Ok. Brace yourself and sit comfortably, this is going to take a while.
What exactly is a scale?
Quite simply it is a sequence of intervals leading in steps from one pitch to another – hence the name “scale” which is Italian for “ladder” or “staircase” (Scalla).
So one way to go from C to C one octave higher is by playing (on the piano) every single note (black and white keys) until you get there. This is the chromatic scale, and the “size” of the step is a half-tone. On the piano, this is the “ladder” with the smallest possible step. You could also try to get there with steps one-tone in size (C – D – E – F# - G# - A# - C) which is the whole tone scale. One interesting fact about these two scales, is that there is really one chromatic scale – no matter which note you start, it is always the same notes. With the whole tone scale, you can only have two possibilities (C# - D# - F – G – A – B being the other one). However, if you have an
unequal pattern on the size of steps, like for instance in the major scale (tone – tone – halftone – tone – tone – tone – halftone), you will have 12 different scales - that is each note of the piano generates a different major scale.
Does this mean that by altering the specific pattern of tones semitones I get different scales? Exactly.
Now let us go back in time. In Medieval times there were no black keys. The only scale around was C-D-E-F-G-A-B-C. It was not called C major either. This came much later. All that musicians knew was that the peculiar sound they got out of that scale was due to the peculiar sequence of tones and semitones. So they had seven “scales”:
CDEFGABC – with pattern – 1 – 1 - ½ - 1 – 1 – 1 – ½ (Ionian)
DEFGABCD – with pattern – 1 - ½ - 1 – 1 – 1 – ½ - 1 (Dorian)
EFGABCDE – with pattern – ½ - 1 – 1 – 1 – ½ - 1 - 1 (Phrygian)
FGABCDEF – with pattern – 1 - 1 – 1 - ½ – 1 – 1 – ½ (Lydian)
GABCDEFG – with pattern – 1 – 1 - ½ - 1 – 1 – ½ - 1 (Mixolydian)
ABCDEFGA – with pattern – 1 - ½ - 1 – 1 – ½ - 1 - 1 (Aeolian)
CDEFGABC – with pattern ½ - 1 – 1 – ½ - 1 – 1 - 1 (Locrian)
To our ears, these “scales” – or to give their proper names “modes” – do not sound like scales at all. In fact they sound like nothing, just some random melodic fragment. Yet, in medieval times, a mode like the Dorian (from D to D) would have been far more familiar than the C major scale (Ionian mode).
For several reasons that are not important for this issue, by the end of the 16th century, most of the modes had fallen into disuse, except for the Ionian (our major scale), and the Aeolian, which is formed by playing the notes of the major scale, but starting and finishing on the sixth degree (the submediant). Hence, if you have a C major scale and play it but starting and finishing on A, you have the Aeolian mode, or
natural minor scale. Even though it has all the notes of C major, it sounds very different because
the sequence of tones and semitones (the steps of the ladder) has been dramatically altered:
CDEFGABC – with pattern – 1 – 1 - ½ - 1 – 1 – 1 – ½ (C major scale)
ABCDEFGA – with pattern – 1 - ½ - 1 – 1 – ½ - 1 - 1 (natural A minor scale)
In comparison, a scale like Gb major which
has no notes in common with C major except for the F will sound exactly the same because the pattern of tones and semitones is exactly the same:
GbAbBbCbDbEbFGb - with pattern – 1 – 1 - ½ - 1 – 1 – 1 – ½ (Gb major)
Natural as the Aeolian mode may be, it presented a serious problem: the distance of its leading note (7th degree) to the tonic was a full tone, when compared to the Ionian (major scale) mode, whose leading note was just a semitone away from the tonic. This is important in terms of melody, because the strong feeling of movement from B (leading note) to C (tonic) in C major, is basically a consequence of how close they are. On the A minor natural scale, on the other hand, the leading note (G) is a full tone away from the tonic, creating far less of a pull towards the tonic.
By the 17th century, musical theoreticians decided to sharp the leading note of the natural minor scales to create the desired attraction between its leading note and the tonic. And since this “sharpening” was completely artificial and had no grounds on the genesis of the scale (form the Aeolian mode), it was considered an “accidental”, and therefore was not included in the key signature of the piece. So now we have:
CDEFGABC – with pattern – 1 – 1 - ½ - 1 – 1 – 1 – ½ (C major scale)
ABCDEFGA – with pattern – 1 - ½ - 1 – 1 – ½ - 1 - 1 (natural A minor scale)
ABCDEFG#A – with pattern – 1 - ½ - 1 – 1 – ½ - 1+1/2 - ½ ( modified A minor scale in order to create a semitone between leading note and tonic)
This solved the problem of the distance between the leading note and the tonic, but created another problem: by pushing the leading ntoe towards the tonic, they increased the gap between the submediant (6th degree) and the leading note, which was now 1 tone and a half. So again – and promising never to meddle with it again – seventeen century theoreticians sharped the submediant, and that produced a satisfyingly uniform pattern:
ABCDEF#G#A – with pattern – 1 - ½ - 1 – 1 – 1 - 1 - ½ ( Melodic A minor scale, ascending)
Now in the 17th century, European music was mostly concerned with polyphony, that is, the weaving together of several melodic lines. So the aim here was melody. Hence the criteria to change the scale were
melodic (providing a strong pull between leading note and tonic, creating a pattern of intervals with more or less regular intervals without large jumps and so on), and so this modified Aeolian mode was called a “melodic” minor scale. And because the priorities were melodic, these modifications were important only when ascending the scale (it is important that the leading note “leads” to the tonic, but there is no such importance the other way around: the tonic is not required to “lead” anywhere). Because of that, the Aeolian mode was modified only when going from leading not to tonic. When going down (descending scale) from tonic to leading note, they just left the Aeolian mode unmodified (that is the natural minor scale):
CDEFGABC – with pattern – 1 – 1 - ½ - 1 – 1 – 1 – ½ (C major scale)
ABCDEFGA – with pattern – 1 - ½ - 1 – 1 – ½ - 1 - 1 (natural A minor scale)
ABCDEF#G#A – with pattern – 1 - ½ - 1 – 1 – 1 - 1 - ½ (Melodic A minor scale, ascending)
AGFEDCBA – with pattern – 1 - ½ - 1 – 1 – ½ - 1 - 1 (Melodic A minor scale descending = natural A minor scale)
Since all these modifications were completely artificial and had nothing to do with the scales and their derivation proper (as modes), these sharps are not represented in the key signatures. This means that a major scale and its
relative minor scale – that is the Aeolian mode (or mode derived form the sixth note of the major scale), have exactly the same key signature, because originally (before 17th century theoreticians started meddling with them) they
were the same scale, just starting and ending on different notes.
By the 18th century however, harmony – which before was simply a consequence of having more than one melodic line at the same time – started acquiring a life of its own. Chords were codified and the very important step of realising that an inversion was still the same chord had happened. While before intervals were the important concept now chords and chord progressions became all the rage. Counterpoint and many of its demands and rules on melodic lines gave way to a single melodic line and an accompaniment (the “gallant style”). From that point of view, it does not really matter if there are large or small gaps from one note to the next to the scale, but rather which chords can we form from each note of the scale. While the fifth degree (dominant) of a natural minor scale will produce a minor chord (in A minor natural, the 5th degree E, will produce the E minor chord: EGB), the fifth degree of a modified minor scale will produce a major chord (in A minor: E major: EG#B). I will leave for you on homework to work this out to the melodic minor scale, but you probably can predict that several different chords will be produced depending on its being ascending or descending. This complicates harmonic thought, no matter how useful it is in terms of melody. And since by the 18th century harmony was more and more prevalent, the modified version of the A minor scale was reintroduced as an “harmonic” form:
ABCDEFG#A – with pattern – 1 - ½ - 1 – 1 – ½ - 1+1/2 - ½ (Harmonic minor scale: the same ascending and descending).
This is the form prevalent in most piano music, simply because polyphony took a different course in the 17th century. Musicians who play medieval and renaissance music are of course thoroughly familiarised with modes and melodic minors. Of course you can still see them in much piano repertory, but who bothers to do an analysis of a piece showing the underlying scales and the modes being use by the composers? In fact, much post-romantic and contemporary music (especially against minimalists, Satie, Debussy, Hovhaness, and so on use modes and alternative scale systems extensively)
So, we have the major scale, the natural major scale (the old Aeolian mode - exactly the same notes of the major scale but starting and finishing on the 6th degree), the harmonic minor scale (a modified form of the natural minor scale where the leading note is sharped) and the melodic minor scale (a modified form of the natural minor scale where both the 6th and 7th degree are sharped when ascending, but which reverses to the natural minor scale when descending – all this for melodic considerations). These scales sound very different because the pattern of tones and semitones are different – contrary to major scales which sound all the same because they share the same pattern of tones and semitones albeit with different notes.
And that is pretty much it. But where does that leave the C minor scale? I am afraid nowhere. The C minor scale is unrelated to the C major scale. The fact that they have many notes in common and most of the chords is a pure coincidence (although expected mathematically if you bother to do the homework). The C minor scale is the relative minor of Eb major, a scale with 3 flats in its key signature, and therefore quite far from C major (which has none). The natural C minor scale – like Eb major – has the same three flats (in fact all the notes are the same). It is only when modified artificially by the sharping of its 6th and 7th degrees that most of the notes become common, and only when ascending. Check it out:
C – D – E – F – G – A – B – C – (C major)
C – D – Eb – F – G – Ab – Bb – C (C minor natural or melodic desc.)
C – D – Eb – F – G – Ab – B - C (C minor harmonic)
C – D – Eb – F – G – A – B – C (C minor melodic ascending)
Why do people then relate both of them? C minor is what is called a
tonic minor meaning that both C major and C minor start on the same note (share the same tonic). This has many implications in
tonal music, including a frequent modulation from C major to C minor. Everything that is used often soon becomes well known even if people don’t quite know why. It is a bit like a C6 chord (CGA). Of course, properly speaking there is no C6 chord. What there is, is an inverted, incomplete A minor 7th chord (ACEG). But try telling that to your pop musician friend strumming his C6 in the guitar. It becomes a mnemonic which is mostly mechanical without much real relationship to the historical evolution of the musical structure.
So, personally I always teach minor scales as relative minors, never as tonic minors, and I always show the derivation from the modes. Part of the scale work should include free modal improvisation, since there is no better way to get oneself acquainted with all these concepts.
I hope this helps.
Best wishes,
Bernhard.
PS: In regards to your musical examples, remember that theory always comes after composition. Most likely CPE Bach and co. were not aware that they had to conform to this or that scale form! (Or they were aware and were deliberately “breaking the rules” a favourite past time of Beethoven
)
Topic: Teaching scales, especially minor scales