and mixolydian and major are too! This is what we'd expect a priori. If this approach had no predictive power, we'd likely see a jumble of different modes intermixed in the plot. So, although it is an extremely simplistic conclusion, we've shown pitch histograms have the power to classify that tunes of similar modes have similar structure, which is a useful starting point! I do think the fact some beginner tunes group together suggests we might be seeing a little deeper prediction of similarity, but this is definitely not proven.
Your point (and I love that you wrote a quick rearranged tune as well to prove it) that the pattern of notes (cadences) matters to its character is absolutely correct, and a pitch histogram will not work for finding it. Cadences are HARD to model. How long a cadence is depends on the type of tune, and sometimes just the music itself and its phrasing. This adds complexity to the data parsing, and a huge amount of dimensions to model.
However! There is a type of model that is able to handle not only looking at the frequency in which notes appear, but also their order called an RNN, Recurrent neural network (a class of deep learning model). This is going to be the topic of a blog post I'm currently working on!
Thanks for your feedback and answers! I agree with starting from a spherical cow, but wanted to advise keeping that simplification in mind when making conclusions. Pitch histograms are a natural start (and, surprisingly to me, there is a long history of musical analysis like this in the literature), but have a lot of caveats to consider.
I was not convinced that two tunes with similar pitch histograms are similar in any way that a human would perceive. You mentioned, about the clustering of tunes in one of the parameter spaces: "These are likely tunes with similar, beginner friendly patterns of notes." But your analysis is not of patterns of notes, only of the number of occurrences of each notes. I suppose a tune that uses only 5 notes would be more beginner friendly than one that uses 12 notes, but I don't think that's the point you're making. I think it needs more analysis to prove that beginner tunes cluster together.
Your point about tunes clustering based on their mode is an interesting one, and I think it works if you assume that a tune will more frequently use notes from the modal scale it is in (or however to say that right). Since note length is not included, a tune with lots of scalar motion might be misleading? Can you check a couple for example?
Spootiskerry has lots of interrupted scalar motion, skipping the F#s and Cs. Does that show up in its pitch histogram?
Lastly, as you've no doubt encountered frequently, grace notes and embellishments are frequent components in Irish traditional music. Compare the many versions of Si Bheag Si Mhor:
Version 16 has the grace notes written in, and those would make its histogram look different than the other versions! it might be a fun baseline to see how much variation you see in all the versions of a given tune on thesession.org? Some of that would be just the natural folk-processing that happens when tunes are shared, but some would give you a sense of how much intrinsic noise there is in a given data visualization/technique.
Anyway, thanks for putting this together, and sharing it here! It's interesting to read, and it's fun to ask you questions about it :)
I'm intrigued by your pitch histograms. Do you weight by note length? i.e., would a whole note count for as much as a 16th note?
Also the histograms don't have a concept of ordering for notes, so I think the following two tunes would have the same pitch histogram, despite sounding extremely different to the ear (I rearranged the notes in each measure, but didn't changes pitches or lengths)
X: 1
T: Off She Goes
R: jig
M: 6/8
L: 1/8
K: Dmaj
|:F2A G2B|ABc d2A|F2A G2B|AFD E3|
F2A G2B|ABc d2e|f2d g2f|edc d3:|
X: 2
T: She Went Off (my own creation)
R: jig
M: 6/8
L: 1/8
K: Dmaj
|:F2 B A G2| AA c d2 B|F2 B A G2|A E3 DF |
F2B A G2|eA d2 cB |ff2g2 df|ec d d3:|
Hi Stephen,
Very insightful questions and comments! Due, I think, to my background in physics, I always try to go first for the classic physics approach of "assume the cow is a sphere", i.e. evaluate first how well the simplest model works and iterate from there. Hence, the pitch histograms with no regard for order or note length at this time. I went back and forth on note length, because it's hard to say with certainty how they affect how similar tunes sound to each other.
I think a good sanity check for the pitch histograms is that tunes of the same mode generally group together: dorian and minor tunes are close, and mixolydian and major are too! This is what we'd expect a priori. If this approach had no predictive power, we'd likely see a jumble of different modes intermixed in the plot. So, although it is an extremely simplistic conclusion, we've shown pitch histograms have the power to classify that tunes of similar modes have similar structure, which is a useful starting point! I do think the fact some beginner tunes group together suggests we might be seeing a little deeper prediction of similarity, but this is definitely not proven.
Your point (and I love that you wrote a quick rearranged tune as well to prove it) that the pattern of notes (cadences) matters to its character is absolutely correct, and a pitch histogram will not work for finding it. Cadences are HARD to model. How long a cadence is depends on the type of tune, and sometimes just the music itself and its phrasing. This adds complexity to the data parsing, and a huge amount of dimensions to model.
However! There is a type of model that is able to handle not only looking at the frequency in which notes appear, but also their order called an RNN, Recurrent neural network (a class of deep learning model). This is going to be the topic of a blog post I'm currently working on!
Thanks for your feedback and answers! I agree with starting from a spherical cow, but wanted to advise keeping that simplification in mind when making conclusions. Pitch histograms are a natural start (and, surprisingly to me, there is a long history of musical analysis like this in the literature), but have a lot of caveats to consider.
I was not convinced that two tunes with similar pitch histograms are similar in any way that a human would perceive. You mentioned, about the clustering of tunes in one of the parameter spaces: "These are likely tunes with similar, beginner friendly patterns of notes." But your analysis is not of patterns of notes, only of the number of occurrences of each notes. I suppose a tune that uses only 5 notes would be more beginner friendly than one that uses 12 notes, but I don't think that's the point you're making. I think it needs more analysis to prove that beginner tunes cluster together.
Your point about tunes clustering based on their mode is an interesting one, and I think it works if you assume that a tune will more frequently use notes from the modal scale it is in (or however to say that right). Since note length is not included, a tune with lots of scalar motion might be misleading? Can you check a couple for example?
https://thesession.org/tunes/1372
Gerryowen has lots of scales! it should be in D Major, but might be a more flat pitch histogram?
https://thesession.org/tunes/857
Spootiskerry has lots of interrupted scalar motion, skipping the F#s and Cs. Does that show up in its pitch histogram?
Lastly, as you've no doubt encountered frequently, grace notes and embellishments are frequent components in Irish traditional music. Compare the many versions of Si Bheag Si Mhor:
https://thesession.org/tunes/449
Version 16 has the grace notes written in, and those would make its histogram look different than the other versions! it might be a fun baseline to see how much variation you see in all the versions of a given tune on thesession.org? Some of that would be just the natural folk-processing that happens when tunes are shared, but some would give you a sense of how much intrinsic noise there is in a given data visualization/technique.
Anyway, thanks for putting this together, and sharing it here! It's interesting to read, and it's fun to ask you questions about it :)