I would advise all students to continue to pay special attention to the Oddballs, Bb Major and B Major. My students learn Db, Eb, Gb and Ab Major rather quickly but often continue to miss Bb Major and B Major.
Note: More advanced students will understand that there are two ways to write any major triad when both the bottom key (the root) and the top one are black keys. I have chosen to write all of them using flats, but sharps are also possible. I will cover the “sharp problem” next, as a separate entry, for those who are interested.
An interval is a measurement of the distance between two pitches. For keyboard players:
- Harmonic intervals are two pitches that are played at the same time; when notated, the pitches are shown vertically.
- Melodic intervals are two pitches that are played successively; when notated, their pitches are shown horizontally.
Here we are only measuring harmonic intervals.
To measure an interval we need to find:
- Its number (also called diatonic number).
- Its size or “bigness”.
To determine the number of an interval, we count the letter name of the bottom pitch and the upper pitch plus all letters skipped. For example, a C—G is a “5th” because we count C and G plus the letters skipped: C D E F G. The total is five. E—D is a 7th: E F G A B C D.
Keyboard players simply use the letter names of the white keys in place of pitches to get the interval number.
(Note: When two people either play or sing the same pitch, that pitch is called a “unison”. However, the same term is used when only one key is pressed. For example, if only F is played, that is called a unison. No measurement is necessary for a unison. It “is what it is”.)
All intervals other than unisons and octaves have two sizes, and for the moment I will simply say that there are big and small intervals. For instance, there are big 2nds and small 2nds, big 3rds and small 3rds, and so on. On a keyboard we can compare “big” and “small” by counting the number of black keys skipped. C—E is a third, and so is D—F. But C—E skips two black keys. D—F skips only one. So C—E is a big third; D—F is a small third.
(Note to advanced students: the “quality” of an interval is determined by the words “Perfect”, “Major”, “minor”, “augmented” and “diminished”. It is my habit to capitalize “Perfect” and “Major”. It is the quality that makes measurement of the interval precise. Those terms will be covered later. At the moment we are only concerned with the number of an interval and its “bigness”.)
When an interval is “flipped”, it forms the ”complement of an interval”; the number of the two intervals always adds up to nine.
For example, when a 5th is flipped, it becomes a 4th. When a 7th is flipped, it becomes a 2nd. And so on…
When a big interval is flipped, it becomes a small one. Examples:
- F—A is a large 3rd. A—F is a small 6th.
- E—F is a small 2nd. F—E is a large 7th.
(Note to advanced students: So far we are only using only white keys to define the lower and upper pitches of intervals. This gives us the interval number, and we are counting black keys skipped to measure size or “bigness”. Later, we will see that sharps and flats also change the size of an interval, and those are also used to name the inverval quality.)
Here the major triads that are checked are correct and preferred.
Those that are blue are slightly less common but are still used often.
Those that are red and marked with an “X” are not incorrect, but they are rare and appear in complicated music with difficult modulations. We avoid using them unless we have no other choice.
Note to advanced musicians: Gb Major and F# Major are both checked as preferred because they represent two keys that are equal in number of sharps or flats in the key signatures in which they are tonic triads.
The key of Gb has six flats. The key of F# has six sharps.
Cb Major/C# Major are tonic triads in keys that have seven sharps/seven flats. Music is written in these keys, but generally musicians choose the keys of Db Major/B Major, which have five flats/five sharps and are thus easier to read and simpler to notate.