Choosing a family or team of notes for a major scale is similar to choosing a football team from a group of friends (in this case we are going to choose the best seven team members from our group of twelve different notes).
A simple definition of a major scale would be that you take one note* and choose the six notes which are most strongly related to it, to make a self-supporting team of seven. We know that the secret of good harmonies is to use notes with simple relationships between their frequencies so that the pressure ripples join together to make a regularly repeating, even pattern. We can achieve these simple relationships if the strings on our harp have lengths with simple fractional relationships such as or ¾. We have already seen that you can’t make a good scale system from these fractions but they do give us the best harmonies.
But our John Powell Ugly Harp is not tuned to simple fractional string lengths; it’s tuned using the ET system by taking a certain percentage off the length of each string. “Oh Woe!” you might say, “All is lost!” But do
not despair—go and get yourself a calming cup of milky tea and I’ll tell you about a handy coincidence.
To create our thirteen-string harp to cover one octave using the ET system, we progressively reduced the length of each string by about 5.6 percent. Luckily this happens to give us a situation where a lot of the thirteen strings are almost exactly simple fractions of the length of the longest string. For example, if we call the longest string number 1, then string number 6 will be 74.9 percent as long as string number 1, which is very close to 75 percent—which is three quarters. The other strings also have lengths which are close approximations of simple fractions. These approximate fractions are so close to the real thing that the harmonies still sound good. For the rest of this chapter I will refer to the string lengths of our harp as fractions of the longest string length. Please remember that I do not mean the exact fraction—I am referring to its close approximation, which we arrived at using the ET system.
Fortunately, the ET choice of string lengths on our thirteen-string harp includes six strings which are a very good match for those used to produce a pentatonic scale—and the pentatonic scale is an obvious starting point if we are trying to create a seven-note scale of strongly related notes. So now we can draw our harp with just these notes and see what it looks like. In the illustration below I have labeled each string with its length and frequency as compared to the longest string so you can see that everything is as we want it—only simple fractions are involved.
The initial choice of notes for our major scale are the notes of the pentatonic scale. Their lengths and frequencies are shown as a fraction of the longest string.
The pentatonic harp in this illustration looks fairly useful, but both our ears and eyes tell us that there are two big gaps: one between strings 3 and 4 and another between strings 5 and 6. The obvious thing to do to increase the number of notes in our scale is to put one string in each of these gaps—but we have to choose between two possible strings in each case.
Let’s look first at the gap between strings 3 and 4. The strongest candidate with the best link with the rest of the group is the longer of the two—because it produces a note which is 1 times the frequency of the longest string.
To fill the gap on the right-hand side we choose the shorter of the two possible strings. It gives a note which is 1 the frequency of the longest string—a good team member—and it also gives us an “almost there” feel
to the final part of the rising scale, like this:
String 1 2 3 4 5 6 7 8
(Home) (Closest
relative)
(Almost there)
(Home again) Once we add these two strings to our scale, our harp looks like this:
The complete major scale of notes chosen from the original thirteen strings. We have added two more team members to the original pentatonic set.
When the “almost there” note appears in the melody or the harmony it makes a fairly clear demand to get “there,” so the listener has a feeling that the next note should be the key note. In fact, this effect is so strong that the technical term for the “almost there” note is the leading note, because it leads us on to the key note. Whenever we hear the leading note
we build up an expectation of returning home to the key note. This anticipation–resolution effect is used a lot in phrase endings, although sometimes the composer might deliberately frustrate our expectations to make life more interesting. The reason why the punctuation of phrases is vaguer in the case of pentatonic music is because there is no “almost there” note in a pentatonic scale.
I’m using the words “phrase” and “punctuation” here in exactly the same way we use the terms when we are discussing written language.
Music has commas, periods, and paragraphs, and uses them in the same way as a storyteller does. The technical term for any phrase ending in music is a cadence.
You will notice that there are now only two sizes of gap (or interval) between adjacent notes on our eight-string harp: either the strings are next to each other and therefore a semitone apart; or they are separated by the gap and are therefore two semitones (one tone) apart. Starting from the lowest note in the octave and calling out the names of the intervals between the notes, we would say: Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. Rather than continue writing out this stream of words, I will, from now on, use just the initial letters: TTSTTTS.
To create our major scale we have taken the strongest group of all, the pentatonic scale, and added two more members, one of which (the leading note) helps to strengthen the punctuation of the music. This addition of two members to our team has also given us a tremendous increase in the combinations of notes available for harmonies, without overstepping the barrier of having too many notes for our memories to cope with—a bargain all around, I think you will agree.
The only drawback to the use of major keys is that there is a continuous tendency toward definite, complete statements. Major key music sounds rather self-confident, and sometimes we want the music to be less cocky. In those situations we use minor keys as well.