Scales, Piano-centric

Despite having spent a considerable amount of time trying to learn scales, I have never liked them. The two main reasons for that are, one, they contain too many notes and, two, they are boring. They sound boring and they are boring to practice. You want to kill somebody's interest in music, tell them to go home and practice some scales.

The way music theory is usually taught, you are first presented with the different modes of the major scale. You are told that in the key of C the 'good' notes are the seven white keys on the piano, except F, the fourth, which is an 'avoid' note. So you have to memorise seven notes out of 12 (more than half of them) and then make an effort to single out one of them for special attention. Then you are supposed to go through the seven modes, which are given weird names (ionian, locrian, mixo-lydian,...) not related to any term you have ever heard of, and in each key you again have to be aware that not all notes are good notes. The 6th in Dorian, as the fourth in major, sounds a bit out on a minor chord. Just to make sure you don't know what to play on a minor chord anyway, you are told that Dorian, Phrygian, and Aeolian are all minor modes. Once you are done with the seven modes in the key of C, you can repeat the exercise in the remaining eleven keys, and along the way you can try to figure out why a specific black key is sometimes notated as a flat and sometimes as a sharp (F# = Gb for example), or, incredibly, why a white key is sometimes notated as an accidental (B = Cb). When information is presented in this way it is useless to 98% of all people who wants to learn to play an instrument, and if you are among the 2% who can work out how to use it in practice I compliment you on your intellect.

The reason music theory, including musical notation, has become so convoluted is probably that it is piano-centric. Unfortunately, the pattern of five black keys and five white keys does not lend itself easily to generalisation. Anybody who has made an attempt to learn to play the piano knows that transposing from one key to another is a mind-boggling task. However, as guitarists we can easily transpose a tune just by moving the left hand a fixed number of frets up or down the neck (assuming we stay away from the open strings). It is not nearly as difficult as on the piano. Play C7-F7 or D7-G7, it requires the same hand motion regardless of the tuning you use, because in both cases the chord moves up five semitones. It is the intervals that matter, not the starting key.

The cycle of fifths

I think the importance of the cycle of fifths is exaggerated but I will admit it has one thing going for it: it explains why keys are naturally ordered five or seven semitones apart in the same way that the individual notes are naturally ordered next to each other.

In conventional musical terminology a fifth is equivalent to 7 semitones, and a fourth is equivalent to 5 semitones. If you take any note and keep shifting it up by 5 semitones you eventually get back to where you started in 12 steps. If you start in C the sequence is C-F-Bb-Eb-Ab-Db-Gb-B-E-A-D-G-C, or in clock notation 4-9-2-7-12-5-10-3-8-1-6-11-4. So all 12 notes are represented, none are left out. If you shift down by five semitones instead of up you get the same sequence in reverse. Consequently, it is suggested that the cycle of fifths is good for practicing improvisation in all keys. Pick any chord and keep shifting the root note up or down by five semitones and you will eventually get through all 12 keys. However, the main advantage of the cycle of fifths is that it explains the occurrances of the sharps and flats in the different keys. The insight you need to understand this is that only one note changes when a major scale is shifted up or down by five semitones. Take a deep breath and have a look at the table below.

Key Major scale Sharps/Flats
B 3-5-7-8-10-12-"2" # 10, 5, 12, 7, 2
E 8-10-12-1-3-5-"7" # 10, 5, 12, 7
A 1-3-5-6-8-10-"12" # 10, 5, 12
D 6-8-10-11-1-3-"5" # 10, 5
G 11-1-3-4-6-8-"10" # 10
C 4-6-8-9-11-1-3 None
F 9-11-1-"2"-4-6-8 b 2
Bb 2-4-6-"7"-9-11-1 b 2, 7
Eb 7-9-11-"12"-2-4-6 b 2, 7, 12
Ab 12-2-4-"5"-7-9-11 b 2, 7, 12, 5
Db 5-7-9-"10"-12-2-4 b 2, 7, 12, 5, 10
Gb 10-12-2-"3"-5-7-9 b 2, 7, 12, 5, 10, and 3 (B = Cb!)

The table lists the seven notes, in clock notation, of the major scale in each of the 12 keys. As you jump from one line to the next, the key is shifted up by five semitones. The number of sharps and flats in each key, as indicated in conventional musical notation, is given in the column on the right. The key with no accidentals, C, is positioned in the middle, halfway down. The quotation marks indicate the only note that is not in the row below it. In row 3, for example, you can see that the note 12 (Ab) in A major is the only one that does not belong to the D major scale. Notice that the further away you get from C in jumps of five semitones, the less notes the shifted major scale has in common with C major. A bizarre outcome of this logic is that Gb, which is as far away from C as you can get, must have six accidentals because in the cycle of fifths it is in between Db with five flats and B with five sharps. So should it be six sharps or six flats? You tell me. There is probably a very clever and very obscure reason for preferring one over the other but I am not bothered. I have made a random choice of six flats.

An interval of six semitones is usually called a b5 (pronounced 'flat five') when it refers to chords but confusingly called #11 (pronounced 'sharpened eleventh') when it refers to notes. For example, an extension of a C major 7th chord with the note Gb six semitones away from the root is notated Cmaj7#11 and not Cmaj7b5. On the other hand, if a Gb7 chord is used instead of a C7 it is called a flat five substitution.