An Introduction to Chords in Music

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!

Cover Sheet

C major triads and inversions 1C major triads and inversions 2The Dominant 7th in C Major

Seventh Chords and Inversions in C Major 1 Seventh Chords and Inversions in C Major 2

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Minor keys and their scales Part 3

Melodic Minor Scales

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.

A Bit of History

The development of melodic and harmonic minor scales as we know and use them in Western music happened over a long period. Their predecessors are modes, which date back to ancient civilisations - notably the Ancient Greeks. Mediaeval modes and scales share certain similarities, but follow different rules and form the basis of two different musical languages with distinctly different sounds.  It was during the Renaissance period, when polyphonic¹ music really came into its own that the modal system, which had served the simpler homophonic² and monophonic³ musical styles of the Mediaeval period perfectly well, began to prove inadequate, as did the notation system. The rise of polyphony meant that music was becoming considerably more harmonically complex. The need for stronger definition in harmonic resolution drove the development of major and minor keys, and in particular the need for different types of minor scales to cater for a strong leading tone (the raised seventh) and the avoidance of awkward dissonance in melodic vocal lines (the augmented second interval in the harmonic minor scale). Dissonance was a major consideration and was avoided wherever possible in the harmonic structure of renaissance music. For this reason we see elements of all three minor scales in minor keys.

By the early baroque era (from 1600 onwards), a harmonic language based on tonality (harmony based on a key center) rather than modality had emerged. Melodic and harmonic minor scales and major scales were in common use. The range of key signatures increased considerably, and the use of key signatures with sharps was introduced. Equal temperament tuning, a system whereby the octave is divided into twelve equal semitones gained wider acceptance by keyboard makers by the 1630s. Although it did not become the principal tuning system for another two centuries, it enabled the 24 keys found in the circle of fifths - the cornerstone of Western art music from 1600 - 1900.

¹Polyphonic: Musical texture in two or more (usually at least three) relatively independent parts [The Oxford Companion to Music Edited by Alison Latham, 2002]
²Homophonic: Music in which one voice or part is clearly melodic, the others accompanimental and chiefly chordal. The term 'homophony' has also been used to describe part-writing where all parts move in the same rhythm; a more precise term for this is homorhythm. [The Oxford Companion to Music Edited by Alison Latham, 2002]
³Monophonic: A term used to denote music consisting of only one melodic line, with no accompaniment or other voice parts (e.g. plainchant, unaccompanied solo song). [The Oxford Companion to Music Edited by Alison Latham, 2002]

The following table shows major keys, their relative minor keys and the associated key signatures.

Minor keys and their Scales Part 2

Harmonic minor scales

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.

Minor keys and their scales Part 1

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.

Major keys and their scales

I posted a similar article on keys in music some time ago, but since it is now buried under about two years’ worth of posts and several of my students have been in need of a study guide for major scales and keys with more focus on how they apply to the cello, here’s a new and improved version

Firstly, let’s define three important terms which often get confused and are therefore important to be distinguished from each other before exploring how they are related.

  1. Key: a family of notes which belong together and have a distinctive sound or “colour”. A key can be major or minor and is represented by a key signature (see definition 2). Every key has 7 individual notes which are represented in the scale (see definition 3) of the key.
  1. Key signature: a representation of the accidentals found in a key. These are shown at the start of each stave just after the clef and just before the time signature* and greatly reduce the number of accidentals that have to be shown in the main body of the score**. The order of accidentals in a key signature does not always follow the order in which they appear in the scale. Instead, they follow the order in which they appear from one scale to the next.
  1. Scale: a representation of the notes belonging to a key in ascending and/or descending order starting and ending on the key note (i.e. the letter name of the scale). A scale of one octave covers eight steps but since the first and eighth steps are the same note, there are only seven individual notes as mentioned in definition 1. There are 3 main types of scales: major (which represent major keys), harmonic minor and melodic minor (which represent minor keys). Each type follows a specific order of intervals***

* Times signatures, unlike clefs and key signatures, are only shown at the start of the first stave and do not appear again unless there is a change of time signature in the music

** Score: a written or notated representation of music

*** Interval: the pitch distance between 2 consecutive notes (e.g. C – D = a whole tone or major second; C – D-flat = a half tone or minor second)

The structure of Major Scales

All major scales – no matter what note they begin on – follow the same structure. They are made up of a sequence of whole tones and semitones as follows:

Step 1 – 2: whole tone

Step 2 – 3: whole tone

Step 3 – 4: semitone

Step 4 – 5: whole tone

Step 5 – 6: whole tone

Step 6 – 7: whole tone

Step 7 – 8: semitone

If we observe how the scale of C major is played on the piano, and then on the cello, we can actually see the difference between the whole tones and semitones. Let’s look at C major on the piano first:

The red notes indicate the notes played in the scale. Notice that no black notes are played (C major has no sharps or flats), and the whole tones are always between the white notes which have a black note between them. The semitones are between the white notes which do not have a black note between them.

Since the cello does not have a logical linear map of the notes like the piano keyboard has, a video is a better way to demonstrate how the scale of C major “looks” as well as sounds on the instrument. Pay attention to the semitones, which sound closer together and are physically closer together on the cello (in this scale played between the third and fourth fingers on both strings).

Key Signatures

Because the sequence of intervals must always remain the same, no two major scales will ever have an identical set of notes. All major scales except C major have one or more sharps or flats. These are shown in the key signature, which is found at the beginning of each stave. We use key signatures to show what sharps or flats will be present in the score without having to clutter the score itself with an accidental sign in front of each relevant note. For example, if a piece of music is in the key of D major, it will have an F-sharp and a C-sharp in the key signature. This means that whenever you encounter F or C in the score, you must remember that they are actually F-sharp or C-sharp. Why not just write the accidentals into the score? There are two main reasons for this. Firstly, a score with lots of accidentals in it is messy and harder to read. The more accidentals there are in the key, the messier the score would get. Secondly, it would make it much harder to recognise accidentals that don’t belong in the key. When the key signature is used, we recognise notes that don’t belong to the key straight away since they have accidentals in front of them while notes that belong to the key do not.

Key signatures never contain a combination of sharps and flats – only one or the other. With C major as a starting point, if we go a perfect fifth up (tone, tone, semitone, tone or seven semitones up), we find G. The key of G Major has one sharp in its key signature: F-sharp. From here, we go a perfect fifth up to find D. D major has two sharps: F-sharp (retained from the previous key) and C-sharp. A perfect fifth up from D takes us to A. The key of A major has three sharps: F-sharp, C-sharp and G-sharp. Are you beginning to see a pattern here? It’s called the circle of fifths. Not only do we find each new “sharp” key by going up a perfect fifth; the new sharp in each key signature is always a perfect fifth up from the previous new sharp. It is also worth noting that the new sharp in each key is always the seventh step of the scale. For “flat” keys, we return to C as our starting point and go down by a perfect fifth each time. Easy to remember: sharp=up, flat=down.

The following graphic shows keys and their key signatures, and should make sense if the above two paragraphs made sense.

Each major key has a related minor key which shares its key signature. But minor keys are a little more complex than major keys, and need to be covered in a post of their own.

Some Thoughts on Intonation

“Intonation is a question of conscience.” – Pablo Casals

So true on so many levels! A burning issue for all us bowed string players and the bane of many of our lives, intonation tends to remain a work in progress for many years. When examined up close this topic becomes less of a discussion and more of a doctoral thesis. And like so many aspects of cello technique, you’ll encounter significant differences of  opinion amongst players and teachers on how to tackle intonation problems.

I suppose this comes as no surprise – when I try to analyse precisely how I play in tune (I should point out that even after twenty-four years of playing this doesn’t always happen), I’m frankly stumped. There are obvious elements essential to good intonation such as accurate finger placement, an excellent grasp of the geography of your cello and well developed relative pitch (assuming you don’t have the rare gift of perfect pitch). But there is definitely more to it than that. Casals called it a question of conscience. Bunting suggests (quite refreshingly) that perfectionist attitudes to intonation annihilate freedom of movement in the fingers essential to so much more than just intonation. Both philosophies point to something other than a technical or mechanical  process. There is a strong  psychological aspect which I believe is all too often forgotten or discarded.

We all have specific feelings about intonation. For many of us those feelings may include fear, frustration and often denial – leading to a high tolerance for inaccurate tuning. Perhaps the ideal relationship with intonation is to view it as part of the artistic palette. Emphasising certain intervals (such as marginally sharper major thirds and sevenths in major keys, or flatter thirds in minor keys) can colour and define keys quite beautifully. To reach this ideal I believe one has to allow for a margin of error, which gradually diminishes as the physical memory becomes more accurate and the ear more exacting. This allowance should not be confused with the previously mentioned tolerance for poor intonation, which I have seen developed to an alarming degree in some cellists despite most of them having a “good ear”.  For a long time I was one of those intonation “deniers”, often thinking my performances had gone rather well only to listen back to those which had been recorded and cringe in horror at the glaring intonation errors.

Based on my own playing experience and that of my students, I believe there are three main negative emotions associated with poor intonation: fear, uncertainty and low self confidence. The first two are relatively easy to combat (although they take time to get rid of); the latter is trickier and varies a great deal from one individual to the next.

So, fear and uncertainty first! High register playing and large interval jumps are prime candidates for inspiring apprehension, which lead to physical tension, and we all know what impact that has on intonation. Take your pick of the major cello concertos for passages in the instrument’s upper range. How often do we hear (or give) performances of these works that are let down by those upper register passages when the sound is thin and some or all of the notes are off-pitch? Even after hours of repeating those passages ad nauseam in the practice room, they often let us down in performance. All too often the practice we do to eliminate the fear factor only perpetuates it. The root of the problem is not in the passage, but in the irrational fear of that portion of the fingerboard. So it stands to reason that getting familiar with that highest octave-and-a-half through slow, relaxed work on scales, arpeggios and studies is a much better use of our practice time than repeatedly trying to play a phrase or passage in an area of our instrument that frightens us because we don’t know it well enough. No matter how hard we try to make it sound beautiful, our attempts are undermined by inaccurate finger placement and incorrect bow placement. With enough repetition of the same high register passage, we might eventually become more familiar with that area of the cello. Equally we are in danger of constantly reinforcing incorrect finger placement and excess tension because our focus is more on trying to play the passage the way we think it should sound and not nearly enough on the mechanics behind the music.

There is certainly no shortage of technical material for the cello that covers the entire range of the instrument or concentrates on perfecting the upper register – Feuillard’s Daily Exercises for Cello, Yampolsky’s Violoncello Technique and the Galamian Scale System for Cello to name a few. Until we can comfortably play such technical material covering every inch of the fingerboard, it is unreasonable to expect ourselves to be able to play repertoire with these technical demands. However you choose to approach familiarising yourself with the full range of your cello, familiarise yourself you must and you really are better off using a method designed specifically for this purpose. When Elgar was composing his sublimely beautiful cello concerto I seriously doubt he ever stopped and thought: “Ah, this will do wonders for the bow technique!” He composed the work with those whose technique was already fit for purpose in mind. But I’m digressing somewhat. The point I’m trying to make is that through consistent, concentrated practising of scales and arpeggios of every shape and size we give ourselves a much better chance of making that magical and essential connection between internal pitch and physical memory – the marriage between the sensitive fingertips and attentive ears.

Low self confidence, as I’ve already pointed out, is a more elusive problem which can have its roots in such a vast range of places that it is not really possible to tackle with a single suggestion. I do believe however, that investing enough of one’s time in the aforementioned study of the fingerboard will at least serve to relieve some of the symptoms of the problem. I also know from my own experience and from watching my students develop, that intonation is often bad because we expect it to be. That expectation is built up over years: the majority of us start out with poor intonation, not because we can’t hear it but because we don’t know where or how to place out fingers. For some cellists the development of a dependable left hand technique happens in a nice upward trend and their fear of intonation disappears as their command of the instrument improves. But for many more – perhaps most – it is more of a jagged affair with frustrating flat lines and almost as many downward as upward spikes. Surely this trains us to feel negative about aspects of our playing and gives us reason to believe that we are more likely to be wrong than right in the placement of a finger or a shift to a new position.

Again, I refer you back to the good old-fashioned daily dose of scales and arpeggios. Add a metronome to that, and remember: it is impossible to practise too slowly whereas practising too fast is not only possible, it’s disastrous.

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© D C Cello Studio 2011

 

Mastering Simultaneous Shifting and String-Crossing on the Cello

String crossing and shifting are two fundamental techniques that present stumbling points on their own. Put them together and they can become an unfortunate blemish in an otherwise good performance. Without the necessary co-ordination between the left and right sides which are performing different physical tasks and a thorough understanding of the positions visited, this particular technique will lack good tone and accuracy of rhythm and intonation. Amazingly, it is all too often skimmed over by teachers who assume that if their students are reasonably capable of each individual technique they will easily be able to combine them. Just because I can easily pat my head and rub my belly doesn’t necessarily mean I can perform both actions simultaneously!

The first step towards mastering any technique is to understand why it exists and what it will enable you to do. The simultaneous string-cross and shift presents itself in two particular situations. The first of these and typically the first time we encounter the technique in our study of the cello is when we play in more remote keys which eliminate the use of some or all of the open strings. The second is when we need to avoid open strings in order to play sustained passages with consistent tone and vibrato or to avoid awkward string crossing in faster passages. One of the great advantages of being able to manage this technique well is the significant increase in potential fingering patterns that become available, which means that we have a much better and more varied sound palette at our disposal.

Most of us first encounter the need to shift and cross in scales: most notably, E Major. However students who play with orchestras frequently come across techniques they have not yet covered in their lessons and this is often one of them. To me it has always made sense to introduce the technique earlier on – while the neck positions are being studied – using home key scales such as F and D majors (two octaves) thus giving the student and early introduction to alternate fingering patterns and making remote keys far less daunting to play and sight-read. All it takes to comfortably manage a piece, study or exercise in a key with four or more sharps or flats is a sensible fingering pattern and the instinct to determine where extended positions are required – a simple matter of knowing where you are in the given scale.

I believe the reason it is easier to learn scales such as D or F majors with fingering patterns that avoid open strings is simply that they are already familiar territory. Furthermore, there are open string targets available to test intonation along the way. Any student who has been introduced to the first four positions on the cello should be comfortable with major keys containing up to three sharps and two flats, and minor keys with two flats and one sharp. They will also have covered extended positions; and string-crossing* is one of the first techniques we are introduced to on the cello. By combining these techniques we can introduce the valuable technique of simultaneous shifting and string crossing to avoid open strings.

Below are two versions of the scale of F major (two octaves); the first with conventional fingering and the second with a fingering pattern that avoids open strings and happens to be identical to the conventional fingering of E major (two octaves), thus making F major an ideal means of preparing for E major.

In the second fingering pattern, each string cross coincides with a position change. Most students find this confusing at first because with the exception of the shift from first to fourth position on the D string, backward shifts lead to a higher pitch in the ascending scale and visa-versa in the descending scale. So to grow accustomed to this counter-intuitive event, the following exercise can be practised until the left hand knows precisely how to move from one group of notes to the next.

Once you’ve mastered this exercise, you should be able to play the new F major fingering pattern fluently with no obvious gaps at the string crosses. Don’t rush: if you can’t play it slowly, there’s no reason why you’d be able to play it three or four times faster! Learning new shifts and fingering patterns, along with hearing the pitch you’re aiming for before playing it takes time and careful, well-planned practice.

The next step is to apply the F major exercise to the scale of E major as follows.

*The fact that it remains one of the most important and subtly difficult techniques to master is another article entirely!

© D C Cello Studio

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