The Oldest Magic
Sixteen: The Language of Music
Lew Paxton Price
Our musical scale can be confusing due to terms that can mean more than one thing. When I say fourth, a musician thinks of a note that is fourth in a heptatonic or diatonic series of notes. A mathematician or physicist may think of a frequency or wavelength being a fourth (one-quarter) of another. An occultist may think of a note one-fourth of the way around the musical circle of notes.
Complicating this confusion is the fact that music is not usually taught as a science. When it is, the teachings are seldom very comprehensive, even though music is not just a science, but a basic science. The whole universe is based upon vibration, which is music in every octave imaginable.
Octaves are doublings or halvings of frequencies. A frequency is the number of times a waveform (sound, light, radio, etc.) disturbs something in the same direction (your eardrum, for instance). Octaves can go up or down, repeating the notes" within them endlessly. Middle C is green in the octave of visible light, and one drum beat in each second in an octave below what we think of as tone.
The diatonic scale consists of two four-note sequences, one above the other, known as tetrachords (four notes). This makes a total of eight notes including the note that begins the next octave. But it is actually a seven note scale called heptatonic because the eighth note is really the same as the first (merely the same note in the next octave).
We number our two-tetrachord scale (diatonic) starting with one and going to eight (there are eight notes but the eighth is the same as the first). We call the first note one," the second two," the third three" and so on. We also call the second note a second," the third note a third, the fourth note a fourth and so on all the way up into the next octave, as high as thirteenth or more when the octave note is the eighth.
If we begin our diatonic octave on a different note, we must introduce other notes between some of the ones we are already using. The interval or step between the first and second notes is a whole one, between the second and third a whole one, between the third and fourth only a half interval; then we again progress by whole intervals until we get to the one between the seventh and eighth which is only a half interval. When we decide to begin the octave on a different note while still using the usual diatonic scale, we must have the half intervals at different places. So we need notes between those that are a whole interval apart. This is where the chromatic scale comes in. So the white notes on the piano can be considered our basic diatonic scale from C to C, and the black notes are the notes we added to get a chromatic scale of twelve notes, or thirteen if we include the octave note.
We call the black notes sharps and flats. If we go up a half interval from C to the black note above it, we call this black note C sharp." But if we go down a half interval from D to this same black note, we call the same note D flat." So the flats and sharps are the same notes with different names, according to whether we go up or down a half interval to get to them.
If we decide to begin our octave with C, and play only the white notes, we have what is called the natural major mode." If we begin the octave in A and again play only the white notes, we have the natural minor mode." There is a different mode for every note in the heptatonic scale for a total of seven. If we wish to change keys and keep the same mode (a key is the name we give to the note in a tune or octave which is the major, or most used, note), we may do so—but then we must begin to use the black notes.
When we speak of going down a half interval from a particular numbered note we call it diminishing." Thus a half interval below a fifth would be a diminished fifth, a half interval below a third would be a diminished third and so forth.
When we speak of going up a half interval from a particular numbered note we call it augmenting. Thus, a half interval above a fifth would be an augmented fifth; a half interval above a fourth would be an augmented fourth, and so on.
Lettered notes are more specific than numbered notes because we can begin our number sequence anywhere we like, while each letter stays with a note of specific frequencies. In our modern scale, `A' can mean 440 Hertz, 220 Hz (half of 440), 880 Hz (twice 440), and so on as long as we either halve or double the number of Hertz each time. But in our scale, `A' cannot be any other frequency such as 425, 650, etc. We can get more specific by designating a note the A below middle C" which means it must have precisely a frequency of 440 Hz and no other.
If the frequency of a note begins too low or slides downward as in the case of certain musical styles (country western for example) we call it flatting the note. If the frequency of the note begins too high or slides upward, we call it sharping the note.
We speak of going from a note such as C to the fourth note up (which is F) as the interval of the fourth. Pythagoras used what is called a circle of fifths to arrive at our approximate musical scale by using the interval of the fifth over and over again until he had every note in our chromatic scale. If we start with C and go a fifth up we have G, a fifth up from G gives us D, a fifth up from D gives us A, and so on. We wind up with the following order which contains every note in the scale but out of normal sequence: C, G, D, A, E, B, F#, C#, G#, D#, A#, F and C again. This sequence is also called the transposition pattern" because it allows us to see how to treat a piece of music when we wish to change it from one key to another (called transposing).
When we go up one fifth (as discussed in the foregoing paragraph), we reduce the frequency to 2/3 of the one with which we start and go 7/12 of the distance around our musical circle. When we go up one fourth, we reduce the frequency to 3/4 of the one with which we start and go 5/12 of the way around our musical circle. When we go up a third, we reduce the frequency to 4/5 of the one with which we start and go 1/3 of the way around our musical circle. Confusing? Yes!
Then we have the diminished third which we also call the minor third, and the diminished seventh which we also call the minor seventh. And we haven't even begun to discuss chord names. Remember this, all of it. There is a test on it in the next article. | 
