Appendix
In traditional Western music there is a series of twelve notes (moving up or down) that make up the chromatic scale and each of these note’s tones are described as being a half interval in pitch from the preceding and following note. The octave is the next note if the sequence were continued (up or down), and its pitch is double ( or one-half) from what ever note begins the twelve tone series. In musical notation the indication to raise a note’s pitch a half interval (augment the note) is given by the sharp sign which can be seen preceding the second, fourth, seventh, ninth, and eleventh notes of the ascending chromatic scale shown above. Conversely the indication to lower a note’s pitch a half interval (diminish the note) is given by the flat sign which is seen in the descending chromatic scale before the second, third, fifth, seventh, ninth, tenth, and twelfth notes.
There are several type of ascending and descending series of notes that make up what are called scales. Three common types are the seven note diatonic major or diatonic minor scales and the five note pentatonic scale. The notes are given names [C,D,E,F,G,A,B] but can also be given a number describing their relationship to the initial note. The first note is called the tonic, second the supertonic, third the mediant, fourth the subdominant, fifth the dominant, sixth the submediant, and the seventh is called the subtonic or leading tone.
II. Intervals and Chords
With regards to naming the relationship between notes only the labels tonic and dominant are used in this book. The other intervals are referred to by there numeric designation. Also there are intervals that exceed the octave and they are referred to as the ninth, tenth, eleventh, etc..
By superimposing combinations of notes musical Chords form the harmonic basis of most Western music. The common chords from left to right are the Major, the Minor, the Augmented, the Major Sixth, the Minor Sixth, the Diminished, the Seventh, and the Ninth in the examples above.
These chord combinations can be rearranged in what is referred to as inversions. They are still the same chord although as more notes are used to form the inversion they can sometimes be given different names. An example of inversions of a Minor Sixth chord is shown because of its important harmonic role in “Der Ring Des Nibelungen”.