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.

Teaching Music: Calling versus Business

Today did not start well. I hadn’t even taken my first sip of tea before I noticed an unread text message on my phone from one of my new students. I knew what it was going to be about. Nonetheless, I opened it and was faced with a lengthy excuse for why she would not be able to make her lesson scheduled for 10 am. I felt the temperature of my blood threatening to reach boiling point, and decided not to reply until I had finished my first cup of tea. This was in the hope that I would feel less inclined to send a message that would make a sailor blush. There are further reasons for why I should react quite so explosively to a cancelled lesson, but they are not important or ultimately what this post is about.

You see, this particular irritation has happened in the middle of what I can only describe as a major reassessment of my role as a teacher and the business I am running. It highlights issues that private teachers (not only in the field of music) face the world over. This is only one of the many issues we wrestle with in our day-to-day professional lives. Other transgressions sure to raise my blood pressure include late or missed payments, failure to practise, and constantly changing what should be a regular lesson time. Some of these problems create financial discomfort, while others are frustrating to my pedagogical sensibilities. In other words, some students can be bad for business while others can be bad for our professional progress. Here I should point out that such students are always in the minority. The majority of people who make the investment in private lessons for themselves or their children do so out of a genuine desire to learn, or to enrich the educational and personal development of their children.

However, it only takes a few time-wasters to cause a disproportionate amount of frustration and stress. At the earlier stage of one’s career, the notion of terminating lessons is unthinkable unless it’s the student doing the terminating, and that’s never easy to accept. This was certainly my perspective when I was building my practice and really needed more students, not fewer. But thinking back, there was never a “problem” student who didn’t end up quitting their lessons within one year of starting. I might have saved myself a good deal of that frustration and stress if I had shown them the door as soon as I realised that they weren’t going to be long-term prospects. One of the reasons I never did (apart from the obvious fear of reducing my earnings) was the voice of my idealistic inner teacher, which told me I could inspire them to become committed cello students with persistence and the exploration of every possible avenue. I am pleased to say that I haven’t lost that nagging voice. I believe it is a very important aspect of what makes me a good teacher. Everyone who embarks on the journey of learning to play an instrument experiences periods of self doubt and despondency. At times like these they need a teacher who recognises what they’re experiencing and refuses to let their self doubt win. Fifteen years after giving my very first cello lesson I have learned to determine when to embrace the idealistic inner teacher voice and when to listen to my business head, which has taken some time to find its voice.

When I began teaching professionally my philosophy was that anyone – no matter what age, background or experience – could learn to play the cello if they really wanted to. Fifteen years later my philosophy remains the same, but I have learned that a person who decides to take cello lessons isn’t always a person who really wants to play the cello. I used to think that only young children who were forced into music lessons fell into that category. I have since learned that the most enthusiastic adult beginners can lose interest very quickly, and the most unwilling young beginners can turn into passionate players. You can never really tell from first impressions.

What I have also come to realise in my gradual epiphany, is that I am running a business which makes up a significant percentage of my overall income as a musician. That may sound like a feeble epiphany, since any freelance activity in which money is charged for a professional service is a business. But we musicians are not known for having business heads. We work in a nebulous, subjective and ever-changing industry which is notoriously difficult to succeed in. Qualifications, while often required depending on which avenue we choose, do not make us musicians in the way that they make doctors, accountants or lawyers. So we enter our field with gnawing doubt and uncertainty, never convinced we’re good enough to do what we do and always convinced that we shouldn’t charge too much for fear of being arrogant or simply being laughed out of the room. It takes a while to shake those feelings and some never do. But the sooner you realise that your students (the bad apples aside) keep coming back to their lessons because they have confidence in what you do, the better. When you realise that, you’ll realise that there is nothing wrong with telling people you’re good at what you do, and nothing wrong with expecting a certain level of commitment and respect from your students. If they have no respect for your business and the value of what you are doing for them, it is unlikely that they will have any respect for your expertise. Would a lawyer or an accountant take on such a client?

You might be wondering about the content of my reply to the hungover student. I told her to get well soon, and that I looked forward to hearing back from her on Wednesday. Does that negate everything I have just written? No. There has to be a certain amount of leeway. She has two strikes, but she has also shown real enthusiasm. She has only just begun and she knows exactly what my expectations are because I have explained them and given them to her (and every other student I teach) in writing. I still see in her the potential that I see in all of my new students. Should she strike again, she’ll have to find another teacher, and perhaps she’ll treat that teacher with a little more respect when she realises that we’re not mugs who were born yesterday. And she may turn out to be a very capable amateur musician under my guidance. I hope it’s the latter, but I’ve made peace with the fact that not every student who comes through my door will turn into a joyful story to add to my memoires.

© D C Cello Studio

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

Can Cello Really be Self-Taught?

Speaking as a classically trained cello teacher who herself underwent years of tuition at school and Music College, I won’t deny that I am extremely biased. I simply can’t get away from the notion that learning an instrument like the cello can only be a successful endeavour under the instruction of an experienced and capable teacher, and even under those circumstances it certainly won’t work out for everyone. Am I being close-minded? As I conduct research for my own video/ e-book companion for cello students, I keep stumbling across teach-yourself cello methods that promise to enable literally anyone to play. Since none of the methods I have encountered thus far have actually given a definition of what “playing” actually is, I suppose they are not necessarily offering false hope – providing those subscribing to the methods do not equate playing with being able to perform great repertoire or play in a professional level orchestra. Many might argue that drawing the bow across the string to make a passable sound is also playing.

Furthermore, I don’t deny that certain instruments have a long list of outstanding self-taught players. It is more than possible to teach oneself to play an instrument and even take that skill to a professional level. However, I don’t believe that certain instruments – particularly the violin, the viola or the cello – lend themselves at all well to self instruction. I should add at this point, that I will not be drawn into the utterly pointless arguement of which instruments are “easier” or “more difficult” to play, and I am not suggesting that stringed instruments fall into either category. What I am considering, is the accessibility of these instruments when the student has no idea how to hold them, how to hold the bow, or where to place their fingers. I’m sure we can all agree that one of the most disagreeable sounds in the world is that of a violin or cello in the hands of a beginner. Whereas a piano or guitar – both instruments being more “user friendly” with a more intuitive interface to those who have never attempted to play them – may sound dull or uninteresting in the early stages, but never quite as dreadful as a stringed instrument.

Perhaps you think I’m being a snob, and that my concern is not based on the actual practicalities of learning the cello without a teacher, but on the implications of this actually being possible. If more and more people begin to realise that playing the cello is an achievable goal without the costly help of a tutor, people like me will be out of a job. I’ll tell you why I don’t lose sleep over the prospect of losing my business to self-instruction methods: even if it is possible to become a skillful cellist with only the assistance of a book and a few videos, there is a limit to the number of people out there who prefer the “DIY” approach.

As for whether anyone can learn to play the cello as well as they’d like to by following video and book instructions, I believe I’m looking beyond my personal bias when I say that I am far from convinced. Without regular feedback and correction on fundamental issues such as posture, balance, intonation and bow technique (and that’s just for starters) it simply isn’t possible to develop technique that isn’t fraught with tension and bad habits. One of the greatest sources of frustration for musicians is physical tension, pain and injury caused by inadequate technique. So even if your motivation for learning the cello is “just for enjoyment”, there is very little enjoyment to be found in trying to do something that just makes us feel out of our depth. Am I saying that those who study cello with a teacher will not encounter these problems? Sadly not. You may find yourself with a perfectly good teacher but simply not “gel” with him. You might end up with a less than capable teacher whose motivation is to earn a few extra bucks as opposed to helping you to find and develop your musicality. Or you might have an inadequate practice routine. There are many factors that can hinder the development of a music student of any instrument. My feeling is that without a good teacher, all of these factors will be stacked much more heavily against you. A good teacher gets to know her students on a number of different levels – personality, intellect, physical aptitudes, musicality – in order to develop an individual approach to each student. She will never take a one size fits all approach when helping a student to solve problems. A book or video series, no matter how well written and demonstrated, can only offer one approach which won’t work for everyone. It cannot offer several alternative means of explaining each concept without becoming saturated, unreadable and far too lengthy.

I would welcome comments from anyone who is currently teaching themselves to play the cello or has ever attempted to do so. What method did you chose and why? How would you describe your progress? What are your goals for your cello playing?

© D C Cello Studio

Order or download my latest electronica-cello feast, Cellotronics