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.


8 thoughts on “Major keys and their scales

  1. Dear Deryn, thanks again. I’m probably the rare type of music student, who understands math better than music. However, this also drives me crazy sometimes, because from a mathematical point of view many things seems unecessarily and artificially overcomplicated, and when You ask a musician why is that so, the answer is not really satisfying from a “scientific” point of view in many cases. Like C major and A minor “feels differently”, and things like that. Anyway, I’m patient and respectful towards music, so I’m hoping to see the whole picture someday, and then give the “mathematical” answer to my old questions. Recently I’ve found a nice article about the physics of the whole stuff, and now I can understand why a semitone is the 12th root of 2, and this partially answeres lot of my earlier questions.

    After this long introduction: the similar way, I can understand that F# and Gb are not really the same always. But in this particular case, if I’d “transpose” a piece written in Gb major to F# major, and give to You the same music sheet but with 5 sharps instead of 5 flats, would You play it differently? And if yes, could You explain it in a few words, what the difference would be?

    Also if these two sounds different, it would make me want to go even further, more specifically to G# major with 6 sharps, and one double sharp on F. And continue that until E# major and then we get back to C (or probably it is Bx not C, but that’s too much even for me for tonight, so let it be C for now :-D). So, regarding this major scales with double (or triple, etc…) sharps (or flats in the other direction) my question is: do such “fanciful” compositions exist for the cello?

    1. The awkward moment, when it is around 3am, you know that you have less then 5 hours to sleep, but you got so interested because of an article, that you go to Wikipedia, and spend your time understanding the concepts of just intonation, equal temperament, 19-TET, 31-EDO, and things like that. But that’s it, I’ll go to sleep after I’ve downloaded Mandelbaums PhD thesis 😀

    2. Well I’m certainly not qualified to offer deeply mathematical or scientific answers to these questions, but I’ll do my best! 😉

      With equal temperament, the tuning system in wide use today and used for tuning pianos, there would be no difference in sound between enharmonic equivalents (i.e. Gb Major versus F# major) because the twelve notes in the octave are separated by logarithmically equal distances (100 cents). However, in tuning systems based on the Pythagorean system including meantone temperament, well temperament, and Syntonic temperament, enharmonic notes differ slightly in pitch.

      Elements of meantone tuning can and often are still exploited by players of intonating instruments – i.e. strings, winds, brass, etc – to bring more expression and colour into a performance. This is often referred to as expressive intonation, and presents itself as a slightly sharper leading note and mediant to enhance the qualities of a major key, or a slightly flatter mediant and slightly sharper leading note in a minor key. However, we would not choose one enharmonic equivalent of a key over another for a difference in sound – it doesn’t exist.

      There are three keys with enharmonic equivalent key signatures:

      C# major (7 sharps) and Db major (5 flats)
      F# major (6 sharps) and Gb major (6 flats)
      B major (5 sharps) and Cb major (7 flats)

      The total number of accidentals in the two equivalent key signatures always add up to twelve – the total number of semitones in an octave. Why would we choose one over another? Normally composers will opt for the key with fewer accidentals – e.g. Db major rather than C# major. There is also harmonic context to consider. For example, if the first movement of a sonata is composed in Db major and the second movement is in the subdominant key, it would be Gb major rather than F# major.

      As for keys with double sharps or flats, they exist in theory but not in practice. Although double sharps or flats may appear as non-harmonic notes within a score – e.g. if I raise the dominant in F# major I would spell it as Cx, not D. But key signatures with double sharps or flats are messy and unnecessary when they have perfectly logical equivalents.

      1. Dear Deryn, thanks for the exhaustive answer. After reading all those stuffs on wikipedia, I was also ending up with a conclusion something like this, but You wrote the things down in a very coherent and understandable way. Many thanks!

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