Theorists and their publishers use compound symbols with impunity and without explanation. It creates symbols that cannot be justified, and no one cries foul. Teachers teach what they have been taught, right or wrong. Colleges and universities use ‘authorized’ texts that their professors must use. Virtually all of these texts are worse than useless. But they make the publishers and the PhD’s who write the texts wealthy since they are required texts in many schools and colleges.
A compound symbol is made up of two elements. The compound symbol, ‘V7’ is the worst offender. ‘V’ is the fifth note of a scale, but when ‘7’ is added to it, it becomes something entirely different. For example, ‘flower’ is something that is pretty and grows. The compound word ‘flowerpot’ however, is something entirely different.
The word ‘dominant’ has one and only one music definition; the fifth note of a scale. The dominant therefore, functions as the fifth note of a scale. It follows then that the definition of ‘function’ is ‘position’ expressed as a number. The dominant has no other definition. The second part of the term, ‘V7’ is also a function, indicating a 7th above the root and expressed as, ‘dominant-seventh’, a compound term with a meaning far removed from the simple term, ‘dominant’. The dominant functions as the fifth note of any scale. A second contrasting definition should be the dominant as a harmonic identity with no functional consideration. But it doesn’t exist. And there lay one of the most enigmatic areas in all of music theory.
‘Identity’ is defined as the thing itself without reference to function. ‘Dominant’ then should have a definition regarding its identity along with an identifier. All chords in music have identity along with an identifier; ‘M’ for major, ‘m’ for minor, ‘o’ for diminished, and ‘Ø‘ for half-diminished. The dominant as an identity is not included in this roster. And ‘V7’ is not that identifier nor is the compound term, ‘dominant-seventh’. With the dictionary definition of ‘function’ as a position expressed with a number, the use of numbers does not define identity. To illustrate this, consider ten people lined up in a row and asked to call off their number. So, they begin, ‘one’ ‘two’, etc. No matter what their position is in this row each retains his unique identity. So, ‘John’ may be the fifth person in this row. But he could be in any position without altering his unique identity. This concept is vital when applied to music: any chord with its unique identity may occupy any position in a scale. Thus, the dominant as a unique sound quality may appear on the first note of a scale, the tonic… or the second, the super-tonic, etc, or any chromatic tone within a scale. Composers use chords in this manner but theorists cannot grasp this. Since there is no identifier for the dominant as a qualitative identity, theorists use their theory of the ‘secondary dominant’ expressed as ‘V/V’, or V/II, or V/of whatever, i.e. ‘five of five’, ‘five of two’, etc with the second part of the equation ‘tonicized’. This ‘theory’ has caused a paradigm of unyielding ignorance within the subject of music as a language.
The concepts of function and identity are not to be found in any music theory text. This creates a theory where every chord, scale, or interval must be a function of something else. Nothing, it appears may have its own unique identity. The major scale for example is always presented with its functional key signature. An interval is always analyzed as a function of the major scale. The modes are analyzed in the same manner… the Ionian mode is 1-1 of the major scale, the Dorian mode is 2-2 of the major scale, etc. There is no unique sound identity indicated apart from a function. The major scale for example has an unmistakable sound. It is made up of a series of steps and half-steps with characteristic intervals of a major 3rd, major 6th, and major 7th. A minor scale is not ‘relative’ to any major scale, but has its own unique identity characterized by intervals of a minor 3rd, minor 6th, and minor 7th. Keys however are relative to one another when they share the same signature, as in ‘C’ major and ‘A’ minor.
It has become fashionable to use lower case Roman numerals to indicate minor, ‘ii’. ‘ii’ then becomes a compound symbol indicating both a super-tonic function, and a minor identity. But the super-tonic is minor in any case. Upper case Roman numerals in contrast indicate major, ‘V’ for example. But ‘V7’ isn’t major, nor is ‘vii’ minor. In a minor key this idea of lower and upper case won’t work in any case since ‘VII’ contains the dominant as a normal and coincidental identity instead of ‘V’, which is normally minor. Numbers indicate position within a key, a scale, or a triad and nothing more. ‘E’ functions as the major 3rd of a ‘C’ major triad, as an example. An ‘F’ minor triad may function as the super-tonic in the key of ‘E-flat’ major, or as the mediant in the key of ‘D-flat’ major, or as the dominant in ‘B-flat’ minor. Function is position. A unique harmonic identity such as the ‘F-minor’ triad may function within different contexts, and without destroying its identity.
Figured bass, or its alternate, ‘thoroughbass’, was a kind of short-hand for a keyboardist in ‘realizing’ an accompaniment of a Baroque orchestra. The figures were intervals, numbers, accidentals, et al, in relation to a bass note. (see ‘figured bass’ in Wikipedia). In the ‘Classical’ period Roman numerals began to be used in conjunction with figured bass symbols. This has created compound symbols that again, become problematic; ‘V6’ for example. ‘V’ functions as the fifth note of a scale. ‘6’ functions as an interval of a sixth above the given note, as per Baroque usage. The understanding of function is imperative if one is to understand music.
The diminished chord cannot function as itself due to the fact that every interval is of equal distance; a step-and-a-half. No one note may claim the root. It functions therefore as the upper four notes of a dominant without a root (sans root). The only exception to this is the diminished triad in a minor key that may function as the super-tonic. The dominant sans root must take a compound symbol, but this symbol does not confuse identity and function: oxm9. ‘o’ before the ‘x’ will indicate the missing root, and a minor 9th will be the fourth tone above the missing root.
One wonders why traditional music theory texts are used and referred to while important texts as those sited below in the footnote below are totally ignored. It leaves the subject incomplete, erroneous, and misleading at best.
Ralph Carroll Hedges, B.Ed., B.M., M.M.
 Ludmila Ulehla, ‘Contemporary Harmony’, chapter 6 ‘A re-examination of the figured bass’
 The theory of the ‘missing root’ (sum and difference tone) may be found in Helmholtz, ‘On the Sensations of Tone’ pg 152 ff, and Ulehla, ‘Contemporary Harmony’ pg 114 ff, and Giuseppi Tartini, “Trattato di musica secondo la vera scienza dell’armonia'” (Padua, 1754), and on the web, (see ‘Tartini’s tone’ in Wikipedia), also see, ‘sum and difference tones’.