Definition of Definitions
Definitions are those explanations of what a word means, and with accompanying explanatory sentences. Words generally have more than one definition, and some words have many definitions. A definition of a word therefore depends on the context of the word that is used. And, the words carry different meanings depending upon such context. In order that the more likely definition be chosen, it is important to read all definitions in order that a feeling for the word be understood in all its facets. Even then, as words have specialized meanings within math, legal, medical, etc., there is frequently none for music. Even when looking up the definition of ‘language’, music is not listed.
The word ‘function’ is an example of a missing definition. It is not defined under ‘music’, nor is it defined in any music dictionary. Therefore, we must create a definition for the word in a musical context. And, such definition must be simple, to the point, and useable. So, ‘function: the position of a note within a scale or chord, expressed with Arabic numbers, 1-2-3, etc. The function of chords are expressed with Roman numerals; I-II-III, etc. The counterpart of ‘function’ is ‘identity’.
The word ‘identity’ is defined in dictionaries in various contexts, but not music. It is not defined in any music dictionary either. So, we must make a definition for ‘identity’ in a musical context, viz; ‘identity’: the thing itself; a scale, interval, or chord without reference to a function, and with its own characteristic intervals. The major scale has a unique identity that may be found anywhere a composer wishes to use it. The dominant has a unique identity that also may be found where ever a composer wishes to use it.
Another word that demands a definition within a music context is the word ‘dominant’. There are several definitions for the word in other contexts, but in music it has only one definition and is defined as ‘the fifth note of a scale’. What is lacking is a contrasting definition. Few words, if any, have but one definition. This definition is a functional definition defined with a number; the 5 th note of a scale. There must be a second definition of ‘dominant’ as an identity, i.e. a unique sound quality. It isn’t there. We must therefore, create a definition that is again, simple, to the point, and useable. So, definition 2. Dominant: a chord identity with characteristic intervals of a major 3 rd and minor 7 th , with a unique identifier, ‘x’. The dominant (V) in a minor key is normally minor, and must be altered if one wants a dominant (x) quality. Without this second definition of ‘dominant’ and with its unique identifier, theorists use the egregious term ‘V7’ (dominant seventh) as the identity of the dominant. Both ‘V’ and ‘7’ are functions, not identities, nor the compound term, ‘dominant seventh’. Period, no exceptions.
‘Syntax’ is used by music theorists, but without a music definition. Not that it isn’t there, but what is there is an academic 1 theoretical description of ‘syntactical analysis’ 2 that few will understand and fewer yet, remember. However, since a simple, direct, and to the point definition isn’t there, here it is… Syntax: the logical order of scales or chords. The ‘key circle’, for example, is the basic syntax in music.
‘Harmony’ is another word that has many academic definitions, and with entire books written on, and called ‘Harmony’. But a simple, to the point definition is difficult to find. However, it may be defined as ‘any simultaneous combination of notes’. How then could there possibly be ‘nonharmonic’ tones as described in theory textbooks?
1 Academic: of theoretical interest only, not for general use, i.e. for the specialist.
2 A counterpart of ‘syntactical analysis’ is ‘functional analysis’, that is equally academic in its description.
‘Secondary dominant’ is another egregious term. Since theorists do not recognize ‘dominant’ as a harmonic identity, with a unique identifier, ‘x’, they use the concept of the ‘secondary dominant’ when a dominant is found other than on the fifth note of a scale. The identity of a dominant falls on the fifth note of a major scale coincidentally, i.e. at the same time. Therefore, they regard ‘V 7 ’ as being the identity of the dominant, and for a dominant on the super-tonic, have come up with the term, ‘dominant seventh of the dominant’ where the ‘V 7 ’ is the identity and ‘V’ becomes the tonic, i.e., ‘tonicized’. 3
‘Dominant with a missing root’ is a concept that is not found in any theory book, except a few that are surprisingly not referred to. 4 5 In addition, there is no symbol for the dominant sans root. Therefore, it must be created; ‘ o x m9 ’.
The ‘diminished seventh’ chord is not functionable under any circumstance. It is however, a chord with a missing root. And, with the missing root identified, it becomes a dominant minor ninth chord; ‘ oxm9 where ‘x’ is the symbol for dominant, ‘ o ’ is the symbol for missing root, and ‘ m9 ’ the fourth note of the chord. For example, the diminished seventh chord, ‘B-D-F-Ab’ contains the tritone, ‘B-F’. These notes then, become the characteristic intervals of a major 3 rd and minor seventh of ‘G’; the dominant minor ninth of ‘G’. The only exception to this is the diminished triad is functionable in a minor key as the super tonic (II).
Information and definitions on music theory in texts, and on the web are ‘academic’ in the extreme. They are mostly erroneous, inconsistent, and misleading at best because of the lack of and indifference to definitions.
In any case …
“If you can’t explain it simply, you don’t know it well enough” …Albert Einstein.
Ralph Carroll Hedges, B.Ed., B.Mus., M.M.
3 Walter Piston in his book, ‘Harmony’ (WW Norton & Co, 1969) was one of the first to subscribe to this nonsense. All theorists have subsequently followed suit. Benward & Saker, one of the current theory texts that do not waver, even though it is illogical and incorrect.
4 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’.
5 PhDs write the theory texts that publishers sell to universities, colleges, music conservatories, and teachers. A PhD degree indicates the highest degree of education. It is assumed that holders of this degree have read the literature on the subject. One wonders why important text as listed in the footnote above are missing any mention or reference in all texts sold by the major publishing houses on music theory. Is it an oversight or intentional?