Lesson 12: 音程 (Intervals), Part 2

This lesson will cover more advanced topics in "intervals".

Enharmonic (異符同音) intervals

It is important to note that the interval number is determined by how the two notes are spelled. E.g. the interval between D and F# is major 3rd, but the interval between D and Gb is diminished 4th. Even though F# and Gb are the same note on the keyboard, because they are spelt differently, they need to be written differently (F is a 3rd and G is a 4th in D major). This applies not only to the upper note, but to the root as well. E.g. the interval between F# and C is diminished 5th, but the interval between Gb and C is augmented 4th.

Inversion of intervals

To invert an interval, simply raise the lower note by one octave. That will bring it above the upper note, and making the upper note the root note. After the notes are inverted, the interval between the new root note and upper note can be determined the way described before.

There is also a shortcut to determine the inverted interval. The interval number of the inverted interval is always equal to 9 minus the original interval number. What about the quality of interval? Here is the rule for inverting intervals (try to verify it yourself!):

Major becomes minor, and vice versa
Augmented becomes diminished, and vice versa
Perfect stays perfect

E.g. the interval from C to A is major 6th, so the interval number of the inverted interval (from A to C) is 9 – 6 = 3. And using the rule above, the inverted interval should be a minor interval. Therefore, the interval from A to C should be minor 3rd.

Compound interval

Up to this point, we have only considered intervals that are not more than an octave. In reality, intervals can go beyond an octave. To determine any interval that is greater than an octave, simply follow the following steps:

1. raise the root note by one octave (or lower the upper note by one octave), so that the notes are now less than an octave apart
2. determine the interval between the notes as described previously
3. add 7 to the interval number to get the actual interval

E.g. to determine the interval between C and high E, we first determine the interval from C to E, which is major 3rd. So, the actual interval is major 10th after we add 7 to the interval number.

Lesson 11: 音程 (Intervals), Part 1

The term "intervals" (音程) refers to the distance between two notes. It can also be considered as the difference in pitches (or frequency) between two notes. The concept of intervals is very important, because they are the building blocks of chords.

There are two types of intervals in music: melodic interval and harmonic interval. Melodic interval is the interval between two notes when they are played one after another. Harmonic interval is the interval between two notes when they are played simultaneously (e.g. in a chord). In both cases, the lower-pitched note is called the “root”, and the interval is always defined as the interval from the root to the upper note.

Melodic interval:

Harmonic Interval:

Calculating intervals

To determine the interval between two notes, you always start from the root and count the number of steps to the upper note. Consider the root as the “doh” of the scale, and determine which note in the scale the upper note is. E.g. to determine the interval between F and A, we start with F as the “doh” of the scale (i.e. F major), then A is “mi” (the 3rd note) in F major.

The interval number is the number of degree of the upper note in the key of the root. So, in the previous example, A is a 3rd above F, or you can say that F and A are a 3rd apart. (doh = unison, re = 2nd, mi = 3rd, fa = 4th, so = 5th, la = 6th, ti = 7th, doh’ = 8th/octave)

But the interval number alone is not sufficient to describe an interval. We need to specify the quality (型態) of interval between F and A (quality of interval). If the upper note is actually IN the major scale of the key of the root, then the interval is either perfect (純音程) (unison, 4th, 5th, octave) or major (大音程) (2nd, 3rd, 6th, 7th). Let’s look at the example again. Since A is in the scale of F major, and it is the 3rd note of the scale, so the interval from F to A is major 3rd.

For a note that is NOT in the major scale of the key of the root, you can determine the quality of interval by counting how many semitone (or half step) it is above or below the note that is in the scale. Here are the qualities of interval that are not major nor perfect:
- augmented (增音程): one semitone larger than a major/perfect interval
- minor (小音程): one semitone smaller than a major interval
- diminished (減音程): two semitones smaller than a major interval, or one semitone smaller than a perfect/minor interval.

Can you tell the intervals between the following pairs of notes? (leave your answers in the comments)
- F and Ab
- F and A#
- F and Abb

In summary, just remember that unison, fourth, fifth, and octave can be (from low to high pitch) diminished, perfect, augmented; whereas second, third, sixth, and seventh can be diminished, minor, major, augmented.