Before we get quite in depth, the notes in the key of C are C D E F G A B. You may be wondering what exactly this means though and where these notes come from.
To really understand where the notes in the key of C come from, you need to begin with acoustical physics. Our system of scales begins with acoustical physics, think of acoustical physics as simply the natural laws of sound. Every note or pitch that we recognize as a single note is in fact made up of a spectrum of notes. The note we identify as the note or *pitch we are hearing is called the fundamental and this spectrum of notes related to the fundamental is called ” the harmonic overtone series”.
The harmonic vibration of the fundamental pitch creates a sequence of sounds that are an integral multiple of the lowest base frequency. A note when sounded by an instrument vibrates or oscillates at numerous frequencies simultaneously whether it be a string, a column of air or any other vibration created by any instrument that can maintain a fixed frequency. Below are the harmonic frequencies of the fundamental note of A, the low A being 110 cycles or vibrations per second. Each octave of A is a doubling of frequency shown as 2, 3, 4 and 5 in the lower numbers, the upper numbers are the numbers of the *partials.
The strongest note in this series other than the fundamental (in any octave) is the “perfect 5th” (P5), it lies halfway between the root fundamental at each octave. This “perfect” fifth is the most closely related frequency to the fundamental and thus the most acoustically present (perfect) within the overtones of the fundamental, these are shown above as partials 3, 6 and 12.
The Key of C
In our system of music we give frequencies or pitches a note name, middle C for example is 261 cycles (vibrations) per second. Let’s examine how the overtone series is expressed on the musical staff from the fundamental of C, note that the musical letter name of the perfect 5th from C is G and is again found at harmonics 3 and 6 and 12. Also note that the intervals get closer and closer together or more complex as the series progresses. The distance from partial 7 to 8 is a tone, partial 11 to 12 a semitone and 14, 15 and 16 all semitones.
The Harmonic Overtone Series from C
It is important to realize that this perfect 5th is not some sonic alchemy but is in fact a sound that is as present in nature as it is in our music and instruments. A violin is tuned in 5ths as is a mandolin, every minor and major chord has a perfect 5th, a guitar and bass are tuned in perfect 4ths which is the inversion of a perfect 5th. Perfectly tuned voices singing a single note can produce an audible perfect 5th overtone. Try playing any note on a piano and then mute the string you have struck, you will now very clearly hear the perfect fifth sympathetically ringing on other strings even though the fundamental is not sounding. Strike the E string 6 on a guitar and then mute it and you will note that both the E1 and the B2 strings will be vibrating in sympathy to their fundamental.
To add an anecdote. I was once directing a young children’s choir and some of the children were not singing the right notes. I soon realized that they were singing the perfect 5th instead of the fundamental pitch being sung by the other children. Oh to have ears that acute once again.
These acoustical truths have not only informed the construction and tuning of all acoustic instruments but are also at the core of all digital and synthesized sounds which are essentially mathematical.
Let’s get back to the notes of a scale and how scales are derived from these natural laws of sound.
The Cycle of Fifths
The fifth of C is a G, if G is the fundamental the 5th is D, if D is the fundamental the 5th is A , or let’s use our musical alphabet to demonstrate this same point.
To further demonstrate let’s continue this logic in a circle, each 5th having its own 5th, this creates a complete cycle of fifths that returns to the starting point. This cycle of 5ths yields the 12 notes of our chromatic scale as well as our scale system. As you can see in the diagram below the all of the notes in the key of C major are also revealed through the cycle of fifths. The notes for the scale of C begin on F for reasons we won’t discuss here but will discuss in the blog on modes. Suffice to say the purest scale sound from a harmonic overtone perspective is not our favoured major scale but is in fact F Lydian, but back to our topic, the notes in the key of C major.
Arranging the Notes in the Key of C Major
Now we have all of the notes in the key of C major and we can now arrange these notes of the cycle in a close linear order with C as the start point. Note that some of the pitches are a tone apart and others are a semitone apart, as previously mentioned these semitones and tones are also expressed “naturally” in the harmonic overtone series in the upper *partials. So the notes in the key of C major are:
C tone D tone E semitone F tone G tone A tone B semitone C
In this order these notes make up our C major scale. Take a look at this spacing on the piano with semitones between E and F and B and C, there are no black keys between these natural notes.
If we now eliminate the letter names of the C major scale and leave only the distances this will give us a clearer representation of what a major scale is. A major scale can start from any root note or naming note provided these distances remain consistent, the scale will derive its name from the root note or “key” center
Tone – Tone – Semitone – Tone – Tone – Tone – Semitone
So in fact a major scale is a series of consistent related distances from a given tonic or “key” center.
What is a Key?
There is another fascinating factor in defining scales that is often overlooked and that is how the listener or the human mind perceives the sound of a scale as an arrangement of organized notes. The mind by nature wants to organize things and so when the human ear hears a single note the mind remembers that note as a tonal centre, in other words, all other notes will now be heard in relation to the first note. We humans “capture” a pitch or tonal centre and keep it in mind and then hear relationally to that cerebrally captured tonal center or “key”. In other
words tension and resolution are created when there is a key center but that is a human perception, this key is not a series of notes, it is simply one pitch, one vibration, one center which the mind captures as “key”.
All of us have this innate ability for internal tonal memory, you can demonstrate this to yourself by simply playing a note and then without the note ringing try to recall that note by singing it. Or to take that even further try sounding a note and then mute the note for a moment and then play a different note. You will notice that you are hearing that second physically articulated note in relation to the note you now have in your tonal memory, you will hear the “relationship” of the two notes, one physically sounding and the other captured by your sonic memory. This sonic memory is the recollection of a very specific vibration and somehow without a sound present we can recall the specific note.
The notes in the key of C or any scale or musical sound for that matter are a reflection of nature and in order for these natural sonic elements to become musical sounds and language they require the human mind to construct, organize, perceive and interpret.
* interval – the distance between two notes
* partial – A partial is any of the sine waves of which a complex tone is composed.
* pitch – a fixed frequency or vibration which can thus be identified as a musical note