And here is what
Andrew McGregor
has to say about this (scroll down for the lyrics):
Musical notes are a really, really, really complicated subject:
The base standard of western music, now, is A=440 Hz, and equal
temperament, that is that there are 12 other tones related by powers of
the 12th root of two, meaning 12 distinct tones in each octave.
That is a convenient approximation to a set of tones you can make out of
the harmonic series, which was known to the ancient Greeks… except that if
you actually try that, you discover as your music gets more harmonically
complex that things sound pretty bad in some combinations, and musicians
start wanting to correct them so they sound ‘right’ despite being
wrong.
If you tune by ear with voices, or instruments that are not entirely
fixed in their tuning, you end up using something called just intonation,
and as you change key the frequencies you use for certain notes change
slightly. That can mean that you can change key several times, change back
to the key you started on, and end up at a different pitch (shifted by an
interval called a comma).
Yeah, it’s complicated all right.
Around about the 16th century several people worked out that you could do
what we now call equal temperament, it seems to have been simultaneously
invented in China and Holland. It became standard in the 18th century in
Europe.
But… lots of contemporary music uses tuning based on guitars, and they
don’t play in exact equal temperament.
Not only that, lots of contemporary music is based on blues scales, which
contain a note that isn’t one of the regular set.
Arab, Japanese and Indian music each use a different set of intonation
schemes… except when they don’t because they’re incorporating Western
instruments (or guitars)… except when they do something like just
intonation around what the equal-tempered instruments or guitars are doing
to make it sound right in their heads… yeah. Complicated.
So, any attempt to define the exact frequencies of musical notes is just
the start of a long, complicated journey. People have written books on the
subject, and there have been several published on this subject every year
for at least four hundred years. It’s that complicated.
Using different intonation schemes can be astonishingly beautiful.
Check this out… there’s an impossible modulation in this
arrangement:
At one point he smoothly modulates into a key a quarter tone sharp (in
exact quarter-tone equal temperament)… by stepping through something like
the just intonation commas on the way there. By ear, multitracking with
himself.
Lyrics
In the bleak midwinter
Frosty wind made moan
Earth stood hard as iron
Water like a stone
Snow had fallen
Snow on snow on snow
In the bleak midwinter
Long, long ago
Angels and Arc Angels
May have traveled there
Cherubim and Seraphim
Thronged the air
But only his Mother
In her maiden bliss
Worshiped the beloved
With a kiss
What can I give him?
Poor as I am
If I were a shepherd
I would give a lamb
If I were a wise man
I would do my part
But what I can I give him
Give him my heart
Give him my heart
