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II.2Part II, Scales and Intervals
Diatonic and Chromatic Half Steps
By the end of this lesson, you'll know how to divide a whole step, and how to tell the diatonic half step from the chromatic half step.
7 min7 questionsDanhauser § 70 to 73
Dividing the whole step
A whole step can always be divided into two half steps (§ 70). Between two notes a whole step apart, C and D for example, you can sound an in-between pitch. From C to that pitch is a half step, and from that pitch to D is another half step.
There are two ways to get this in-between pitch:
You can raise the lower note with a sharp, which gives C♯, since the sharp raises a note by a half step.
You can lower the upper note with a flat, which gives D♭, since the flat lowers a note by a half step.
Two ways to write the in-between pitch between C and D.
Two kinds of half steps
Now let's look closely at the half steps themselves. The diatonic half step, or diatonic semitone in the UK, lies between two notes with different letter names, that is, from one degree to another: E to F, B to C, C♯ to D, or C to D♭ (§ 71).
The chromatic half step, or chromatic semitone, lies between two notes with the same letter name, one of them altered, that is, from a degree to the same degree altered: C to C♯, D♭ to D, or F to F♯ (§ 72).
The order of the two half steps
So a whole step always contains two half steps of different kinds, one diatonic and the other chromatic (§ 73). Their order depends on the sign you use:
If you go from C to D by way of the sharp, C to C♯ is chromatic, and then C♯ to D is diatonic.
If you go from C to D by way of the flat, C to D♭ is diatonic, and then D♭ to D is chromatic.
The chromatic half step keeps the same letter name; the diatonic half step changes it.
Exercisein the method's spirit
For each pair of notes, write the sharp note and the flat note that give the in-between pitch, a half step from each: C and D, D and E, F and G, G and A, A and B.
Solution
Between C and D, you can write C♯ or D♭; between D and E, D♯ or E♭; between F and G, F♯ or G♭; between G and A, G♯ or A♭; and between A and B, A♯ or B♭.
Exercisein the method's spirit
State which kind of half step lies between these neighboring notes.
Solution
G to G♯ is chromatic, B to C is diatonic, A♭ to A is chromatic, F♯ to G is diatonic, and D to E♭ is diatonic.
You may have noticed that C♯ and D♭ fall on the same piano key. The next lesson explains why. For now, try the quiz.
Check your understanding
7 questions
1.
From C to C♯, the distance is a:
2.
From E to F, the distance is a:
3.
What kinds of half steps does a whole step contain?
4.
Going from C to D by way of D♭, which half step comes first?
5.
What kind of half step do these two notes form?
6.
What kind of half step do these two notes form?
7.
Between G and A, the in-between pitch can be written as:
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