Key signatures and tetrachords.

Hi everyone, and welcome to  this lesson on key signatures. By the end of this one, you will have a clear definition of key signatures and why we employ flats or sharp alterations for all major scales, except for C major. A key signature is a series of flat or sharp signs placed at the beginning of a music piece, after the clef and before the time signature. But, what do these alterations mean? 

The practical answer is that key signatures indicate which notes in the following composition will be altered from their natural state. The following is the key signature's flat series:

As you can see, the flat series follows the circle of descending fifths, from C to Cb, and the number of flats are related to a specific key of the major scale. Remember that, starting from Bb for the key of F, the notes altered follow the circle of descending fifths, so Bb, Eb, Ab, Db, Gb, Cb and Fb.

Differently from the flats series, in the sharp series we follow the circle of ascending fifths, from C to C#, and the number of sharps designate the key. Remember that, starting from F# for the key of G, the notes altered follow the circle of ascending fifths, so F#, C#, G#, D#, A#, E# and B#.

 

While this is a very practical way to study key signatures, it doesn’t tell us why we alter certain notes in relation to a specific major scale. If you’re curious to know, just keep reading. 

For our theoretical explanation of flats and sharps, we have to make a digression to scales and diatonic system. Scales, as a succession of tones and semitones in a specific order, are at the basis of music since immemorial time, and from different parts of the world. In the Western music system, a scale is a combination of two or more sounds among the twelve available.

 

Generally speaking, there are two main categories of scales: 

Chromatic: a succession of all twelve semitones

Diatonic: simply said, all the other succession of two or more notes, not employing all the twelve semitones.   

The diatonic system is still by far the most used in music compositions of all styles, and for centuries the major scale has been, and still is to this day, the one elected as a reference among all scales. This means that normally a music composition will be based on a given major scale, carrying one or more alterations. Therefore, when writing a musical composition in a key other than C major, we will notate the alterations at the beginning, after the clef and before the time signature, in order to avoid the notation of each alteration during our musical piece. 

Moving forward in our investigation, you might ask why each major scale has a set number of flats or sharps, and where do they come from. In order to answer this, we need to go back to the ancient Greek music system, where basic scales were made of four tones called tetrachord. Two tetrachords joined together were called “harmony” (roughly our today’s major scale), and could be connected in two different ways: 

  • by synafè, when the connecting degree was shared by the two tetrachords. For a C Major scale, this will be the F note.

  • by diazèusis, when the two tetrachords were connected by two different degreesFor a C Major scale, these will be the F and G notes.

From now on, we will call lower the first tetrachord, and upper the second one.

Keep in mind these two points: 

  • the distance between the single notes of a lower tetrachord is always the same, this being tone-tone-semitone;

  • when tetrachords are connected through a common tone (sinafè), the distance between the upper tetrachord notes is always of three tones, while in the other case (diazeusis) we have tone-tone-semitone.

 

All this being said, we will divide the C major scale in two parts, moving the upper tetrachord in the lower position: the prerequisite for the new lower tetrachord is to keep the tone-tone-semitone pattern, therefore introducing flats or sharps in the new ones.

When the two tetrachords are connected by synafè, or common tone, our new scale will start with the F note. In order to keep the tone-tone-semitone pattern in the new lower tetrachord, we need to introduce flat alterations, as shown below here.

This example shows the passage from C to F Major scale. To keep the tone-tone-semitone pattern of the lower tetrachord, the last note of the upper tetrachord becomes Bb. 

On the other side, when the two tetrachords are connected by diazeusis, or connecting tone, our new scale will start with the G note. In order to keep the tone-tone-semitone pattern in the new upper tetrachord, we need to introduce sharp alterations.  

 

This example shows the passage from C to G Major scale. To keep the tone-tone-semitone pattern, the third note of the new upper tetrachord becomes F#. 

And now it's time to see now how this process can affect all the other Major scales.

Series of flat key signatures through synafè: the connecting degree is shared by the two tetrachords. 

 Cmaj                             lower tetrachord                                                               upper tetrachord

to Fmaj              new  lower tetrachord from the upper one                        new upper tetrachord

to Bbmaj             new  lower tetrachord from the upper one                      new upper tetrachord

to Ebmaj             new  lower tetrachord from the upper one                      new upper tetrachord

to Abmaj             new  lower tetrachord from the upper one                      new upper tetrachord

to Dbmaj             new  lower tetrachord from the upper one                      new upper tetrachord

to Gbmaj             new  lower tetrachord from the upper one                      new upper tetrachord

to Cbmaj             new  lower tetrachord from the upper one                      new upper tetrachord

Series of sharp key signatures through diazèusis: the two tetrachords are connected by two different degrees.      

Cmaj                                  lower tetrachord                                                                     upper tetrachord

to Gmaj              new lower tetrachord from the upper one                                 new upper tetrachord

to Dmaj               new lower tetrachord from the upper one                                new upper tetrachord

to Amaj                new lower tetrachord from the upper one                                 new upper tetrachord

to Emaj                  new lower tetrachord from the upper one                                 new upper tetrachord

to Bmaj                   new lower tetrachord from the upper one                                new upper tetrachord

to F#maj                 new lower tetrachord from the upper one                                 new upper tetrachord

to C#maj                  new lower tetrachord from the upper one                               new upper tetrachord

To recap: 

  • when the two tetrachords are connected by synafè (common tone), the new Major scale will have flat alterations;

  • when the two tetrachords are connected by diazeusis (two notes at one tone distance, or connecting tone), the new Major scale will have sharp alterations.

In both cases, the upper tetrachord will move in lower position, creating a new one.

That's all for our theory lesson on key signatures. Thank you for reading and see you in the next lesson!

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