And with respect to tonality, I included this picture of
an ancient flute here to make the point that the tonalities
that have been used in music have been around for a very long time.
So this flute was discovered in a French cave and
has been carbon dated to about 32,000 years ago.
That's a very long time, well before the recorded history of music.
And the point of showing you this, and of course there are many ancient instruments
that have been found in all sorts of eras of music in prehistory.
The reason for showing this particular flute is that the distance between
the holes in the flute are pretty much the same as the distance
between the holes in this bamboo flute that is a contemporary instrument.
The point being that the tones that we’ve liked, and the tonal
relationships that we’ve liked, have been around for a very, very long time.
And that's indicative, and I'll come back to this later,
about how music got started, where it came from.
But there's a good deal of information about ancient instruments
that are informative in this respect.
Now [COUGH] let me turn to just kind of a menu of what we're going to be talking
about today which are some of the central issues in musical tonality.
And I'll just list them, we're gonna go over all of these.
Not all of them today, some of them in the coming modules as well.
But let me list this sort of menu of topics because these are the issues that,
whatever else your theory of music may be indicating,
if it can't give you an explanation of these issues,
then frankly it's not worth all that much.
These are really the challenges in music.
A lot of music theory just take these as givens, the existence of the octave and
octave similarity and so on.
But we're going to be talking about potential explanations for
these phenomena, and let me just go through these very quickly.
So the first of these is this issue of octaves and octave similarity.
I'm going to talk a lot more about octaves.
But an octave, as you would gather from the name, is an interval of eight notes.
We're gonna talk about the eight-note scale,
the diatonic scale, in the next module.
But let me just say that the octave is defined by a doubling of the fundamental
frequency of a tonic note in a composition of music or in anything else.
Octaves are used in electronics, having sort of borrowed the idea from music,
but the name comes from the eight notes that are in the commonly
used do re mi scale that we'll talk about next time.
And the definition of the octave is a doubling of frequency.
The really fundamental aspect of music that needs some kind of
explanation is octave similarity.
So those of you who play a keyboard instrument, or the piano in particular,
will know that there are about seven octaves on a piano,
a little more than seven octaves on a piano.
And the notes,
the scales that you play in any of those octaves are musically similar.
The next issue is the chromatic scale.
The chromatic scale, which I'm gonna talk about in the next lesson,
is the set of intervals over an octave that divides an octave.
And this has been a very longstanding issue in music, how you divide an octave,
what the tuning system that divides an octave most reasonably is.
We're gonna spend a lot of time talking about that, but the chromatic scale is
a division of an octave into 12 intervals that we'll come to very shortly.