Piano Power: Intervals
Here are the answers to the intervals that I left you with last article. Check them out and make sure you understand the results before going on to the next section.
Constructing Intervals Above A Given Note
In addition to identifying intervals you should also be able to construct them above and below a given note. We’ll start by constructing intervals above a given note.
Construct a Minor 7th (m7) above B.
* By definition, we know that steps 1-7 of the B major scale (B-A#) form a Major 7th (M7).
* By definition, a Minor 7th (m7) is a half step smaller than a Major 7th (M7).
* Lowering the A# to an A gives us an interval that is a half step smaller.
* Therefore, the interval (B-A) is a Minor 7th (m7).
Construct a Diminished 7th (d7) above C.
* By definition, we know that steps 1-7 of the C major scale (C-B) form a Major 7th (M7).
* By definition, a Minor 7th (m7) is a half step smaller than a Major 7th (M7), and a Diminished 7th (D7) is a half step smaller than a Minor 7th (m7).
* Therefore a Diminished seventh (D7) is a whole step lower than a Major seventh (M7).
* Lowering the B to a Bbb gives us an interval that is a whole step smaller.
* Therefore, the interval (C-Bbb) is a Diminished 7th (D7).
At this point you may be wondering why we didn’t choose to use C-A instead of C-Bbb to represent our Diminished 7th interval. After all, they both sound the same. The answer is that music theory and intervals are not as concerned as much with sound as with the relationships of notes written on a page. Pictorially, C-A is very different than C-Bbb. The former describes some kind of sixth (C-A = Major 6th), while the latter describes some kind of seventh (C-Bbb = Diminished 7th ).
Construct an Augmented 5th (A5) above Bb.
* By definition, we know that steps 1-5 of the Bb major scale (Bb-F) form a Perfect 5th (P5).
* By definition, an Augmented 5th (A5) is a half step larger than a Perfect (P5).
* Raising the F to an F# gives us an interval that is a half step larger.
* Therefore, the interval (Bb-F#) is an Augmented 5th (A5).
Construct a Minor 6th (m6) above Bb.
* By definition, we know that steps 1-6 of the Bb major scale (Bb-G) form a Major 6th (M6).
* By definition, a Minor 6th (m6) is a half step smaller than a Major 6th (M6).
* Lowering the G to a Gb gives us an interval that is a half step smaller.
* Therefore, the interval (Bb-Gb) is a Minor 6th (m6).
Construct a Major 6th (M6) above D#.
* Since there is no D# major scale, we’ll use D major as a reference.
* By definition, we know that steps 1-6 of the D major scale (D-B) form a Major 6th (M6).
* If we do exactly the same thing to each note of the interval and still use the letter names D-B as our base, the resulting interval should still be a Major 6th (M6).
* Therefore, raising both the D and the B a half step to D# and B# respectively, results in the interval (D#-B#) which is also a Major 6th (M6).
Try completing some intervals on your own by filling in the proper notes below:
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