Interval

Definition

Interval describes the relative distance in pitch between two musical notes.

Properties

1. An interval is always measured from the lower sounding note to the higher sounding note, regardless of their chronological sequence of appearance.
2. Intervals have two properties: quantity and quality. When combined, quality appears before quantity.
3. Quantity is the measurement of distance between the alphabet of the two comparing notes, starting with the starting note as 1, adding 1 for each different alphabet (octave sensitive) it goes through after landing on the targeting note.

• In English, quantity is named as positions with the exception of the first as unison and the eighth as octave.

4. Quality marks the offset an intervalic quantity deviation from the major scale built upon the lower note. The naming scheme is as followed:
5. For interval with quantity of 1, 4, and 5, when wrapped into an octave, the quality matching that of the major scale is called a perfect interval.
6. For the rest of the quantities - 2, 3, 6, and 7 with their equivalence beyond one octave, if the pitch name equals to the same degree from the major scale, the quality of the interval is a major one.
7. Those with a semitone lower from the major interval is called a minor interval.
8. Extending the range of the qualities from above, intervals with a semitone higher than the norm is named augmented, and diminished for the lower counterpart.

Explanation

If you ever encounter any school of teaching regarding intervals telling you to count numbers of semitones, make your best effort to run away from it as fast as you can and never look back. Okay, that’s a bit of an exaggeration. But the truth is, the number of semitones between two notes is the absolute distance, although related to intervals, does not have the same context. It’s like introducing the one next to you as a person n years above or below your age, rather than introducing as your spouse. In music composition, we rarely care for absolute distance, because it does not contain the connotation and motivation behind the notes. To understand the connection between musical pitches, we need to separate quality from quantity.

Quantity, the distance between the alphabets of two pitches, is used to describe an approximated distance of pitch, the aural sensation of pitch difference, being either a step (second) or a leap of various size - small (thirds and fourths), medium (fourths and fifths), large (sixth, seventh, octave), or disjoined (beyond an octave). This approximation persists even after sharpen or flatten a member of the interval. Thus intervals with the same quantity, meaning notes from the same scale degree, can be interchanged for musical purposes.

Quality, however, is used to indicate their musical relationship. This will be explained in details when we get to counter-point and harmony. For now, let us focus on distinguishing the the quality of various quantities.

The key to learning and internalizing intervals is to remember that all of them are based on the major scale of the lower note. Then by finding the deviation from the scale degree matching the intervalic quantity, we can apply the rule of alternation to derive its quality. Let’s break that up into steps with the following examples

Examples

E to G

1. We see that the lower note is E, thus we look up E major scale with method described in the Major Scale Article to get the following notes: E F# G# A B C# D#. It takes some time initially, but as we become more familiar with the process, we will naturally internalize all major scales.
2. Then find the scale degree that contains the same alphabet as the higher note of the interval. In this case, we count 1E 2F 3G, therefore G(#) is the third degree in E major scale. This is the quantity of the interval.
3. Now look for the quality. The target note G is a semitone lower than G#. Since the quantity is a third, we look up 4.3 in the properties section, stating that when quantity is 2, 3, 6, and 7, a semitone lower than the major scale is called a minor interval.
4. Combine quality with quantity, we realize that E to G is a Minor Third interval.

Ab to Db

1. The lower note is Ab, so look up Ab major scale: Ab Bb C Db Eb F G.
2. In the Ab major scale, find the degree containing the alphabet D. We count 1A 2B 3C 4D. Thus the fourth.
3. Db is identical to the target note. And since the quantity is a 4, we look up 4.1 and find that the term for such quality is perfect.
4. Combine quality with quantity, Ab to Db is a Perfect Fourth interval.

C# to Bb

Let’s speed this up.

1. C# major: C# D# E# F# G# A# B#. (Or C major with all notes sharpened).
2. 1C 2D 3E 4F 5G 6A 7B, so the seventh.
3. The seventh is a major interval. However Bb is two semitones lower than B#. We know from 4.3 that one semitone lower than major interval is a minor interval. We also know from 4.4 that another semitone lower than that is called a diminished interval.
4. Result is Diminished Seventh.

Another way to solve this.

1. Look at C major: C D E F G A B.
2. We can also count backwards since octave repeats, 1C 7B.
3. 7B is major. Thus Bb a semitone lower is the minor seventh. However since the lower note C# is a semitone higher than C, we have to further decrease the distance between these two notes. Thus making a minor interval diminished.
4. Result is again Diminished Seventh.

More Examples

1. F ascending to B. F G A Bb C D E. 1F 2G 3A 4B, a fourth. B is a semitone higher than Bb, thus an augmented fourth.
2. G# ascending to E. G# A# B# C# D# E# Fx (double sharp). 1G 2A 3B 4C 5D 6E, a sixth. E is a semitone lower than E#, thus a minor sixth.
3. D descending to C#. Same idea but start with the lower note C#. C# D#… 1C 2D. D - D# = -1 (meaning a semitone lower). Thus minor second.
4. For intervals above an octave, reduce the octave first, then add 7 to the quantity. Bb ascending to G# an octave higher. Bb C D Eb F G A. 1B 2C 3D 4E 5F 6G. Add 7 to 6 and we get quantity of thirteen. G# - G = 1, sharpen a major interval and we get augmented. Thus augmented thirteenth, or an octave and an augmented sixth.