Music is a language, therefore follows much of the same principles as the spoken language. For example, we may see an octagonal sign on the side of the road while driving at night. It’s red color may be dark because of no light on it, but we still read it as a stop sign because of its characteristic shape. Advisory traffic signs are yellow with the characteristic triangular shape, etc. Missing musical elements may be thought of in the same manner with characteristic and missing elements.
The following lines are taken from the Chopin Prelude Op 28 nr 15 in D-flat major. The ‘A-flat’ major triad on the dominant (V) changes to minor on the third beat that now may be regarded as the super-tonic in the key of the Sub-Dominant (IV), ‘G-flat’ major with a II-V-I progression. Measure 11 moves back to an ‘A-flat’ minor triad, but I think may be indicated as a tonic triad in the key of the minor Dominant (Vm), ‘A-flat’ minor with a I-V-I progression. ‘A-flat’ minor is relative to the key of ‘C-flat’ major with seven flats. The signature contains five flats with ‘C-flat’ and ‘F-flat’ in measure 12 to complete the seven flat ‘parent’ signature. The chord on the third beat is a dominant without a root (ox). Within this half measure there is a tritone; ‘B-flat’ to ‘F’ flat, the major 3rd and minor seventh respectively of the dominant (x) on the leading-tone (VII), a normal dominant in a minor key. ‘B-flat’ is the major 3rd of ‘G-flat’ the root of the chord. The major 3rd and the the minor 7th, ‘F-flat’ are the characteristic notes of the dominant (x). The chord is, (G-flat) – B-flat – D-flat – and F-flat. ‘A-flat’ is the 9th. But listening to it, it doesn’t sound that way. An alternate analysis is below this line.
As an alternate analysis, the last half of measure 12 is seen as a half-diminished chord (Ø) on the super-tonic (II), where ‘B-flat’ is the root and ‘A-flat’ is the minor seventh, and ‘F-flat’ the diminished fifth. This seems to make a bit more sense, even though ‘B-flat’ to ‘F-flat’ is the tritone of a dominant with a missing root as in the above analysis.
Measure 13 is almost identical to measure 9. The key of the Sub-Dominant (IV), ‘G-flat’ is the same. We have to assume ‘C-flat’ and ‘E-flat’, the minor 3rd and 5th respectively of the minor triad. It could be played again so that the ‘II-V’ is explicit. ‘V’ does not move to ‘I’ as in measure 10, but moves to the sub-mediant in measure 14. In linguistic parlance, ‘V’, the verb, moves to its object, ‘I’, therefore is transient. ‘V’ moving to ‘VI’ however, becomes intransient because ‘VI’ is not the direct object of ‘V’, the verb. Therefore, I think, measure 14 should begin a new phrase. VI-III is a reverse progression since III-VI is normal ‘circle’ progression. Measure 15 moves to a ‘B-flat’ minor triad with its 5th as the lower-most note. To indicate this draw a line under ‘I’ and write ‘5’, the 5th, and becomes the root of the dominant (V) in the key of the Sub-Mediant (VI), ‘B-flat’ minor. The chord in the last half of measure 16 is the same as in measure 12, a dominant without a root. ‘C’ to ‘G-flat’ is the tritone with ‘C’ the major 3rd of ‘A-flat’, the missing root, and ‘G-flat’ the minor 7th. The chord is, (A-flat) – C-flat – E-flat – G-flat. ‘F’ might be considered a ‘pedal’, or the 13th of the chord. But that’s unlikely because it doesn’t sound that way. Another analytical possibility is under this line.
The leading-tone chord (VII) is a normal dominant (x) in a minor key. The dominant (V) must be altered if it is to be dominant (x). Conversely, the dominant (V) in a major key is a normal dominant (x), and the leading-tone chord is diminished if a triad, and half-diminished (Ø) if a seventh chord.
Another possible, and more probable analysis is below where the last half of measure 16 shows a normal diminished triad (o) on the super-tonic (II). But then, what to do with ‘F’ on the bottom… possibly as a ‘pedal’ or maybe an 11th, which is unlikely since it doesn’t sound that way. In any case, ‘F’ as a pedal does stay constant for five measures.
Indicating I-VII in measures 12 and 16, or as I-II keeps a certain consistency between the two lines, but one must make a choice based upon both that is logical and what it sounds as. Choices like this may be resolved in a future month or year. Work with the choices until one or another becomes clear as the winner.
The following is another example of the same leading-tone (VII) dominant (x), taken from the Chopin Nocturne Op 65 nr 1 in F minor. The leading-tone in the first measure is a normal dominant (x) containing the tritone, ‘G’ and ‘D-flat’, the major 3rd and minor 7th. When analyzing with pencil, draw a line under ‘VII’ and write ‘3’, indicating the note on the staff is the 3rd of the chord. Do not use figured bass. VII moves to III, ‘E-flat’ to ‘A-flat respectively as a normal ‘circle’ progression. The dominant (V) in measure two is an altered dominant (x). The 3rd must be altered to a major 3rd, ‘E-natural’ in this case. Again, it is the lower-most note and may be indicated ‘3’ under a line drawn below ‘V’.
The following is taken from the Debussy’s Prelude, La Fille aux Cheveaux de lin. The first two measures are based on the sub-dominant major 9th (oM9). The treble shows an ‘E-flat’ minor 7th arpeggiated chord, the upper four notes of a ‘C-flat’ major 9th chord. The symbol, ‘o’ to the left of ‘M’ indicates a missing root, ‘oM’. This root does not appear until the last eighth note in the second measure, Measure 28 confirms this with a solid ‘C-flat’ major chord on the sub-dominant (IV).
Chords may be missing parts of chords. For example, Bach’s ‘C’ major ‘Short’ Prelude ends with only the root, ‘C’ and 3rd, ‘E’. Do we understand this that Bach ended the Prelude with an interval? …or do we regard the two notes as part of a triadic harmony with a missing 5th? Does that chord sound any less complete that the one before it; the dominant, ‘G-B-D’, the root, major 3rd, and the 5th, ‘D’? Theory manuals provide the student with information regarding types of cadences, so that the final cadence below is describes as a ‘perfect authentic’ cadence. Even this is a distraction, a detour if you will, from the important issues of function and identity, where ‘B’ on the fourth beat functions as the major 3rd of the chord, and as the leading-tone of the scale that moves to the root of the tonic in the final measure. But theory manuals do not describe function and identity.
Analyses may be written within the score, as above, or written out on note paper. The analyses must make sense for the pianist, and be useful for the pianist. The chord names may be included above the treble; ‘Fm’ – ‘E-flat x’, even spelled out if necessary. However, analysis for analysis sake is nonsense. One must know what one is playing within every beat of every page of a composition. This takes work – it takes practice, and lots of it. The result is a performance that has meaning, opposed to a performance of notes with no understanding of what those notes are made up of. The ear must be an active participant, hearing the characteristic intervals, for example, and hearing in the mind’s ear the identities of scales, intervals, and chords, and their functions. Performance security depends upon it. Without this knowledge performances take on a hit or miss, ‘hope I don’t forget the notes’ kind of thing that plagues the usual piano student.
The measures above are examples of the missing elements in music. Nevertheless, compositions must be analyzed in their entirety…and re-analyzed, and re-analyzed and practiced until one knows exactly what one is playing during every beat, every measure, and every page of the music. Universities, colleges, conservatories, and piano studios do not require this. The reason, unfortunately, is that traditional music theory is unable to handle it. And, what it attempts to describe is convoluted, illogical, and lacking definitions. The most glaring lack of definitions are, 1. A second, contrasting definition of the word, ‘dominant’. 2. A definition of the word, ‘function’ is completely missing. 3. The concept of identities and identifiers is missing. In music, one identifies an interval by its size and its identifier; M, m, Ø, etc.. The dominant as an identity has no identifier, and ‘V7’ is not it. ‘V’ is a function, a position within a scale. ‘7’ is an interval and a position above a root note. The chord, ‘B-F-G’ is not a ‘V7’ chord, but a ‘V6/5’ chord. And on and on it goes with misleading, missing, and overly academic therefore useless, descriptions. I think you get my point.
Missing elements; missing roots, missing 3rds, Missing 5ths, etc, etc. abound in all periods of music. They must, for the sake of clarity, be assumed. One cannot… one must not, take everything at face value. Characteristic intervals must be seen, understood and heard because it is they that provide the substance of harmony.
Let me ask you… wouldn’t it be wonderful to know exactly what you are playing at all times in a performance so that your attention and your ‘ear’ is on functions and identities rather than memorized notes?
However, if you prefer to play notes… carry on… don’t let me disturb you!
Ralph Carroll Hedges, B.Ed., B.Mus., M.M.
 A ‘parent’ signature is created by the accidentals in the music. The ‘existing’ signature is next to the clef signs.
 A diminished triad on the super-tonic is the only place a diminished chord may be functionalized as a super-tonic (II). Diminished chords elsewhere are to be analyzed as dominants without roots. (ox)
 The term, ‘pedal’ or ‘pedal point’ comes from the Baroque to denote a non-harmonic note that is held for some time over which there may be changing harmonies, with a foot on an organ’s pedal, hence the term.
 Figured bass was a kind of short-hand system developed during the Baroque period for keyboardists to improvise as an accompaniment for a Baroque orchestra. Roman numerals were not used – only the numbers indicating intervals, chromatic changes, etc. It has no practical use for today’s analyses. However, if one is to be a Baroque specialist it must be learned.