A chàirdean,

This was on the news yesterday in Scotland.

http://www.dailymail.co.uk/news/article-1209371/Secret-code-etched-Stirling-Cast\
le-revealed-oldest-written-music-Scotand.html

http://news.bbc.co.uk/1/hi/in_pictures/8079126.stm

Several things strike me as significant about this.

The first is that there are three elements to the 'notation' rather than two: O,
I and II. It seems obvious to assign the usual Welsh meanings to the 0 and I
element. The II element could represent

i) a third set of sonorities
ii) a specific way of playing either 0 or I sonorities, or
ii) the presence of, for example, two crotchet beats within the left hand in the
measure if 0 and I represented a minim beat.

The sculptor has planned his sculpture very carefully to produce even-numbered
sequences of 28 outer shapes, 36 inner shapes (the loops) and 68 elements
inbetween them. There are twenty one 0 elements, thirty eight I elements and
nine II elements. The 0 and II elements taken together number thirty. There is
therefore no direct numerical correspondence between the number of outer and
inner shapes and the number of the various elements sonorities.

Outer shapes: 28 Number of O and II elements: 30
Inner shapes: 36 Number of I elements: 38
Total: 64 Total: 68
Difference: 4

No 0 sits beside another 0, likewise no II sits beside another II. As extended
Welsh measures usually contain pairings of 0, this might indicate that the two
sonorities 0 and II are closely related and, to some degree, substitutes for
each other.

As John Donaldson has noted, one of the inner loop shapes is deliberately
squashed thin. Its strange positioning might indicate that it is the solution
to the 'musical circle' puzzle left by the original sculptor, ie, where does the
sequence begin?

If the elements are grouped together into groups of four elements, eg. II I 0 I,
the internal patterns of the groups created can be seen to be repeated here and
there in other groups.

One can treat the element II as actually being two I elements notated more
closely together, or see it as a distinct element in itself. Regardless of
which approach is taken, it is significant that most repetition of four element
groups actually occurs only when one starts at the squashed loop, rather than
two, three or four steps away from it.

If II is taken as a distinct element in itself, the following pattern appears,
starting at the squashed loop. I express 0 I II as 0 1 2 here and organise the
lines to optimise the appearance of repititions. This is reading clockwise;
reading anti-clockwise flips the pattern but does not affect the amount of
repetition of patterns.

2 1 0 1 - 1 1 0 1 - 2 0 1 1

0 1 0 2 - 1 0 1 0 - 1 1 0 1

2 1 0 1 - 1 1 0 1 - 2 0 1 1

1 0 1 2 - 0 1 0 1 - 1 0 1 2 - 0 1 0 1

1 1 0 1 - 2 1 0 1 - 1 1 0 1 - 2 1 0 1

Only 0 I 0 II and I 0 I 0 are unrepeated under this arrangement. The sign II
appears regularly at the beginning or end of a group.

If II is taken as an unusual way of writing two I elements, the following
pattern appears, starting at the squashed loop but, importantly, at the second I
of the II element.

/1 1 0 1 - 1 1 0 1 - 1 1 0 1 - 1 0 1 0

1 1 1 0 - 1 0 1 1 - 0 1 1 1 - 1 0 1 1

1 0 1 1 - 1 0 1 1 - 1 0 1 1 - 1 0 1 0

1 1 0 1 - 1 1 0 1 - 0 1 1 1 - 0 1 1 1

1 0 1 1 - 1 0 1 1 - 1 1 0 1 - 1/

Only I I I 0 is unrepeated under this arrangement.

This is perhaps a more foursquare shape than the previous pattern but is, at
least with regard to the total number of elements, uneven. This might add
weight to the notion that II is to be taken as a distinct element in its own
right rather than a (perhaps inexplicable)doubling of I.

The II element, which I indicate below with a tilde connecting two I elements,
can be seen to appear in this pattern in three positions within each group
rather than two, pairing the beginning and end elements of groups, pairing the
first two elements of a group, and pairing the last two elements of a group.
This could also be seen as unevenness.

/1 1 0 1 - 1 1 0 1 - 1~1 0 1 - 1 0 1 0

1~1 1 0 - 1 0 1 1 - 0 1 1~1 - 1 0 1 1

1 0 1 1~-~1 0 1 1 - 1 0 1 1~-~1 0 1 0

1 1 0 1 - 1~1 0 1 - 0 1 1 1 - 0 1 1~1

1 0 1 1 - 1 0 1 1~-~1 1 0 1 - 1/~

Unevenness is not the be all and end all for musical structure, however, nor for
musical notation. There are three distinct elements to this notation, for
example.

If this is music, and if the piece works for the most part using four element
groupings, then I'm quite convinced that the squashed loop most likely indicates
at least where the four element groupings break; this is because the squashed
loop coincides with the point where 4 element patterns produces the greatest
amount of repeated patterns.

I'm also convinced that the squashed loop also indicates the beginning of the
piece; the resultant shape of the overall measure would seem to support this.

What I remain unsure of is whether II is to be taken as a single element, or a
pairing of I elements which would have indicated some unknown feature related to
the I elements. Do the group members have any preferences?

Beannachdan,




Alasdair