User:Chopinman

The Dominant; An Identity Crisis
All information in music theory texts, manuals, books, and articles on music analysis violates the laws of logic to one degree or another. There seem to be no exceptions. The basic issue is that the dominant has no identity. It is never described as itself, but as a function of something else. It is always allied to another entity and has no identity in-and-of itself, evidenced by the fact that there is no label for the dominant. All other chords have identity; major, minor, half-diminished, and diminished with appropriate syntax; 'M' 'm' 'o' 'ø'. But nothing for the dominant. 'V7' is not a syntax of identity, but of function. It is a gross error to label the identity of the dominant as 'V7'. Theory texts violate the many laws of logic. These laws are;

1. The law of Identity. ‘...each thing is inseparable from itself’ 2. The law of Contradiction. ‘Contradictory statements cannot both be true at the same 	time.’ 3. The law of Excluded Middle. ‘It is impossible that there should be anything between 	the two parts of a contradiction.

In addition, there are certain principles of consistency that may be included. 1. Consistency; that no theorem in the system contradicts another. 2. Validity; that which never shows a false inference from a true premise. 3. Completeness; if a theorem is true it can be proven. 4. Soundness; that the premise is true and valid.

And... Gestalt; Gr, ‘form or shape’ (Pragnanz). A concept of wholeness expressed as; ‘The whole is greater than its parts’.

Gestalt is also expressed as the ‘Law of Simplicity’, where ‘Every stimulus is perceived in its most simple form.’

Starting with simple musical elements and their identity...

The object below is a ‘chord’ in its most simple form. We may add complexity by saying it is a ‘C major triad’. And it may be broken up into its component parts; a major 3rd, a minor 3rd, and a perfect 5th. And we may add its ‘figured bass’; 5/3. It may be given a function; ‘tonic’ (I). And it may be given a quality; major (M). Within a framework of a composition it should be described by its most simple designation, whatever that may be. When a fourth note is added the chord now becomes a larger entity, but remains a ‘chord’ and is perceived in its entirety. Theorists add complexity by saying it is a, ‘major seventh chord’ and is made up of a major triad and a major seventh, and is described as a, ‘major-major seventh chord’. In addition it may be given a function; ‘I7’, and/or designated, ‘M7’. But it’s not heard that way. It’s--Chopinman (talk) 02:20, 3 March 2011 (UTC) heard as a major chord, albeit a larger major chord than the major triad above. ‘7’ becomes an added complexity tøøhat is really redundant, and confusing since ‘7’ is used in many different contexts. The simple description, ‘major’ (M) does not violate its identity.

The following is a scale. It is perceived as a ‘scale’ as opposed to an arpeggio where the notes do not occur one-after-the-other step-wise. We perceive this as a ‘C’ major scale because of our acquaintance with the form, just as we perceive a word because of our acquaintance with its form. We may analyze the scale by step into whole-steps and half-steps. But until the whole scale is performed we cannot judge its quality as a major scale. And when the scale is performed we perceive its ‘wholeness’, and not so much its parts.

In the chord below a flat is added to the 4th note of the previous chord the sound quality is changed. Even so, the chord is perceived as itself and not in relation to anything else. Theorists may describe the chord with its make-up; a major triad and a minor seventh ‘major/minor seventh chord’. It may be analyzed as a ‘five of four’ (V/IV) in relation to the key signature. It may even be described as a ‘dominant seventh chord’. It is none of these. It is simply itself and is perceived in its singular wholeness but isn’t able to be labeled as such. It should be called ‘dominant’ not a function, (V), …but ‘dominant’, and there is no symbol for ‘dominant’. And there presents one of the greatest problems and unnecessary illogical complexities in the subject of all of music theory.

Similarly, a flat may be added to the seventh note of a major scale. As a whole scale it is a different aural quality than a major scale. Again, it is what it is. It has a singular identity. Theorists label it with varying terms; ‘mixolydian’ for example. But mixolydian implies a scale built from the 5th to the 5th of a major scale. It may be called a dominant scale. But again, ‘dominant’ implies a scale built upon the 5th of another scale. It doesn’t sound that way, however. It sounds simply what it is. It has a unique quality that is completely separate from anything else.

The above examples apply the first law of logic; Identity. An object, chord or scale, must have an identity of its own. It must also conform to the Gestalt principle of simplicity; ‘Every stimulus is perceived in its most simple form.’

The importance of this is in the listening of what one is performing. One should ‘hear’ a major triad no matter its context, for example. One should hear a ‘dominant’ quality chord without reference to what is around it, where it is going or to what it is allied. These extraneous complexities impair the basic truth of Identity. In the case of the term, ‘dominant’ there is a semantic problem. It means more than one thing. But to theorists it means ‘V7’, and is usually described as, ‘dominant seventh’. But this connects it as the 5th of another entity. It is not heard that way. Therefore the label is in violation to its identity.

The ending to the Gershwin 2nd Prelude ends on a dominant, not a ‘V’, but a dominant. So does the ending to the Chopin Prelude Op 28 Nr 23.

Gershwin Prelude Nr II… Chopin Prelude Op 28 Nr 23 in ‘F’ major, measures 21-22. The dominant is created apparently with the lowered 7th. And that is what is heard. Not ‘V’ but the lowered 7th. Giving it a syntactic label is the problem however. Indicating ‘b7’ is only indicating how the sound is arrived at. In any case, the function of the final chord in both cases is tonic (I). That cannot be changed to dominant (V) since that would violate the second law of logic; ‘Contradictory statements cannot both be true at the same time.’  The sound in both cases cannot be both tonic and dominant at the same time. But again, semantics confuse the issue. When the term, ‘tonic’ is used, it is used as a function. When the term ‘dominant’ is used it is invariably also used as a function. And therein lay the conflict as stated in the second law of logic. ‘Dominant’ then must have another meaning, a qualitative meaning rather than a functional or quantitative meaning. There is no discussion of these phenomena in any text on music theory, and that is what leads to the error of all analyses within these texts. Because of this, the law of Simplicity is grossly broken with complex and illogical theories of the secondary dominant, and its corollary, tonicization.

What if a syntactic symbol is created that refers to the dominant as a quality and not a function? What if we used ‘x’ as denoting the dominant as a quality? This would give the dominant as a quality an identity; a label. The dominant thereby becomes an aural quality. And this quality is its identity.

Identifying this as a solution to the semantic and syntactic problem of the dominant, all theories of secondary dominants and tonicization are thereby totally negated. Those theories were based on a false premise that ‘dominant’ means one thing and one thing only; ‘V7’. There was no possibility that the chord might have its own identity apart from its function. It seems incredulous that all chords in the theoretical spectrum have separate qualitative identities except the dominant. They may be altered; CM, Cm, CØ, etc., but not the dominant. If we include the new syntax, ‘x’, a ‘C’ chord then may be identified as ‘dominant’ the quality; ‘Cx’. And the lowered 7th in the Gershwin and Chopin Preludes as quoted above as ‘dominant’; ‘x’, an aural  identity and not a function.

With this new tool all problems in the analysis of compositions from the Baroque to the Romantic periods may be analyzed adhering to the laws of logic and the principles of Gestalt. Pianists in particular may now study their repertoire and hear all chord identities and interpret accordingly. The dominant may now be itself!

Analyses may now be applied on two levels; the qualities of chords, and the function of those chords. Quality and function must be kept as two different subjects. When they are intermingled the second law of logic is broken; the law of Contradiction; ‘Contradicting statements cannot both be true at the same time’. A chord may not be a super-tonic and a dominant at the same time, as in ‘V/V’. A dominant may not be ‘tonicized’ …even temporarily. It is a violation. It is illogical, and violates another principle of logic; Consistency. ‘…no theorem in the system contradicts another’.

The validity in a proposition is contained in its conclusion. And that conclusion may be thought of as the analysis of an entire composition, or section thereof and not just a small part taken out of context. The question is, does the analytic system cover all bases and without extraordinary and illogical complexities? Are the syntaxes complete and the symbols with meaning? If this is not so, then laws of logic are strained to incomprehensibility. In music the logic must be two-fold; firstly it must conform to the laws of logic, and secondly it must conform to aural recognition, i.e. that which is heard. The mind and the ear must be in agreement. Any analysis must provide fruit for both the mind and the ear. The simplest is the most accessible due to the fact that music is an art of continuum, as opposed to say, architecture. There must be an instantaneous recognition of what is happening at any given moment. But to go into an extended ‘song and dance’ over whether a chord is a super-tonic or a secondary dominant is the most viral attack on logic. To say that a dominant may be ‘tonicized’ is also the most flagrant violation of the most basic laws of logic. Both negate the law of Identity.

The following analysis will demonstrate firstly, a separation of the concepts of function vs quality. Secondly it will demonstrate the identity of chords apart from their function. And thirdly it will demonstrate the validity of correct syntax within the analysis.

The following is an analysis of the first four measures of the Chopin Nocturne Op 55 Nr 1 in F minor…

The first chord is an ‘F’ minor triad, the second chord is a dominant seventh with the 3rd as the lower-most note, and this chord moves to a major triad in the second measure again, with the 3rd as the lower-most note. This chord might have been designated a minor triad with the 3rd again as the lower-most note, except that a root, ‘F’ is not present. What is heard is ‘A-flat’ and ‘C’, a major 3rd, making up the basis of an ‘A-flat’ major triad. The syntax is expressed as qualities.

Adding functional designations to the line...

Please understand that if a chord is normal within the key it needs no further indication of its quality. The VII7 chord is normally a dominant quality in a minor key. Likewise, the III chord is normally a major triad in a minor key. Therefore VII – III is like a V7 – I in the relative key.

It may be expressed as...

Now we may see that an ‘E-flat’ dominant moves to an ‘A-flat’ major, V – I in the key of ‘A-flat’ major, the key of the Tonic (I). However, the line modulates back and forth from ‘F’ minor to ‘A-flat’ major and back again to ‘F’ minor. Not only is this cumbersome but take a look at the treble theme. It represents a descending normal minor scale fragment that shows no signs of any modulation from a minor to a major key and back again, albeit that the two are relative.

Traditional theory texts would describe the second chord in measure 1 as a ‘secondary dominant’ where the ‘E-flat’ chord is V of III. Of course it’s ‘V of III’! And what is V of III? …‘VII’. Dah....!! It is no secondary dominant!

Let’s look at the identity of each chord… The first chord is an ‘F’ minor triad, and it is heard that way. The second chord is an ‘E-flat’ dominant quality. And this is easily verified in the listening. The chord in the following measure contains only the root and the 3rd, but is heard as ‘major’. The next chord in the measure is an altered dominant; the 3rd is raised. What is its aural identity? … ‘dominant’, and not the dominant of something else. This is easily verified in the listening.

And finally… does the syntax of the description of the chords in both their function and quality agree with the ear? Are they simple enough to convey their identities? If so, you have it. If not… back to the drawing board!

Chord progressions in a minor key have had virtually no discussion in theory texts. These progressions function so much more differently than those in a major key that a great deal of explanation should be forthcoming. So far there is none. And, so much of the literature is in minor keys that it is vital to understand these progressions in order to understand music and its intentions. The laws of logic are especially vital to the minor and modal keys.

It’s amazing how far agreement with things we have been taught can take us. That’s the way we were taught and that’s the way we will pass it on... to the detriment of those whom we ‘teach’. Ralph C. Hedges February 2011