This is part 9 of my live blogging analysis of the 365 double jigs in O’Neill’s 1001. The last part reviews where I have been. In this part I look at the time-pitch series of the collection. I create these series by single nearest neighbor regression on tuples of pitch and time observations extracted from a transcription. As an example, here is jig #201 (“Biddy’s wedding”):

Its four pitch-time series appear like so:

This feature has a clear relationship to the transcription because it shows which pitch occurs at what time over 8-measure segments. I can extract a time-interval series from these series by moving stepwise along time and finding and holding subsequent differences. The time-interval series for “Biddy’s wedding” appears like so:

The step of 5 semitones for series 2-4 come from the G pitch at the end of each line. I am making the first interval of the first series always be zero.

Here is the transcription I found at the center of a multidimensional scaling of the collection of transcriptions, jig #134 (“Young Tim Murphy”):

And here is its time-pitch series:

The two parts appear quite different save for the last two measures. Here is the time-interval series I extract from this:

In terms of intervals, we see the two parts are similar in measure 4 as well.

One difference between the two jigs above is the anacrusis. This in effect shifts to the right each series of #134 with respect to those of #201. If I am comparing only the series extracted from one transcription, there’s no problem since they all have the same shift. But if I want to compare series across transcriptions, some with an anacrusis and others without, I need to account for the shifts, i.e., align the measures. This will be important to consider when looking at tunes as sequences of measures.

The music21 library provides an easy way to detect an anacrusis, so I have rewritten my feature extraction code such that all series are aligned by measure. Let’s continue looking at the time-pitch series of the collection.

The dots of jig #17 (“The eavesdropper”) are:

and results in the following time-pitch series:

Note that middle C is pitch 60, but I have transposed all jigs in this collection to have a root of C. Here is the time-interval series I extract from the time-pitch series:

One major difference in extracting the time-interval series from the time-pitch series as to how I was doing it before is that this new approach considers repeated pitches as one. So the run of B quavers in the first measure are grouped together in an interval of 4 semitones over 3 quavers. I think this is preferable from the standpoint of considering melody. Playing 3 quavers in place of a dotted crotchet does not change the melody other than its rhythmic characteristic.

(This motivates extracting a “time-duration” series from a transcription to describes its rhythmic characteristics. Instead looking at what pitch is playing when, look at what duration is playing when. Ignoring graces, rolls, and trills, the collection has only pitches of seven durations. From shortest to longest these are triplet semiquaver, semiquaver, triplet quaver, quaver, dotted quaver, crotchet, and dotted crotchet. I will explore this additional feature at a later time… but keep in mind that the features I am extracting are not exemplary of how these tunes are experienced in performance. These are just the bones of the tune as it was in someone’s hand in the early 20th century, without any meat, flesh or movement.)

In the time-pitch series for “The eavesdropper”, we also see how its B part departs from the A part by going higher in pitch, and then descends back to join it. A typical feature of two-part jigs in this collection is that the B part sits above the A part in pitch. To get an idea of how typical it is, let us sum the set of differences between time-pitch series 3 and 1, and of 4 and 2 for each two-part jig in the collection (N=291), and make a histogram of them:

A positive difference means part B of a tune spends more time at pitches higher than part A. I find 268 of the 291 two-part jigs (>92%) have a positive difference. The two-part jig that has the largest difference is #190 (“O’Mahony’s frolics”):

Here are its time-pitch series:

Notice how the first ending of the B part stays high, and the second ending takes the melody down back home.

Of the 23 two-part jigs with a negative difference, the most negative one is #57 (“The blazing turf fire”):

Here are its time-pitch series:

What happens in jigs with more than two parts? Here’s the time-pitch series of the four-part jig #286 (“Strop the razor (2nd setting)”):

We see the melody goes highest in penultimate part (series 5&6). we see the same in the three-part jig #320 (“The piper’s welcome”):

This is not the case in the three-part jig #344 (“The stolen purse”):

Another interesting feature I see in some tunes is contrary motion of the parts, e.g., jig #223 (“The rambler from Clare”):

The time-pitch series show this “mirror image” effect:

This is probably not an accidental feature, but done consciously or planned in composition. Jig #237 (“The Fardown farmer”) has the same kind of construction:

Here are its dots

The A part of this jig and the A part of “The rambler from Clare” are so similar it makes me wonder if the Fardown farmer was the that rambler from Clare

Other tunes have similar intervalic motion in their parts. Here’s jig #249 (“The flitch of Bacon”):

And here’s the corresponding time-pitch series

This also shows how I disregard rests in my extraction of the time-pitch series, just extending the duration of the pitch preceding it.