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.
  2. 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.
  3. 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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A Beginner’s Guide to Keys in Music

Firstly, let’s define three important terms which are easy to get confused and 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.
2) 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.
3) Scale: a representation of the notes belonging to a key in ascending and descending order starting and ending on the root note of the key. 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)

Understanding major and minor keys and their relationships

The reason there are related major and minor keys is because they share the same key signature. Major keys are easier to understand because they do not deviate from their key signature, and have only 1 scale to represent them. Major scales are based on the following sequence of intervals:

Whole tone; whole tone; half tone; whole tone; whole tone; whole tone; half tone.

So let’s see how that relates to the actual notes of C major:

C – D: whole tone

D – E: whole tone

E – F: half tone

F – G: whole tone

G – A: whole tone

A – B: whole tone

B – C: half tone

Now let’s look at F major:

F – G: whole tone

G – A: whole tone

A – B-flat: half tone

B-flat – C: whole tone

C – D: whole tone

D – E: whole tone

E – F: half tone

So no matter what the key, major scales follow an identical sequence of intervals. This is why they all have different key signatures. In order to follow the same sequence, they have to follow a unique pattern of notes.

Minor keys are more complex than major scales. Every minor key has 2 different types of minor scale as previously mentioned: a harmonic minor scale and a melodic minor scale. Each type of scale deviates from the key signature in a slightly different way.

But let’s forget that confusing fact for a moment and look at how major scales and minor scales relate to each other.  Every key signature relates to both a major key and a minor key. The table below shows 3 ascending major scales. The numbers above the scales relate to the steps of the scales.  The red note in bold print in each scale is the root note of the relative minor.

You’ll notice that it is always the 6th step of the major scale that is the root note of the relative minor key. This is the easiest way to find out which minor key shares the key signature of a major key.

In contemporary rock and pop music, we often come across “natural minor” scales (also known as the aeolian mode). These are minor scales that do not deviate from the key signature and take on the following sequence of intervals:

Whole tone; half tone; whole tone; whole tone; half tone; whole tone; whole tone.

This is a (natural) minor, which is related to C major (as you can see in the table above)

A – B: whole tone

B – C: half tone

C – D: whole tone

D – E: whole tone

E – F: half tone

F – G: whole tone

G – A: whole tone

The next table shows the three natural minor scales related to the major scales above. This time, you’ll notice that the bold print red note, which is the root note of the relative major key, has changed to the third step.

In classical music, minor scales are altered in 2 different ways. This gives minor keys a more distinct and defined sound, and distinguishes them from major keys. The first alteration is the harmonic minor scale, in which the 7th step is always raised up by a half tone as shown in a harmonic minor below:

A – B: whole tone

B – C: half tone

C – D: whole tone

D – E: whole tone

E – F: half tone

F – G#: augmented second

G# – A: half tone

The augmented second is the largest interval you’ll find in any classical scale, and is only found in the harmonic minor. Play and listen to the scale several times to hear its distinct sound.  The table below shows 3 examples of harmonic minor scales. The altered 7th steps are in bold italic.

Now for the melodic minor scale, which I like to call the chameleon scale because it changes its colours on the way down.  Melodic minor scales raise the 6th and 7th steps by a half tone in the ascending half and lower them back down by a half step in the descending half. This means that the scale has a different sequence of intervals in its ascending and descending halves as shown in a melodic minor:

Ascending

A – B: whole tone

B – C: half tone

C – D: whole tone

D – E: whole tone

E – F#: whole tone

F# – G#: whole tone

G# – A: half tone

Descending

A – G: whole tone

G – F: whole tone

F – E: half tone

E – D: whole tone

D – C: whole tone

C – B: half tone

B – A: whole tone

Note also that the descending melodic minor scale is a natural minor which follows the key signature.  Play and listen to the scale, and be sure to hear the difference between the melodic minor and the harmonic minor. The table below shows 3 examples of melodic minor scales. The relative majors are once again marked in bold red; the altered notes in the ascending scale are shown in bold italic green, and the lowered notes in the descending scale are shown in bold italic blue:

The altered notes in harmonic and melodic minor scales are always shown as accidentals within the score, and not in the key signature.

So how do we know whether a piece of music is in a minor key or a major key? First look at the key signature and make sure that you know which major and minor key it belongs to. Then look at about the first 8 bars of the music. If you see any accidentals within the score (not, the key signature – you’ve already looked at that) check what they are. If they happen to be the 6th and/ or 7th step of the minor key, then you can be certain that the music is in a minor key and not a major key.  If you see no accidentals within the score, or accidentals that are not the 6th or 7th steps of the minor key, you can be certain of it being a major key.

© D C Cello Studio

Order or download my latest electronica-cello feast, Cellotronics

© D C Cello Studio