Tonal music, or ‘Western’ tonal music is based on the major scale, and the major scale in turn is derived from the ‘key circle’, aka ‘circle of fifths’, or simply the ‘Circle’. The major scale is constructed with steps and half-steps. But these steps are different in music composed before the middle of the 18thcentury, and music thereafter.
In music prior to the middle of the 18thcentury the major 3rdwas made up of two steps with the mean of their mathematical sum, creating a ‘mean-tone’ system whereby the major 3rdwas a ‘just’ major third, i.e. a ‘true’ major 3rd. ‘Perfect’ 4ths and 5ths were also ‘perfect’ in their mathematical ratios. This system created beautiful harmony in keys not more than two, maybe three sharps or flats. Harmony in keys of four and more sharps or flats created harmonies that were so ‘out of tune’ that they ‘howled’. Modulations therefore, were seldom if ever employed.
It was JS Bach that realized that the 5ths and 4ths must be ‘tempered’, i.e. the 4ths made a very small amount ‘wide’ (sharp), and the 5ths a small amount flat in order that all keys might sound ‘in tune’. He was one of the first to tune his keyboard instrument in ‘the tempered’ scale, hence ‘well-tempered’. This system replaced the ‘mean-tone’ system of the 17thcentury. To test his theory of the ‘tempered’ scale he created one of the world’s great masterpieces with each set of pieces in all keys. His ‘Wohl Tempierte Clavier’ was published in the middle of the 18thcentury; around 1750.
The concepts of ‘consonance’ and ‘dissonance’ was well established up to Bach’s time. Major and minor 3rds, and perfect 4ths and 5ths were ‘consonant’ because the 3rds were ‘true’ and 4ths and 5ths were ‘perfect’. But with the tempered tunings from Bach’s time to today, 3rds are not ‘true’ and 4ths and 5ths are not ‘perfect’. Therefore, these intervals are not ‘consonant’, theoretically. This has resulted in a re-evaluation of the theory of consonance and dissonance, and the concepts of what is beautiful. Even the theory of the ‘figured bass’ has been re-evaluated by the 20thcentury.
‘Figured bass’ was developed during the Baroque period (1600-1750) for the keyboardist to ‘realize’ an accompaniment for the Baroque orchestra. Roman numerals were not used, therefore the system was based purely on intervals. By the 19thcentury theorists began combining figured bass with Roman numerals, resulting in a theory using compound indications of chords that confuses function and identity. The ‘dominant-seventh’ (V7) is such an indication that confuses function, the numbers, with the aural identity of the unique sound of the dominant.
Analysis of music of the ‘Western’, or ‘European’ based music must now be done with harmonic function and harmonic identity separate so the compound figures do not confuse the reader, …or the writer for that matter.
Ralph Carroll Hedges, B.Ed., B.Mus., M.M.
See L. Ulehla, ‘Contemporary Harmony’ and the section ‘Figured bass re-evaluated’.
The unique identity of the dominant is made up of the characteristic intervals of the major 3rdand minor 7th, not to be confused with the function, ‘V7’. Its symbol therefore, is not ‘V7’, but ‘x’, as used by many theorists, John Mehegan of the Juilliard School for one. ‘x’ must be used to replace ‘V7’ as the identity of the dominant so that musical analyses be thereby demystified.