I think it was Bryan that wrote
"Whichever you like as long as you specify all the notes unambiguosly."

It has just occurred to me that the notion that the notes are in some way
more fundamental than the mode is actually wrong.  It assumes that the tune
is always played/sung the same way.  That does seem to be more or less true
for songs (the singers I've heard don't seem to change the tunes much) but
is *not* true for instrumental tunes.  The better (folk) musicians that I
know are *always* taking liberties with the tunes and if they wrote the tune
themself then it can change every time.

But there is something that doesn't change.  I've heard it called "the bones
of the tune".  So the real tune is the sum total of all the variations that
the composer would regard as not straying so far as to be a different tune.
(A cloud of points in a high dimensionsal, abstract, tune space if you like
sesquipedalion language).  So what's actually written down is one sample
version (one droplet from the cloud) which is somehow supposed to capture
the essence of all those variations and ambiguities.

The chord structure of the tune gives another stab at capturing it.  That
can have variations too.  (Does John Brown's Body have the interesting B Em
| A7 D7 |  G  ending, or does it just go G G | D7 D7 | G) so there's another
set of dimensions to the cloud.

The tonic and mode are yet another way of describing the tune.  These too
can be played about with (our band plays a minor key version of Black Jack),
but to my mind they are usually a little more stable (we call it "White
Jill" - so we sort of acknowledge that it's become a new tune).

Laurie

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