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# Theory Project 6: The C Major Scale

## Three Intervals

### Primes and Unisons

The distance between two notes is called an interval. The distance from one note to itself, a note of the same pitch, is a unison, as c’ to c’ or c’ to b. The distance from one note to another on the same line or space is a prime, as c’ to c’ or c’ to c’. Although there is usually no actual distance in pitch in a prime or a unison, these are not zero intervals, they are ones, so to speak. There is no zero in this arithmetic. In terms of scales, primes or unisons are not intervals at all, but in other contexts they certainly can be. In sum, for today they don’t count as intervals, but you must count them as ones, not zeroes. ☺

### Octaves

Of course the distance from any note to the next with the same name is an octave, because the span is eight notes. c to c’ is an octave: [c d e f g a b c’] Eight.

Notice again that intervals are inclusive. There is no zero interval.

### Seconds

The distance from each of the notes to the next in [c d e f g a b c’] is a second. How many seconds in an octave?

You have undoubtedly noticed that natural seconds come in two sizes. The smaller [e-f] and [b-c’], are called “minor” and the remainder which are the larger are called “major”. It is customary to refer to seconds as “scale steps” when constructing scales, so the minor seconds will be half steps and the major seconds will be whole steps.

## The C Major Scale and Its Intervals.

### Definition

For today, a scale is an ordered list of eight notes spanning an octave. The list of natural notes from c to c’ is the C Major Scale.

### Intervals

What are the intervals of a C Major scale? Here they are!

```c --> d              2nd
c ----> e            3rd
c ------> f          4th
c --------> g        5th
c ----------> a      6th
c ------------> b    7th
c --------------> c' octave
```

The notes of the major scale are generalized by names and Roman numbers. The numbers are usually used in writing and the names are used in speech, but one should know both. The Roman numbers correspond to the intervals, but they name notes, not intervals.

## Writing the C Major Scale

### With Roman Numbers

Write this scale in half notes, evenly filling about 85 % of the length of each staff. Each note should have its Roman number above it. (The extra space will be for writing key signatures.) On the following system, write downwards, c’ to [c], with the Roman numbers above each note, in reverse order of course.

```I   II  III IV  V   VI  VII I
c'  d'  e'  f'  g'  a'  b'  c''
```

### With General Names

Take another page and write the notes again without the numbers. On both the rising and descending scales, the first and last notes are the tonic, or tonus if you prefer Latin. The fifth note up, V, is called the dominant. (The term came from Gregorian chant, but now the importance of the names and numbers relates to chords and chord construction.) The dominant, not the tonic, is the most important note of a scale. Label that note as the dominant, or just “dom” if you like, on every instance in the rising system. On the descending scale the fifth note down, IV, is the subdominant. Label those “subdom” for short if you like, on the descending scale. Halfway to the dominant is the mediant, “med”. Halfway to the subdominant is the submediant. Label those. In the lower system, immediately below the tonic, I, is the subtonic, VII. In the upper system, the note immediately above the tonic, II, is the supertonic. If the subtonic is a minor 2nd below the tonic, as it is in the major scale, then the subtonic is also a leading tone. Write (leading tone), in parentheses, above or below “subtonic”.

Now, after taking in how simple it all is, fill in all of the blanks so that every note has its names and numbers.

### Test Yourself

```Roman      General Note
numeral    Name
-----------------------
I          tonic
VII        ?
VI         ?
V          ?
IV         ?
III        ?
II         ?
I          ?
```

Try it upside down too. Don’t just look at it, write it out.

## Scale steps completely define the major scale.

Here are the scale steps of a C Major scale. The whole steps are w’s, the half steps are h’s:

```  w   w   h   w   w   w   h  <-- Seven scale steps in the octave
/ \ / \ / \ / \ / \ / \ / \
c   d   e - f   g   a   b - c' <-- Eight notes in the octave
```

Again, which natural notes are a half step apart? You have to know that, forever. Remember it. Most of traditional music theory is simply dealing with that.

Write your C Major scale up and down on two systems as before. Bracket and label the scale steps as above, both up and down. Put the names E, F, B, and C to the right notes also, in their correct register, that is, punctuated.

## Step Scheme

w-w-h-w-w-w-h is called the step scheme of a major scale. Some theory books start with an ancient Greek major tetrachord, wwh, and consider the major scale to be two of those joined by a whole step: wwh-w-wwh. The historical connection is tenuous, to say the least, but it doesn’t hurt to know it.

(todo: perfect or greater perfect system optionally??)

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