Tunes that start in the 2nd octave

[Guinness]

But sometimes it's fun to look at statistics like this anyway.

Interesting! What program are you using to generating these stats or are you using a Perl script?

I think it would be kind of useful to get a frequency distribution for each note played in the ITM repertoire, from (G,) to (d,) to justify getting certain keys on the flute (low C, low C#, Eb, Fnat long, Fnat short, G#, Bb and Cnat) given that each of these keys can cost hundreds of dollars each.

[pancelticpiper]

Most old time tunes have the A part starting in the octave.

I have often wondered why Irish tunes mostly start in the low octave and the B part in the high and the old time tunes are reversed except for the cross over tunes such as Fisherman's Hornpipe and Hop High Ladies (Miss Mccloud's reel).

You bring up an interesting point.
Mrs MacLeod of Raasay (the Scottish Highland reel, perhaps the original) starts on the high part. The Irish version (McCloud's reel) I learned reversed the order of the parts. The old-time version I've heard (Hop High Ladies) retains the (original?) Scottish order.

[pancelticpiper]

I think it would be kind of useful to get a frequency distribution for each note played in the ITM repertoire, from (G,) to (d,) to justify getting certain keys on the flute (low C, low C#, Eb, Fnat long, Fnat short, G#, Bb and Cnat) given that each of these keys can cost hundreds of dollars each.

This has been treated at length in Traditional Music In Ireland by Tomas O Canainn.
The section headed "note frequency" begins:
"There is a tendency in much of the dance music to concentrate on only a few notes of the available scale, and to return to these again and again throughout the tune. The result, far from being boring- as it could be in the hands of an inexpert player- is a tune which attains a unity of purpose and a build-up of tension eminently satisying or both the first-class performer and the discriminating listener."
Later he continues:
"All this leads to a method for assessing the relative importance of notes in a tune, based on the following criteria:
1) a tone-frequency count giving a point for each appearance of the note
2) the addition of a further point (a) to a note which occurs on a strong beat, (b) to the highest note on its first appearance, (c) to the lowest note on its first appearance, (d) to a note proceeded to by a leap greater than a fifth, (e) to the first stressed note, (f) to a long notes."
(He then applies these formulae to the jig Cailleach an Airgid.)
"This gives the interesting reslut that the most important note in the tune is A... and the next in importance is D...This differs from the tonality that one would deduce from an analysis of either the key signature or final note of the tune, and if one calls the most frequently occurring note the tonic and the next most frequently occurring note the dominant, one is led to conclude that this tune has complex tonality, with a tonic A and dominant D."

I hardly need to state that this theory is open to question, for one reason that in music there is no connexion between a note's frequency and its place in the scale or its harmonic role. The author is openly re-defining the concepts of "tonic" and "dominant".

In Folk Music and Dances of Ireland Breandan Breathnach uses a more conventional approach to the topic of modes in Irish music. He states that over 60% of traditional Irish music is in the "Doh mode", in other words, a normal Major scale.

Both authors couch their discussion of scales and modes in terms of a D uilleann chanter, whistle, or flute. C and F are the notes most often "inflected" (Breathnach's term for a note's propensity to switch between natural and sharp).

The discussion of which whistle keys are useful to have at sessions has been covered in several threads. At sessions I use D for the vast majority of tunes, and also need E, A, C, and G for a few tunes each.

[srt19170]

So, in a random distribution you might expect that 35% of the tunes would begin in the second octave. The fact that it's actually 25% means that the tunes are only slightly weighted (by 10%) toward the 1st octave or below.

That's interesting, although you take the fact that the high octave is underweighted and comprises only a third of the normal range and the result is that most tunes start in the first octave. It's also my impression (although this certainly varies by session) that the weighting is even heavier for the most commonly played tunes. It says something that the "High Reel" is called that because having a reel start high is so unusual!

Boys of the Town

Confusing, since I always think of the "other" Boys of the Town that starts on the low D:

http://irishflute.podbean.com/2007/04/3 ... -the-town/

A marvelous version of this appears on the Wooden Flute Obsession CD, btw. I don't think I've ever heard the high version. Offhand, can you think of a recording or source to listen to it?

[kenny]

http://www.thesession.org/tunes/display/3963

[srt19170]

I think it would be kind of useful to get a frequency distribution for each note played in the ITM repertoire, from (G,) to (d,) to justify getting certain keys on the flute (low C, low C#, Eb, Fnat long, Fnat short, G#, Bb and Cnat) given that each of these keys can cost hundreds of dollars each.

(This is quoted from a posting several years ago...)

Irish music seems to have a very formal structure, so I've
decided to write some programs to examine a corpus of Irish music to
see what structures there are beyond the obvious tune & turn. I
thought this forum might enjoy seeing some preliminary results.

MUSIC CORPUS

This work is based on a collection of approximately 775 reels
available from *Henri Norbek*.

OTHER NOTES

For consistency (and because the tinwhistle is typically played in D),
all music was transposed into the key of D. I did not typically write
out the F and C sharps.

Further, all tunes (and note patterns) were normalized into a base
octave. That is, if I found two note patterns:

abc
ABC

I recognized them as the same pattern by "normalizing" the pattern in
the higher octave into the base octave.

RESULTS

NOTE FREQUENCIES

The simplest feature to look at is the frequency various tones occur
in the music. With songs transposed into D, these are the relative
frequencies of the notes:

23223 D (21%) Unison
18780 A (17%) 5th
18750 F# (17%) 3rd
18333 E (17%) 2nd
14105 B (13%) 6th
8841 G (8%) 4th
7780 C# (7%) 7th

The relative paucity of 4ths and 7ths suggests that many of the reels
may be written in a pentatonic scale, but this turns out not to be the
case. Only 14 of the 779 reels completely avoid the 4th and 7th. I'd
be interested if anyone has an explanation for this distribution.

It's also interesting to look at the relative frequencies of the notes
with duration:

19483 D
17497 F
16871 A
16362 E
13154 B
8066 G
7536 C
2876 D2
1639 A2
1510 E2
971 F2
796 D3
764 B2
606 G2
445 E3
282 F3
264 A3
185 B3
167 G3
152 C2
92 C3
68 D4
16 E4
6 A4
2 G4
2 B4

There is a strong dominance of quarter notes.

A common rule of musical composition is to end the song on the tonic
note. The following table shows the notes most commonly used to end
songs in the corpus (after transposing all songs into Dmaj):

196 D
135 E
122 A
113 B
97 F
58 G
52 C

Interestingly, although D is the most common resolution note, it is
not an overwhelming favorite. One reason for this may be that some of
the tunes are modal. Another reason may be that many Irish dance
tunes do not properly "resolve". This makes the playing of a "set" of
tunes easy, and musicians are expected to add their own resolution
when ending a set.

The durations of ending notes is shown in the following table:

563 1/4
177 2/4
25 4/4
14 3/4

Examining the resolution of the songs suggests looking at the opening
note of the song as well:

190 D
176 A
128 E
123 F
102 B
36 G
23 C

442 1/4
226 2/4
111 3/4

Opening notes demonstrate a more even distribution, although it's
interesting that not a single tune begins with a whole note.

INTERVAL FREQUENCIES

Next I looked at the interval from one note to the next (in whole
tones). A step up of a whole tone is written as +1; down as -1; thus
+1 corresponds to an ascending 2nd, while -3 corresponds to a
descending 4th. Here are the top eleven intervals:

24544 +1
21874 -1
14173 -2
9460 +2
9239 +0
5982 -9
5098 +5
5035 +6
4904 -6
3613 -4
3601 +8
3227 +3
3038 -5
2915 +9
2610 +4
2013 -3
1861 -8
[...]
574 +7
214 -7

Most (61%) intervals are 2nds, 3rds, or unisons. Of the simple
intervals, eighths (octaves) are very seldom seen, and to a lesser
extent fourths and fifths.

NOTE SEQUENCES

Although the distribution of tones and intervals is interesting, it is
more interesting to ask if there are common musical "phrases" in Irish
music. There are several different ways to define phrasing, but for
the moment let's consider the simplest case: any sequence of notes
within a song.

From a composition viewpoint, note sequences aren't very useful
because they can cross phrasing, bar and repeat boundaries. From a
performance viewpoint they are more interesting, because they identify
the most common sequences or runs a musician will have to play to
perform the corpus.

PLAYING COMMON SEQUENCES

In general, we could find the most common note sequences by leaving
all songs in their original key, extract sequences notated in C, and
retain the original octaves. For example: For reels in the key of D,
these are the ten most common 4 note sequences:

291 dBAF#
271 def#d
257 dc#AG
256 edc#A
231 c#AGE
230 ef#de
221 Bc#de
217 f#edB
207 f#edc#
205 def#g

Any musician could use this list to identify common note sequences
needed to play the corpus.

However, as a tinwhistle player I'm really more interested in the
common *fingering* sequences. In addition to being diatonic, the
tinwhistle has the interesting property that tones an octave apart
have the same fingering.

The D tinwhistle is the traditional choice for Celtic music, and is
commonly used for tunes in Dmaj or Gmaj. Analyzing the corpus of D
and G reels, and normalizing into a base octave to collapse similar
fingerings produces this list of common 2 note sequences:

3801 DE
3688 ED
3350 AG
3344 EF
3153 FD
3093 FG
3081 AB
2906 GE
2871 GA
2862 BA

All told there are 80,000 2 note sequences in this part of the corpus.
There are about 155 unique "fingerings", and the top ten fingerings
comprise 40% of the sequences. Note that these top ten fingerings
also reflect the common distribution of intervals (primarily 2nds and
3rds).

This short "song" includes the top ten sequences:

X:1
T:Practice Fingerings for D Tinwhistle
M:C|
K:D
FGAB AGEF | DED2

As it turns out, maintaining octave and duration information only
changes the top ten fingerings slightly (replacing GA and FG with dB
and AF).

INTERVAL SEQUENCES

The previous analysis looked at *note* sequences. We can also examine
the intervals between sequences of notes. For example, the four most
popular 2 note sequences (DE, ED, AG, and EF) are all intervals of
seconds. That is, the second note in the sequence is one whole tone
(a second) above or below the first.

Here are the ten most common intervals:

24544 +1 (ascending 2nd)
21874 -1 (descending 2nd)
14173 -2 (descending 3rd)
9460 +2 (etc.)
9239 +0
5982 -9
5098 +5
5035 +6
4904 -6
3613 -4

The five simplest intervals make up about 60% of the corpus.

MUSICAL PHRASES

Let's now consider a more sophisticated definition of a musical
phrase:

A phrase is a sequence of notes that begins on
an emphasis beat and ends just before an emphasis beat.

In 4/4 time, emphasis is on the first and third beats of a measure, so
a phrase could start on the first beat and end after the second beat,
start on the first beat and end after the fourth beat, start on the
third beat and end after the fourth beat, etc.

Consider this reel from the corpus:

X:7
T:For the Sakes of Old Decency
R:reel
D:Chieftains Live.
D:Michael Tubridy: The Eagle's Whistle.
Zhn-reel-7
M:C|
K:G
d2BG AGEG|DGBG A2AB|d2BG AGEG|1 DGAG EGAB:|2 DGAG EG~G2||
|:~G3B d2Bd|eaag eg~g2|~G3B d2Bd|1 dega bged:|2 dega bage||

In the first bar of this reel we could select "d2BG", "d2BG AGEG" or
"AGEG" as phrases. All these repeat in the third bar. We would not
want to select (for example) "GAG" as a phrase from the first bar.
Although it repeats in several places, it violates our common sense
notion of a musical phrase by starting in the middle of a beat and
ending after an emphasis beat.

To begin with, we looked at two beat phrases that begin on an emphasis
beat. (In the first bar of the reel above, these would be "d2BG"
"AGEG"). The corpus contains about 35,000 phrases of this sort, of
which 3662 are unique. (The average phrase appears about 10 times in
the corpus; 1439 phrases appear only once.) The top ten most common
phrases are:

507 dBAF
340 FDD2
273 edBA
261 D2FD
259 edBd
243 DEFD
241 ABde
233 AFF2
224 fedB
209 EFGE

These represent about 7% of the total phrases in the corpus. The most
popular phrase, dBAF, is far more common than any other phrase. It's
also interesting to compare this list to the most common two note
sequences above.

We can perform a similar analysis on intervals, to find the most
common interval sequences that make up a two beat phrase:

883 -2+0
707 +1
575 +1+1-2
533 -4+0
532 +2-2
435 +1+1+1
416 +2-1-1
413 +2+0
397 -1+0
372 -1

Note that because we're measuring these phrases in beats, they can
have differing numbers of notes. The most common interval pattern,
+2+0, matches (among many other sequences) the second most common note
sequence: FDD2.

The second most common interval pattern, +1, (usually) represents a
dotted quarter note followed by an eighth note. This pattern is
surprisingly common, as in e.g.,

X: 46
T:Galtee Ranger, The
T:Humours of Galteemore, The
T:Callaghan's
R:reel
Zhn-reel-46
M:4/4
K:D
|:AF~F2 FEDE|~F3E F2dB|AF~F2 FEDE|1 FBBA FEEF :|2 F2EG FDD2||
~A3B AF~F2|ABde fe~e2|fedc BcdB|ABde fedB|
~A3B AGFG|ABde fe~e2|fedc BcdB|ABde fedB||

where it appears as A3B twice in the turn. The similar pattern -1
appears in the second bar as F3E.

Next we looked at four beat phrases. We would expect far fewer
"common" phrases at this length. And indeed, the average four beat
phrase appears only about one and a half times in the corpus -- versus
almost ten times for two beat phrases. (15,000 four beat phrases
appear only once.) The top ten most common are:

42 d2fdAdfd
37 D2FDADFD
29 G2BGEFGE
28 DFAFBFAF
28 A2FADAFA
27 dBAFDEFA
27 AFF2ABde
26 edBcdBAF
24 FAA2BFAF
23 dBAFFEE2

Note that the top two phrases differ in only one note (ignoring the
octave shift).

Let's return to two beat phrases. Are some phrases particularly
common to begin a bar? To answer this question, we found all the
phrases that began on the first beat of a measure. Here are the top
ten:

298 dBAF
232 D2FD
170 AFF2
163 Beed
149 DEFD
149 Add2
144 FDD2
140 ABde
135 edBA
129 FAA2

Three new phrases sneak into this list: Beed, Add2 and FAA2. Five
phrases in this list have doubled notes, versus only two in the list
of phrases starting on all emphasis beats.

How about phrases that end a bar? Here are the top ten:

222 edBd
209 dBAF
196 FDD2
176 BAFA
159 EFGE
158 edBc
141 fedB
138 edBA
136 BcdB
116 BFAF

Four new phrases show up: BAFA, edBc, BcdB, BFAF. Two of these use C,
the most uncommon tone in the corpus. Note also that edBd, edBc and
edBA all appear in this list.

Let's extend the idea of "phrases that end a bar" a bit and look at
phrases that end a "passage" -- where a passage is a portion of the
song ending in repeat bars or at the end of the song. There are about
3000 "passages" in the corpus. Here are the top ten passage-ending
phrases:

147 FDD2
79 FEE2
79 D2DE
57 BAA2
56 D4
48 FDDE
46 D3E
43 EFGE
43 DEFG
38 d2dB

Amazingly, FDD2 accounts for more that 5% of the phrase endings in the
corpus. Altogether, the top ten phrases account for over 20% of the
endings. (D4 appears only 68 times in the corpus, but 56 times as the
ending phrase of a passage.) Repeated notes (FDD2, FEE2, BAA2) are
popular phrase endings.

[MTGuru]

Wow, it's going to take some time to digest all that! Very interesting.

[Guinness]

x2

Thanks, that was great.

[MTGuru]

are you using a Perl script?

Yes, exactly. Just treat the abc file as a text database, treat abc as a record format, then suck the tunes into a data structure or pick them apart with regular expressions.

Like srt, I like using the Norbeck collection because the selection, quality, and regularity of his transcriptions are all very good.

It's also my impression (although this certainly varies by session) that the weighting is even heavier for the most commonly played tunes.

My impression, too. It's interesting to speculate about both technical and aesthetic reasons that the distribution is not, in fact, random.

I don't think I've ever heard the high version. Offhand, can you think of a recording or source to listen to it?

There's a nice setting by Patrick Street on "Street Life", Track 1. This is the "Boys" that gets played at our local session. It's this one: http://www.thesession.org/tunes/display/1264

[srt19170]

Yes, exactly. Just treat the abc file as a text database, treat abc as a record format, then suck the tunes into a data structure or pick them apart with regular expressions.

That works for some things, but as you get into more detailed analysis you need to actually parse the ABC, which is a pain

Like srt, I like using the Norbeck collection because the selection, quality, and regularity of his transcriptions are all very good.

And easily available, let's not forget! Actually, for my latest round (which has concentrated on automatic generation of tunes) I scraped the entire set of reels from the Session. That was interesting. There was lots and lots of broken ABC, tunes in weird keys and so on. It's obvious that many of the contributions to the Session never get a second look.

I have a number of cleaned up reel corpi now, that I could share if there's any interest.

BTW, here's an example of a reel written by the computer:

X: 1
T: The Mechanical Reel
K: D
|: "D"d2AB "G"dGG2 | "D"F2FG "D"E2FD | "D"d2AB "D"EDDA | "Bm"Bddf "G"BGGF :|
|: "D"FDFG "D"ABFA | "D"FDFG "G"BGAB | "D"FDFG "D"ABFA | "Bm"Bddf "G"BGGF :|

In this case, the actual note sequences are pretty unique, but overall structure of the tune is based upon a common reel. Can you guess what reel?

There's a nice setting by Patrick Street on "Street Life", Track 1.

Thanks, I'll try to dig that out.

[colomon]

That works for some things, but as you get into more detailed analysis you need to actually parse the ABC, which is a pain

I've been vaguely meaning to write a Perl module to parse ABC files for about a year now. I got sidetracked when I worked out that jcabc2ps was close enough to what I wanted to do in the short term that it just made sense to hack some new functionality into it instead.

[Anglorfin]

Yipes that's a lot to wrap my head around! I'm glad for such a great discussion though and just to clarify, I did mean whole phrases and not just the first note being second octave.

I'm getting the impression that these types of tunes are easy to transition into or (as in the case of my limited experience) feel even less "resolved" than other tunes which lends them to be good lively middle tunes in a set.

[dlovrien]

He states that over 60% of traditional Irish music is in the "Doh mode"...

What a coincidence - I spend over 60% of my time in "D'oh!" mode too!

[MTGuru]

That works for some things, but as you get into more detailed analysis you need to actually parse the ABC, which is a pain

For what you're doing, I'll bet. Fortunately, my queries tend to be pragmatic and ad hoc, and don't require full parsing of the BNF spec. "Show me all the G tunes with octave leaps", that sort of thing. The Perl regex engine makes a good parser for that.

In this case, the actual note sequences are pretty unique, but overall structure of the tune is based upon a common reel. Can you guess what reel?

I'd guess something like The Humours of Tulla. If you assign a unique letter to each unique half-measure, as if scanning a poetic rhyme scheme, you get the same structure for both: |:AB|CD|AF|GH:|:IJ|IL|IN|GH:|. I could be terribly wrong.

[srt19170]

That works for some things, but as you get into more detailed analysis you need to actually parse the ABC, which is a pain

For what you're doing, I'll bet.

My current work (in Lisp) is pretty hacky. I just keep adding more to the parser as I run into or need to deal with new aspects of ABC. Or I edit them out of the corpus . But how anyone can parse the full ABC in all its myriad details is beyond me.

I'd guess something like The Humours of Tulla.

Great guess. The actual tune was "Rolling in the Ryegrass" but Humors has the same fairly common single reel structure.