# An analysis of the 365 double jigs in O’Neill’s, pt. 10

This is part 10 of my live blogging analysis of the 365 double jigs in O’Neill’s 1001. In the last part, I revise and tune the procedure by which I extract time-pitch series from the collection, and then analyze several examples. The part before that reviews where I have been.

While reading O’Neill’s “Irish minstrels and musicians: with numerous dissertations on related subjects” (1918), I found the following quoted from “A History of Music in England” by English composer Earnest Walker (1907). I believe it really encapsulates  implicit and explicit properties of Irish traditional music:

Few musicians have been found to question the assertion that Irish folk-music is, on the whole, the finest that exists; it ranges with wonderful ease over the whole gamut of human emotion from the cradle to the battlefield, and is unsurpassed in poetical and artistic charm. If musical composition meant nothing more than tunes sixteen bars long, Ireland could claim some of the very greatest composers that have ever lived; for in their miniature form the best Irish folk-tunes are gems of absolutely flawless lustre, and though of course some of them are relatively undistinctive, it is very rare to meet with one entirely lacking in character. (pg. 335)

I wonder if the convention of Irish tunes being sixteen bars long relates to physical limits of human memory, and the aural transmission of tunes?

Anyhow, in this part I investigate extracting a feature complementary to time-pitch series: one describing rhythmic aspects of a transcription. Let’s consider jig #201 (“Biddy’s wedding”):

We see notes of four different durations. From shortest to longest: semiquaver, quaver, dotted quaver, and crotchet. In the entire collection, there are notes of three other durations: triplet semiquaver, triplet quaver, and dotted crotchet. One way to describe the rhythm of any transcription in this collection is by expressing it as a sequence of encoded durations where. Let’s try a simple one: 1 means a triplet semiquaver, 2 means a semiquaver, …, and 7 means a dotted crotchet. So the series describing “Biddy’s wedding” starts: 5, 2, 6, 4, 4, 4, 4, 4, 4, …

Even better would be an encoding that directly describes time. Dividing each quaver of a 6/8 measure into 6 segments (Fs = 6 segments/quaver) results in a triplet semiquaver lasting 2 segments, a semiquaver lasting 3, a triplet quaver lasting 4, a quaver lasting 6, a dotted quaver lasting 9, a crotchet lasting 12, and a dotted crotchet lasting 18. Hence, such a series extracted from “Biddy’s wedding” starts: 9, 3, 12, 6, 6, 6, 6, 6, 6, … In this way we can easily isolate measures, and accumulate the values of the series to create a series of onset times, i.e., for “Biddy’s wedding”: 0, 9, 12, 24, 30, 36, 42, 48, 52, 58, … Call this indexed series $O$.

The problem with both of these approaches is that the length of a series is equal to the number of notes in a transcription. I want a feature that facilitates the comparison of transcriptions and their parts. This can be done by making all series the same length. Hence, I create the onset-time series of length Fs*6*8 = 288 according to the following:

$o = 1_{O}(n) : n \in [1,288]$

using the indicator function. So the onset-time series is just a series of 288 ones and zeros. For “Biddy’s wedding” the onset-time series looks like:

Each spike shows an onset. Those of the A part are shown in blue and orange, and those of the B part are shown in green and red. It’s hard to differentiate between the series, so let’s view these in an alternative way:

Series 1 and 2 are from part A and 3 and 4 are from part B. Time in each sequence is going along the x-axis, six steps for each quaver, six quavers for each measure, and 8 measures for each series. Series-time in each tune is going along the y-axis, where each part contributes two series since there are repetitions. There is a change in pixel value where an onset occurs.

Let’s have a look at some others. Below is the onset-time series for jig #24 (“The maid at the well”):

This shows each part is built from two measures with the same rhythm: 10 quavers and a crotchet. Here’s the dots:

The onset-time series below shows a sequence of 22 quavers and a crotchet:

This is from jig #32 (“The basket of Turf”):

And here we see quavers all the way:

Those are the onset-time series of jig #125 (“Wasn’t she fond of me?”):

The pickup doesn’t appear in the onset-time series (or any of the other series) because it does not occur in any repetitions. Its existence is seen in the time-interval series, however (start of blue line):

Here’s a strange pattern of onset times:

That’s from jig #357 (“The Hibernian jig”). The dots show what is going on:

For some reason, O’Neill has explicitly notated an exaggerated jig rhythm. The transcription could also be notated with straight quavers and interpreted in the manner above.

How many jigs in this collection have such exaggerated jig rhythms? Only 14 of the 365 notate the dotted quaver semiquaver rhythm at least 8 times: #8, 76, 101, 148, 181, 201, 212, 222, 229, 256, 257, 294, 322, and 357. Jig #101 (“The idle road”) is one of these I looked at in part 5, which is played by Joe Burke with an unbroken rhythm.

Here’s another interesting one:

This is of jig #95 (“The sheep on the mountains”). This is the only jig in the collection with a structure different from all the others: ABAB, where each part is 16 measures long:

Here’s another, of jig #200 (“Daniel of the sun”):

The B part of this tunes looks to be more syncopated than the other two parts. The transcription shows plenty of broken rhythms, including Scotch snaps, in these parts:

The below are the onset-time series for jig #226 (“Tim Hogan’s jig”):

It appears that the parts become more and more dense with notes. Here’s the transcription:

We see the crotchets of the A part are notated as trilled, or rolled. The B part features mostly quavers. Then the C part has semiquaver passing tones.

Here’s another unusual one:

That is for jig #361 (“The Drogheda weavers”). There appears to be a flourish of notes starting each four measure section of the B part. Here’s the transcription showing what is happening in that part.

By way of summary, let’s look at the ways in which we can describe the characteristics of a give transcription from O’Neill’s 1001. Let’s consider one of my favorite jigs, “Scatter the Mud” (#187). Here’s the ABC notation:

M:6/8
K:Am
d|eAA B>(cB/A/)|eAA ABd|eAA B>(cB/A/)|dBG GBd|
eAA B>(cB/A/)|eAA AGE|GAB Bge|dBA A2:|
|:d|eaa egg|dBA ABd|eaa egg|dBG GBd|
ea^f ({a}g2)e|dBA AGE|GAB Bge|dBA A2:|


And here’s the dots:

Here’s the onset time series of “Scatter the Mud”:

Here’s the time-pitch series:

As is convention, the B part goes higher in pitch than the A part. And the two parts echo each other in the middle and end. Here’s the time-interval series:

And finally, here’s the circular autocorrelation of the time-interval series:

We see the A part is has high self similarity at lags of one measure, and the greatest value at four measures (other than zero lag). The B part has more self-similarity with a lag of  two measures.

In the next part, I think I will look at clustering transcriptions according to their onset time series.