# Guitar/Scale Theory
## The Invention Of Notation

By the ninth century Western music had become standardized into a notational form called nuemes which were shapes that represented notes. One 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 notational system was more of a memory aid rather than a complete notational system showing exact pitch and duration. To read nuemes you needed to be familiar with the piece of music beforehand. In the tenth century Guido d'Arezzo, a Benedictine monk and Choir Master, extended the one line to four lines and set the exact pitch of each note. This new invention of the stave allowed music to be notated more precisely. Guido d'Arezzo also devised the solfeggio system where a different syllable is sung to each note of an ascending scale:
Do - Re - Mi - Fa - Sol - La - Ti
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 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 Thessaly 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 Ancient Greeks 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 music nomenclature rather than practice and the Ancient Greeks used their modes in an entirely different manner to the Medieval musician. 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 quote above is from Aristotle's Politics which is a work about government and society and the individual's role in both. This Aristotelian analysis of music influenced the early Church fathers who sought to lay the foundations for the liturgy of the Christian mass which had always contained musical elements.
The Church Modes derive from Gregorian Chant which is a body of liturgical vocal music named in honor of Pope Gregory (590CE to 604CE) who set others to collect all the earlier Christian plainsong for codification. Pope Gregory instigated the revision of the existing liturgical music into a coherent whole and in doing so defined the musical practices of the early Christian faith. With regards to secular (non-religious) music there is not much contemporary information available for the modern reader. The church filling the vacuum left by the demise of the Roman empire became the main conduit of information and therefore the earliest substantial musical literature we have available to study is primarily to do with the musical practices of the Christian church.
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 position (first four frets) so that a C major chord is in tune with itself. You will find that the chords in the first position 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. Roman numerals are used to label the scale degrees.
| Roman Numeral | I | II | III | IV | V | VI | VII |
| Note | C | D | E | F | G | A | B |
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 on the keyboard 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 adjacent 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.
The C major scale has no sharps of flats so that the chords are formed using only the white keys. The most basic chord you can play is a triad which consists of three notes. The piano student will be asked by their tutor to play the seven triads in the key of C major almost immediately. Once the piano student has formed the shape of the C major triad (C-E-G) it is only a case of moving that shape up through the scale degrees while naming the chords. A beginner on the piano will learn the chords in the key of C major within minutes.
The guitar exercise below will allow you to quickly learn the chords of the C Major scale. For the Dm triad and Bdim triad use your little finger for the lowest note and for the lowest note of the last triad (C major octave) use your third finger.

## Structure of the Major Scale

The major scale (or Ionian 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" where each note is sung using a syllable - "Do, Re, Mi, Fa, Sol, La, Ti, (Do)" - may help in illustrating 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.
For example:
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

## Structure of the Minor scale
### Natural minor

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