Methods for Learning Tunes

[nigelgatherer]

The fascinating subject of music, mathematics and compromise is a large one, and I have no objection to become more enlightened here. I have dealt with mandolins which were sufficiently deformed that they required a measure of compromise: in order for it to be nearly in tune on, say, the fifth fret, it was necessary to tune the string slightly sharp in open. I didn't like it, but it meant that an unplayable mandolin became playable, almost, sort of, like. I would imagine someone with true perfect pitch would prefer fiddles to mandolins or pianos.

[Eric Renshaw]

I guess it's because a lot of the mathematics I have worked with over the years has involved using the frequency rather than the space domain that I have picked up bits and pieces of fascinating theory that relate to musical scales en route. However, I really must read Ian's book and get a far better and wider picture. So many thanks for all your contributions which are most helpful. Alistair asks whether anyone might detect the difference between a pure and a compromise note? If anyone is interested in this, or indeed the more physical aspects of musicology, you might like to note that Edinburgh University runs a highly active Acoustic Research Group (e.g. http://www.ph.ed.ac.uk/acoustics/research.html). When I first started there as a young (yes, I was once!) lecturer in 1969 I seem to remember that there was just one person involved. Now there is a whole team.

[Trish Santer]

Takes me back to school physics days and messing about on the Wheatstone bridge! Sure there are things fiddles and some other stringed instruments can do in the way of wonderful "glissandos" by virtue of being unfretted, as well as trombones can slide to great effect.
But there's also this thing about accordions being "wet-tuned " (when to me they sound ever so slightly off-key or "Paris Metro" - and "dry-tuned" when (again to me) it sounds a much purer on-key note.

[Calum Galleitch]

Speaking as a piper, it's very obvious to me that a scale played on a piano is not exactly the same as a scale on a set of pipes. Try striking a major third on a well tuned piano sometime - the discord is actually very obvious. However, that said, it's not really something to worry about until everyone you're playing with is within those rather small limits - which will be quite a while for me and my fiddle!

Cheers,
Calum

[alistair]

As you may know there is a German maker of mouth organs who sells a model tuned to the bagpipe scale. I once phoned Scales to enquire about it and the guy I spoke to said, "Oh you mean the mixolydian model, sir". To which my only answer was "Do I?". Anyway I looked up the word in Wikipedia (which is how I found out how to spell it) and it was quite fascinating though it did not specifically mention the Highland or any other bagpipe. However I also found a US web site about tuning bagpipes (at http://www.hotpipes.com/tuning.html ) which uses the term extensively.
There is also a demonstration on UTube (at http://www.youtube.com/watch?v=rI-sOJfa744 ) of how to tune a guitar to a mixolydian mode.

[Calum Galleitch]

Isn't mixolydian occasionally used in blues? I wouldn't really call what the bagpipe does a mixolydian scale, although it is the notes of the mixolydian scale that are present. It's more just a clever twist on a standard major scale that lets you get away with an awful lot more in terms of choice of key and possible chord sequences. There are not many pipe tunes that really exploit an actual mixolydian scale.

Cheers,
Calum

[alistair]

Well you could argue that all use the G mixolydian mode. At least, this would be the conclusion from the web page referred to earlier ( http://www.hotpipes.com/tuning.html ), which is the source of what little understanding I have gleaned. To quote:
'A final dollop of confusion is tossed in the stew by the way the notes of the Great Highland Bagpipe are labeled. The piper simply ticks off whole letters, in sequence, starting with the lowest note, G, then A, B, C, D, E, F, G and finally the highest note, again A. This is very convenient and makes the written music easy to read for the piper, but it again deviates widely from standard musical practice. When one plunks out this series of notes on a piano the sequence doesn't sound anything like the scale of the bagpipe, even when ignoring the already explained overall higher pitch and the lack of "equal tempering." It's a whole different set of intervals than the conventional musician would expect. This is because the wily piper, having only one C available, simply discards part of that note's conventional label, which is C-Sharp (written C#). The same applies to the F - it's "really" F#. Within the tight confines of the GHB and its music, it's just more convenient to call (in speech and written music) these tones by their first names only - but it can drive a non-piping musician nuts. So, in conventional musical language and notation (and again ignoring overall pitch and tempering) the scale of the GHB would read G, A, B, C#, D, E, F#, G, A. If the G were sharp, this would be an A-Major scale, but as it is, it's called a Mixolydian Mode. (Don't worry, I'm not going to attempt to explain "Mixolydian" except to mention that it's a neat word (pronounced mix-o-lid'-ian) that will impress your musical friends when you utter it.) What's important here is to understand that there is a gap between the GHB and the rest of the world in the way music is described in words and in notation. So, as a piper you cannot play even the most simple tunes as written in your kid's third-grade music book, and likewise you won't hear anything recognizable when you hand your pipe music to a guitarist.'

[Eric Renshaw]

If anyone wants a brief and quick introduction to the huge field of 'scales' then the Wikipedia entries are fairly transparent, e.g.
http://en.wikipedia.org/wiki/Harmonic_series_(music)
http://en.wikipedia.org/wiki/Music_scales
whilst a basic description of other Renaissance scales to the Mixolydian is given in
http://en.wikipedia.org/wiki/Musical_mode

[nigelgatherer]

I have obtained a copy of the book Music and Mathematics, and while it is daunting in scope, depth and erudition, I will be dipping into it every so often, and regurgitating snippets in the middle of conversations and classes to impress people with my scope, depth and erudition.