The training of piano students with traditional theoretical principles; figured bass, secondary dominants, types of cadences, etc. are an egregious waste of time, as they contribute nothing to the understanding of a musical composition. Josef Lhevinne in his book, ‘The Principles of Piano Playing’, had this to say…
“Study of this kind is not only a great waste of the pupil’s time but also a disgusting waste of the time of the advanced teacher, who realizes that he is not training a real musician but a kind of musical parrot whose playing must always be meaningless.”
And, from Dr Leopold Mannes’ Preface to Dr. Felix Salzer’s book, ‘Structural Hearing’…
“Theory, as it is called, has always been upheld as the promised gateway to this broad understanding, but there are thousands upon thousands of eager young musicians as well as disappointed older ones who will testify to the seemingly unbridgeable gap between their theoretical studies and the living experience of music itself.”
What if… we have two equally talented piano students and we train them with different means. The first piano student will learn for example, a composition from Bach, Chopin, Debussy, etc. by practicing and memorizing the work with little or no understanding. The second student will study the same composition by the chosen composer, but will understand the function and identity of the scales and harmonies, and memorize that analysis as the work is being practiced.
I submit that the difference of the performance of these two students will be obvious even though they have both had training with their respective teachers.
What if, for example we take two equally talented opera students. The first student will learn an aria by rote, i.e. practicing and memorizing the selection but no understanding of what the lyrics mean; syntax, function or identity. The second student will study the aria with attention to word function, i.e. syntax and word identity, i.e. parts of speech; verbs, nouns, adjectives, etc.
I submit that the difference of performance between the performance of these two students will be obvious to a native speaker of the language.
The purpose of language is to communicate, for that is what languages do. The spoken language is made up of parts of speech; nouns, verbs, adjectives, etc.. We identify these parts of speech by their functions; nouns function as people, places, or things. Verbs function as action words, and adjectives function as modifiers, etc.. We also identify words by their sounds, i.e. their pronunciation, as well as their spelling. But a logical order of the parts of speech must be present for communication to occur, called ‘syntax’.
While the spoken language has parts of speech, music has parts of chords; major, minor, dominant, half-diminished, and diminished. We identify these parts of chords by their functions; ‘function’ comes in two parts – position (look it up) and use. The ‘tonic’ is the first note of any scale, therefore it functions as the basic note of the scale. The dominant functions as the fifth note of a scale, therefore its position is number five, etc. We identify each of the types of chords by their sound, i.e. their characteristic intervals as well as their spelling. The ‘logical’ order is the ‘key circle’ in which chords progress up a fourth or down a fifth; C-F, F-Bb, Bb-Eb, etc. Chords built on those notes, in that order sound ‘logical’, i.e. within a framework of our experience.
But contemporary theory manuals do not teach identity, nor function. They have no definition for these concepts since they don’t include them in their manuals. They teach distractive concepts as ‘figured bass’, that distracts from the function (position of the lower-most note of a chord), and the identity of chords; the chord, B-F-G for example, is not a ‘V7’, ‘dominant-seventh’ chord. Both terms are functions, not identities. And, ‘V6/5’ does not describe ‘B’ in said chord as the major 3rd, its function, except a round-about process where ‘6’ is the root, and ‘5’ is the seventh, and the 3rd is… ? Make sense?
Objects have identities and identifiers. A piano who’s strings are horizontal, and it’s shape is like a wing is called a ‘grand’ piano. A piano who’s strings are vertical and shaped like a box is an ‘upright’ piano. And, a piano that is controlled electronically is an ‘electric’ piano. We know objects by their characteristics. Music is no different since scales, intervals, and chords are known by their characteristics, not their functions. Function is position and use. An accountant in a company has the position as an accountant and his use is crunching numbers. And, his function has nothing to do with his personality, the beauty of his handwriting, or his religion, etc. His identity on the other hand, is his characteristics and his identifier. For example, ‘Bob’ is 6’1”, grey hair, soft voice, and Social Security number xxx-xx-xxx, etc. You will notice there is nothing regarding his function. You will also notice that his function may change depending on where he might be and what he might be doing, e.g. home cooking dinner. There must be a concept of the difference between function and identity.
Theory manuals continuously confuse function and identity with such symbols as, ‘ii’ that combines function and identity that doesn’t hold up within any scale. ‘II’ is a function. ‘m’ is an identity. ‘ii’ is a function/identity. ‘vii’ is also a function/identity, but not the same identity. ‘ii’ is minor in a major key, but a diminished or half-diminished in a minor key. ‘vii’ is, who knows what? …in a minor key, ‘VII’ is major in a minor key? …sorry! ‘v’ is a function/identity; the fifth note of a scale and a minor identity. ‘V’ then is major, right? But ‘V7’ is not major. ‘II’ as a dominant quality is a ‘secondary dominant’, and is designated, ‘V/V’ (five of five). Wonderful! We now have its identity… but what happened to its ‘II’ function? But is ‘V/V’ an identity? Must be! ‘Bob’ mentioned earlier was given an identity and an identifier, but according to ‘V/V’ theory ‘Bobs’ identity is accountant/cook. He has no other identity other than his functions. I know this is a weird comparison, but I hope you get the point. Function and identity are two separate concepts, and they must be kept separate in musical analyses.
Music analyses must be indicated tn hierarchies, of which one may choose the more important as one goes along. For example, one may have trouble finding roots of chords. That then, becomes the primary effort before one tries to identify chords. Hierarchy then, becomes part of the decision of what is important, and that is a concept of gradients in learning.
The line below is taken from the Chopin F minor Nocturne. Roots of chord are indicated above the staves, chord identities between the staves, and chord functions below the staves. Note that the Roman numeral functions are always ‘upper’ case. These functions cannot possibly be known unless the roots are found. So, if you so like, the Roman numerals could be placed between the staves, then their identities below the staves. Chord identities could be included with root designations as, ‘Fm’, ‘Ebx’, ‘AbM’, ‘Cx’, etc., but never as part of the designation as in ‘ii’ inferring minor. Identities might also be included with functions as in, ‘Im’, ‘VIIx’, ‘IIIM’, etc. ‘VII’ in a minor key is normally dominant (x). However, it is suggested that you keep indications separate so that confusion doesn’t up-end logic.
Ralph Carroll Hedges, B.Ed., B.Mus., M.M.
 See https://anmde.com/wp-admin/post.php?post=1028&action=edit for ‘Compound Symbols’ for further discussion of the issue.
 No theory manual includes an identifier for the dominant. Why this is has never been explained. All other chords have identifiers: ‘M’ for major, ‘m’ for minor, ‘o’ for diminished, and ‘ Ø‘ for half-diminished, but none for dominant. Harmonic identifiers are expressed with symbols or letters, not numbers. Harmonic function is expressed with numbers, either Arabic or Roman. In addition to the lack of an identifier, there is only one definition for ‘dominant’; 1. The fifth note of a scale. A second, contrasting definition for ‘dominant’ as an identity is missing. Therefore one must be created, viz., 2. Dominant; a harmonic identity characterized by a major 3rd and a minor 7th, and with an identifier, ‘x’.