This post is a diversion from Bowing Technique 101, which will continue soon. I recently gave an introductory harmony lesson and thought I’d share it here. Although this does not relate specifically to cello playing, I have always found that an understanding of harmony and chords greatly enhances the study of any repertoire, especially when it comes to the interpretive stage of learning the music.
This lesson deals with the triads and seventh chords found in the key of C major. The chord labels (based on the baroque system of figured bass or Basso continuo) are relevant to the triads and seventh chords of all major keys, making it a wonderfully diverse system. As the building blocks of music harmony, chords are best studied in their simplest form in order to understand their use in music. So without further ado, I present to you An Introduction to Chords in Music!
I like to think of the melodic minor scale as the chameleon scale as it changes its colours. The ascending scale creates more tension by sharpening the sixth and seventh steps, and the descending scale relaxes that tension by flattening the seventh and sixth steps. The sequence of intervals for the ascending scale of A melodic minor is as follows:
Step 1 – 2 (a – b): whole tone
Step 2 – 3 (b – c): semitone
Step 3 – 4 (c – d): whole tone
Step 4 – 5 (d – e): whole tone
Step 5 – 6 (e – f#) whole tone
Step 6 – 7 (f# – g#) whole tone
Step 7 – 8 (g# – a) semitone
The descending half of the melodic minor scale is identical to that of the natural minor scale:
Step 8 – 7 (a – g) whole tone
Step 7 – 6 (g – f) whole tone
Step 6 – 5 (f – e) semitone
Step 5 – 4 (e – d) whole tone
Step 4 – 3 (d – c) whole tone
Step 3 – 2 (c – b) semitone
Step 2 – 1 (b – a) whole tone
So the ascending scale shares its first five steps with the natural and harmonic minor scales, and its sixth to eighth steps with its major counterpart (note: the major key with the same keynote and NOT the relative major). As already mentioned, the descending melodic minor scale is identical to the descending natural minor scale. We now know that harmonic minor scales form the harmonic basis of minor keys, so it stands to reason (and the name suggests) that melodic minor scales form the melodic basis. The raised sixth step prevents the dissonant augmented second interval found in harmonic minor scales and the raised seventh provides a strong resolution from a leading tone to the tonic. Since descending passages don’t require the tension and definition provided by a leading tone, the descending melodic minor offers a sound truer to the overall minor structure.
The diagram below shows the structure of A melodic minor ascending on the keyboard:
Here’s a video diagram showing the lowest octave of A melodic minor ascending and descending on the cello.
Now that we have studied the natural minor scale, we will look at and listen to the harmonic minor scale. The sequence of intervals in A harmonic minor is as follows:
Step 1 – 2 (a – b): whole tone
Step 2 – 3 (b – c): semitone
Step 3 – 4 (c – d): whole tone
Step 4 – 5 (d – e): whole tone
Step 5 – 6 (e – f) semitone
Step 6 – 7 (f – g#) augmented second¹
Step 7 – 8 (g# – a) semitone
The only difference between the structure of the harmonic minor scale and the natural minor scale is the seventh step, which is raised in the harmonic minor to create a leading tone². This means that there is an unusually large and dissonant interval between the sixth and seventh steps – an augmented second. For this reason the harmonic minor scale, true to its name is typically used as the harmonic foundation of minor keys. This means that it forms the foundation of the chords used to enrich melodic lines. The keyboard below shows the structure of a harmonic minor. The seventh step has been raised from the g natural found in the natural minor scale to g#. In spite of this the scale still shares its key signature with C major. The g# is shown as an accidental within the music. The same rule applies to all harmonic minor scales: the seventh step is raised and shown as an accidental within the music score, but never in the key signature.
¹Augmented second: an interval consisting of three semitones. An augmented second is the same size interval as a minor third but is spelt differently. If we were to spell the augmented second in a harmonic minor as a minor third we would spell it either as E# – G# or F – Ab.
²Leading note: the seventh step of a scale always a major seventh above or a semitone below the tonic. When the seventh step of a scale is a minor seventh from the tonic it is called a subtonic rather than a leading tone.
Here’s a video diagram showing the first ascending octave of A harmonic minor on the cello. The augmented second requires an unusual extension from the second to the fourth fingers.
Now that the subject of major keys and their scales has been covered, we can look at minor keys, how they relate to and differ from major keys, and the structure of their scales.
Before we look at the structure of minor keys and their scales, it is vital that we hear how they differ in sound. Major keys are thought of as having a happy sound while minor keys sound sad. Although this is a very simplistic and subjective description, it’s a good start. The following two sound bites are the tonic¹ triads² of C major and C minor. The C major triad sounds brighter (“happy”), while the c minor triad sounds darker (“sad”).
The crucial note in these triads is the only one that changes and in doing so dramatically alters the sound of the triad. It is the middle note – the third step of the scale, also referred to as the mediant. In a major triad the mediant is an interval of a major third up from the tonic, and in the minor triad it is a minor third up. While this is not the only note that changes when we compare a major and minor scale with the same keynote, it is the first note to define whether the scale is major or minor.
¹ Tonic: the technical name for the first step of a scale, also known as the keynote
² Triad: a chord stacked in thirds (a tonic triad is made up of the first, the third and the fifth steps of a major or minor scale
Types of minor scales
Apart from the obvious difference in sound, minor keys differ from major keys in that they are more complex, and have three types of scales for each key as opposed to just one major scale for each key. The names of the scale types are natural minor, harmonic minor and melodic minor. All three of these scale types have an unmistakably minor sound, but each follows a different sequence of intervals. What they all share in common is the first five notes of the scale with that crucial minor third interval between the keynote and the mediant.
Natural minor scales
Using the key of a minor, which has no sharps or flats in its key signature, we’ll look at and listen to the natural minor scale first. The sequence of intervals is as follows:
Step 1 – 2 (a – b): whole tone
Step 2 – 3 (b – c): semitone
Step 3 – 4 (c – d): whole tone
Step 4 – 5 (d – e): whole tone
Step 5 – 6 (e – f) semitone
Step 6 – 7 (f – g) whole tone
Step 7 – 8 (g – a) whole tone
The natural minor scale is the oldest of our three minor scale types and is also referred to as the aeolian mode. The name is taken from the music theory of Ancient Greece, and was applied to this particular scale by the Swiss music theorist, Heinrich Glarean in the mid sixteenth century. A natural minor can also be thought of as the scale of C major started on the sixth step instead of the first. On the piano keyboard it uses only white notes, and looks like this:
It is worth mentioning at this point that every major scale has a related minor key which shares its key signature The relative minor keynote is always located an interval of a minor third down from the keynote of the major key (in other words, the sixth step of the major scale). Based on this and the fact that they share the same notes, it is easy to see that C major and A minor are related. Let us now observe and listen to the scale of a natural minor on the cello.
The Cello Companion 