The Invention Of Notation
For scales to be theorized; a system needs to be in place. Whether this system takes the form of oral traditon or written is of great importance. The oral tradition has its problems; in that there is no clear record for each stage of development. Each generation can embellish, add or change the music thus obscuring origins and evolution. So with that in mind we start our study of scale theory with a brief overview of the invention of notation.
By the 9th century Western music began to become standardized into a notational form called nuemes. In the 10th century Guido d'Arezzo set down a form of notation that replaced this earlier system. Guido d'Arrezo's system is regarded as the starting point for modern notation. Nuemes were shapes that represented notes. A single line was used to indicate the middle pitch with nuemes above the line being higher in pitch and the nuemes below the line being lower in pitch. This primitive sytem was more a memory aid rather than a system showing exact pitch and duration. To use nuemes you needed to know the piece of music beforehand. Guido d'Arrezo extended the one line to four lines and therefore set the exact pitch of each nueme. This new invention of the stave (or staff) allowed music to be notated in a way that allowed anyone to play the music without having previously memorized it.
Today a scholarly approach has been applied to the music of the past in relation to ensuring that the notation is interpreted correctly. An example is baroque music; where modern research into the instruments, techniques and approach of this period has led today's musicians to revise their interpretation and performance of baroque notation.
During the Renaissance (15th CE) Italian composers tried to recreate the plays of Ancient Greece and their experiments led to the invention of Opera. Musicians have always mined the music of the past for ideas and maybe some clue as to the roots of contemporary musical practices. From a musicologist point of view we are living in a Golden Age simply from the fact that mankind for the first time has the ability to record sound. Though we take recorded sound for granted today; it must be said that the future musicologist will find a rich legacy of sound recordings from which to base their research. We can never hear the music of Ancient Greece or the Medieval period; we can only attempt to recreate it. The importance of notation as the only mechanism we had for preserving the music of the past becomes self-evident.
The Church Modes
The music up to the baroque period was created from a form of scales known as the Church Modes which took their names from the tribes of Ancient Greece.
- Ionian (the Greeks who settled on the coast of modern day Turkey)
- Dorian (the Greeks who settled on Crete, Sparta and Corinth)
- Phrygian (the Greeks who moved further inland in Turkey to settle Anatolia)
- Lydian (a Greek tribe also from the Anatolia region of Turkey)
- Mixolydian (the Mixolydian mode was invented by Sappho, the 7th century B.C. poet and musician)
- Aeolian (originally Greeks from Thesally who spread to the Greek islands and Asia-minor)
- Locrian (inhabitants of the ancient region of Locris in Central Greece)
The Ancient Greeks laid the foundation for the study of music and intervals in a way that has defined Western music ever since. They investigated intervals using mathematics and used ratios to describe these intervals. The Church Modes are not scales from Ancient Greece. The Greeks themselves used a scale system based on the idea of tetrachords. However the debt that the Medieval period owes to the Ancient Greeks is reflected in the naming of the Church Modes. The Ancient Greeks also described their modes as Dorian, Lydian, etc. However this shows a continuity of musical theory rather than practice and the Ancient Greeks used their modes in an entirely different manner to the Medieval method. Here is Aristotle's view of the modes:
"The musical modes differ essentially from one another, and those who hear them are differently affected by each. Some of them make men sad and grave, like the so-called Mixolydian; others enfeeble the mind, like the relaxed modes; another again, produces a moderate and settled temper, which appears to be the peculiar effect of the Dorian; the Phrygian inspires enthusiasm"
The above quote is from a work by Aristotle called Politics; a work about government, society and the individual's role in both. As you can imagine this analysis of music must have appealed greatly to the early Church fathers who sought to find the "right" music with which to worship God.
The Church Modes form the basis for Gregorian chant; named after Pope Gregory (590CE to 604CE) who set others to collect all the earlier Christian plainsong for codification. Pope Gregory revised the existing system into a coherent whole and in doing so defined the medieval period's practices. With regards to secular (non-religious) music; from 4CE onwards there is not as much information available as we have on Gregorian chant. The church, filling the vacumn left by the demise of the Roman empire, became the main conduit of information and therefore the musical literature we have available to study is primarily to do with the Christian church's musical practices. We can presume that secular music was played and we can infer that the Church Modes may have been used. If secular music used such modes then we can be sure it was in a less formal way.
As instruments and forms evolved, some of the Church Modes became redundant as musicians found that those modes did not suffice for their musical needs. A few of the Church Modes went on to form the basis of our "major-minor" system and it is from these modes that baroque musicians created the harmonic theory that has dominated music right up to the twentieth century. The earlier Ionian mode is now called the Major scale.
The Piano Keyboard
The keyboard layout of the harpsichord and organ became standardized in the 15th century and the invention of the keyboard played a large part in laying down the foundation of modern tuning practices and theory. Tempered-tuning was adopted as a direct result of these inventions. The earlier system of mean-tuning meant that the errors introduced by the problem of the Pythagorean Comma allowed only a few keys to be played. If a piano was mean-tuned to C major then the player would find that keys further away from this C major center would be unusable. The guitarist can hear this by tuning the guitar in the first postion (first four frets) so that a C major chord is in tune with iself. You will find that the chords in the first postiion are usable but as you further progress up the neck the chords start to sound out of tune. Tempered-tuning spreads the errors introduced by the Pythagorean Comma evenly across the entire range of an instrument. By the time the piano was invented in the 17th century, the tempered C major scale had become the foundation for teaching music theory.
Since the keyboard has been such a dominating force in music, a complete study of scale theory must make some reference to it. Thus, it is best to first look at the piano keyboard and then compare it to the guitar fretboard.
Before you begin it is good idea to familiarise yourself with the notes of the C major scale. Note that it is the convention to use Roman Numerals to label scale degrees
If you play each key on a keyboard ascending from the middle C (diagram on the right), you will have played the 12 tone chromatic scale. These are all the notes available in Western music. The keyboard of a piano is laid out so that when you play the C major scale, you use only the white keys. The C major scale has no sharps (#'s) or flats (b's) which means that no black keys are used. Only the C major and its relative minor have no sharps or flats; all other scales will have a sharp or flat in their notation.
It is important to recognize that the distance between two adjacent keys is always a semitone. On the guitar the same applies to adjacent frets. Looking at the keyboard diagram you will see that between the C and D is a black key which is a semitone above the C and a semitone below the D. Between E and F there is no black key but it is still notated as a semitone interval. There is also no black key between B and C so they are also semitone neighbours. The 12 tone chromatic scale consists of 12 sounds which are all a semitone apart. The C major scale has seven notes which are represented by all the white keys. At this point it is best to remember that adjacents keys are a semitone apart and that a tone describes keys two semitones apart. Therefore C to D is a tone because there are two semitones - C to C# and C# to D. E to F# is also a tone. All instrumentalists start with learning the C major scale.
As an exercise find the semitones E-F and B-C on the first three frets of the guitar. You'll need the open strings to do this. How many times do these two intervals appear?
In general the pianist will depress notes to form chords that are derived from the scale of the key. Since we know that the scale of C major uses only white keys it follows that the chords to be played are formed using only the white keys. The most basic chord you can play is a triad which cosists of three notes. The simplicity of the keyboard layout means that a piano student will be asked by their tutor to play the seven triads in the key of C major almost immediately. Once they form the shape of the basic C major triad (C-E-G) on the piano it is only a case of moving the shape up through the scale keeping the same fingering and naming the chords appropiately. This is why guitarists sometimes lag behind pianists in understanding harmony because there is no easy visualization of triads. Another area is the quick location of the E-F and B-C intervals. These intervals are easily located on the keyboard by the absence of a black key. The guitar offers no easy visualization. The best approach would be to learn where all the E-F and B-C intervals are in the first position (first four frets) and then do the same for the fifth position (frets 5 to 8). A beginner on the piano will learn where these intervals are within minutes but a guitarist will have to put in a little more time.
Below are the triads for the key of C major. Note that for the Dm and Bdim it is recommended that you use your little finger for the lowest note and for the last triad (C major octave) you use your third finger.
Structure of the Major Scale
The major scale (derived from the medieval Ionian church mode) is the main scale currently used in music. It is made up of seven notes, plus an eighth which duplicates the first an octave higher. The Italian music system "solfeggio" (a system that has been used for centuries in Italy and is still in use today) where each note is sung using a syllable - "Do, Re, Mi, Fa, Sol, La, Ti, (Do)" may help in illustating this concept.
The interval pattern for any major scale is:
meaning that the difference from the first note to the second is 2 frets, from the second to the third is 1 fret, etc.
The difference in notes can also be called steps, 2 notes being a whole step, and 1 note being a half step. This pattern in steps can be written as:
It can also be represented as:
with "t" meaning "tone" and "s" meaning "semitone". The choice is yours as to which of the three descriptors you choose to use.
The scale below uses the "tone-semitone" method:
Please note that there is a distinction in terminology between American English and UK English. It is common to find the word "tone" used in American English to describe notes whereas in UK English the word "tone" is never used.
American English: "The leading-tone is always a semitone below the octave in a major scale"
UK English: "The leading-note is always a semitone below the octave in a major scale"
Major scale in the key of C
C - D - E - F - G - A - B - C
Two Octaves Of C Major:
This shape is moveable, and the fingering is shown below
7th e:---x---|---x---|-------|-------| B:-------|---x---|-------|---x---| G:---x---|-------|---x---|---x---| D:---x---|-------|---x---|---x---| A:---x---|---x---|-------|---x---| E:-------|---x---|-------|---x---|
Structure of the Minor scale
The natural minor scale (or Aeolian mode) is one of the diatonic scales along with the major scale. The word "diatonic" in a modern sense refers only to the major and natural minor scales. In the key of A minor, the harmonic form would be called "non-diatonic" because the seventh note is sharpened.
TIP: Any natural minor scale can be changed into a harmonic minor scale by sharpening the seventh note.
The natural minor scales are all "diatonic" because they consist of the notes from the key they are derived from without any changes. The harmonic and melodic form both contain changes to the original natural minor scale and are therefore "non-diatonic".
Natural minor scales can be created for any key using the formula:
Below is the Am natural (or relative) scale with tones and semitones shown:
Minor scale (diatonic) in the key of C:
C - D - Eb - F - G - Ab - Bb - C
Two Octaves Of C Minor:
This shape is moveable, and the fingering is shown below
7th e:-------|---x---|-------|-------|-------| B:-------|---x---|---x---|-------|---x---| G:---x---|---x---|-------|---x---|-------| D:-------|---x---|-------|---x---|-------| A:-------|---x---|-------|---x---|---x---| E:-------|---x---|-------|---x---|---x---|
Change the C natural minor scale above into a C harmonic minor scale.