Scales
As we know, there are 12 tones in each octave (e.g., between 110 Hz and 220 Hz). Usually, we do not need all 12 tones in one composition. We choose a smaller set of 5, 6, or 7 tones out of 12. This smaller set of tones (and a method for building that set) is called a scale.
Major Scale
Almost all music is created using major scales. It is a set of seven tones out of 12. We start by choosing a key tone (e.g., a tone of G for the G major scale, also called the Key of G Major) and add six more tones using this pattern:
0 2 4 5 7 9 11
To build the G major scale, we need these tones: G, A, B, C, D, E, F#. Below, you can see a "template" of the major scale. Drag it to any key, e.g. to D#3, to see which tones belong to the D# major scale.
Observation
- white piano keys correspond to the C major scale (C D E F G A B)
- piano was built to make it easy for people to play the C major scale (by ignoring black keys)
- major scales other than C always have at least one tone with "#" in its name (black key)
As we can see, a major scale is just a "template" for picking 7 tones, which can be placed at any location (any key tone). When we have the C major scale, and we want to create the E major scale, we can just move each tone four semitones higher: C, D, E, F, G, A, B turns into E, F#, G#, A, B, C#, D#.
When a song is too high to sing for a singer, the singer can sing it one octave lower (the scale of the song will stay - a band keeps playing the same music). They can also shift (transpose) it, e.g., only four semitones lower, but then, the key (scale) changes! E.g., the D major scale becomes the A# major scale after shifting four semitones lower (A#+4 = D).
Chords in a Scale
As we said, for a musical piece, we choose a set of 7 tones (a major scale), which we can use in that piece. But we also want to play some major or minor chords. Can we even make any chords, when we are restricted by the scale?
Yes, we can build exactly 3 minor chords and 3 major chords inside any major scale! Let's write a "diagram" for chords inside a major scale!
Within the C major scale, we can create these six chords: D minor, E minor, A minor, C major, F major, G major. These are the only chords that don't have any "sharps" (black piano keys) in them.
Renaming Intervals
Thousands of years ago, musical instruments could play only the C Major scale, with tones C, D, E, F, G, A, B. When talking about intervals, people simply counted these tones from C. The first interval was C (C to C = 0 semitones), the second interval was D (C to D = 2 semitones), and so on.
| Step | as semitones | English | Italian |
|---|---|---|---|
| C to C | 0 semitones | First | Prima |
| C to D | 2 semitones | Second | Seconda |
| C to E | 4 semitones | Third | Terza |
| C to F | 5 semitones | Fourth | Quarta |
| C to G | 7 semitones | Fifth | Quinta |
| C to A | 9 semitones | Sixth | Sesta |
| C to B | 11 semitones | Seventh | Settima |
| C to C | 12 semitones | Eighth | Ottava |
Finally, we know why 12 semitones are called an octave! You need to touch eight white piano keys to move from one C key to the next.
When people realized that it is useful to have 12 tones instead of only 7 C major tones, they had to create names for the "missing intervals". E.g., one semitone was named a "Minor Second", three semitones were named a "Minor Third", and so on.
Also, people had to make names for the five new tones (e.g. a tone between C and D), so they used the "#" symbol, which has been used for "moving up by a semitone". Also, a symbol "♭" can be used, which means "moving down by a semitone". So C# = D♭, D# = A♭ and so on.
Chord Names
When we talked about chords, we mentioned the Suspended Second chord (0,2,7). It is named this way because the interval between the first two tones is the second (Seconda). Similarly, in the Suspended Fourth chord (0,5,7), the interval between the first two tones is the fourth (Quarta). Lastly, the Major Seventh chord (0,4,7,11) is the major chord, with the new tone that is the seventh (Settima) from the root.
Other Scales (optional)
Scales can be analyzed scientifically, e.g. by the number of tones from the octave:
- pentatonic - 5 tones
- hexatonic - 6 tones
- heptatonic - 7 tones (e.g. the Major scale)
A scale can be described by the distance of each tone from the root, e.g. for the Major scale, we get (0, 2, 4, 5, 7, 9, 11) or by "gaps" between consecutive tones, e.g. for the Major scale, we get (2, 2, 1, 2, 2, 2, 1) - the sum of numbers must be 12 (the octave).
There are many ways to pick 5, 6 or 7 tones out of 12. We usually try to pick them as evenly as possible. E.g. a pentatonic made of F,F#,G,G#,A is not very useful, because we get a huge gap between A and the next F (a 8 semitone gap). All five gaps are 1,1,1,1,8 (sum is 12).
Diatonic Modes
A heptatonic scale is described by a list of any seven numbers (gaps), which add to 12. Simple math: there must be at least two 1s in such a list (if we had just one 1-semitone gap, there would be six gaps of 2 or more semitones, a total sum would be 13 or more).
We want to place tones as evenly as possible (all gaps the same, ideally). But all gaps cannot be the same (for seven 1s, the sum would be 7, for seven 2s, the sum would be 14 and even bigger for seven 3s, 4s ...).
The "most equal" gaps we can get are two 1s and five 2s: 1,1,2,2,2,2,2. We try to place 1s as eveny as possible (with two or three 2s between them).
Such a scale is called a diatonic scale and there are exactly seven ways to make it (modes), with their historical names.
| Mode | Gaps |
|---|
Ionian:
The Ionian mode is also called the Major Scale. The Aeolian mode is also called the Minor Scale (if we start at A, we get A, B, C, D, E, F, G - the same tones as the C Major scale). Each mode can be made from a previous mode by taking the first gap and putting it to the end of the list. Let's name a few examples:
- C, D, E , F, G, A, B - Ionian mode with the root of C
- D, E, F , G, A, B, C - Dorian mode with the root of D
- C, D, D#, F, G, A, A# - Dorian mode with the root of C
To rewrite our music from C Ionian to C Dorian, we must replace all E with D# and all B with A#. Some minor chords become major and vice versa.
Arabic Scale
This scale has a pattern of
0 1 4 5 7 8 11 || gaps: 1, 3, 1, 2, 1, 3, 1
We can think of it as the Major scale with the second and the sixth tones lowered by a semitone.
Major Pentatonic
This scale has a pattern of
0 2 4 7 9 || gaps: 2, 2, 3, 2, 3
We can think of it as the Major scale with the fourth and the seventh tones removed.
Minor Pentatonic
This scale has a pattern of
0 3 5 7 10 || gaps: 3, 2, 2, 3, 2
We can think of it as the Minor scale with the second and the sixth tones removed.
Blues Scale (hexatonic)
This scale has a pattern of
0 3 5 6 7 10 || gaps: 3, 2, 1, 1, 3, 2
It is the Minor Pentatonic with an added "blue note" between the 3rd and the 4th tone.