I could open this blog by making a slick comment such as ‘Well, there AREN’T any, actually’.
This isn’t too far away from the truth but, as always, the matter is a little more complicated.
I think I’ll probably be correct if I say that the majority of people approach music theory, especially the theory of harmony, with fear and trepidation. But why is this? We all know that, even in the arts, we have to push our boundaries in order to progress but I’ve always believed that, if we aren’t enjoying ourselves (most of the time), we’re doing something wrong.
Mindful of my own struggle with mathematics at school – partly because it was badly taught – I was determined to breathe some life into the subject of music theory when I wrote the book. I’ve always believed that, to explain something to someone, a person needs a thorough knowledge and understanding of the particular subject. To achieve this, an understanding of the rules-behind-the-rules is required, otherwise we’ll apply them ‘parrot-fashion’, as so many do, even those who should know better.
Music theory, as it is generally presented to us, consists largely of a catalogue of the preferences of prominent composers over the last 300 years or so and as such is obviously not without value. It has always been one step behind practice. A successful theory would embrace the music of the past, present and future. There would be no need for us to say that certain rules do not apply to certain types of music.
Every rule of music has been broken many times by talented writers. The sole criterion is that a composer’s music should demonstrate a clearly defined, strong artistic purpose.
We should never say ‘that is forbidden’ but rather, ‘if you do this, that will happen’. It’s a subtle but important difference. Students of music should be fired by an enthusiasm to write and not feel intimidated before they even start.
The commonest rules of all are those pertaining to parallel intervals, especially the perfect fifth.
The least complex interval is that of the octave, each octave being in a simple 2/1 ratio to the one above or below. The relationship is so simple that we give each note in the series the same letter name but they are not all the same note. Parallel octaves are common where the bass is reinforced in the octave or where the melody is duplicated an octave below. They are also common in counterpoint, where they provide added thickness to voices – even if the lower octave of one voice overlaps the upper octave of another. (The lower octave is perceived to be a reinforcement of the upper notes, rather than a voice in its own right.)
Next in complexity is the perfect fifth, in fact the effect of the fifth is so ‘perfect’ that a succession of them (between the same pair of voices) in a simple, diatonic harmonic continuity will stand out at the expense of the other voices, producing an ugly effect. And yet, to remain true to the above claim regarding a ‘clearly defined, strong artistic purpose’, we will find many instances where consecutive fifths will serve us very well:
Discounting the many stylistic treatments such as those found in rock riffs* and Red Indian, and other, programmatic associations, the effect of large masses of sound in orchestration may be enhanced by having a fifth between the bass (which will not necessarily be the ‘root’) and the note immediately above it in the harmony. In practice, there will most often be an octave between the lowest voices, with the fifth placed above the upper octave.
In the period of Organum parallel fourths and fifths were common. I’m sure no one on here needs to be reminded that a fourth is an inverted fifth.
Successive compound fifths, especially when more than one octave is added to the interval, become more and more harmless the wider the notes of the interval retreat from one another (which applies to other parallels, too).
In other cases, the movement of a parallel fifth will be become virtually unavoidable. Using the substitute dominant in place of the regular chord (Db7>C in the key of C) often provides an example of this.
The ‘rules’ of melody can be even more obtuse
There isn’t space here to deal with this topic in its entirety but a few pointers might help to convey the purpose of this blog:
Regular note resolutions may be overridden by inertial forces in, for example, a scale run. In this context a scale run is one that entails four or more notes moving in the same direction by stepwise motion. Similar principles are involved in sequences and in many other circumstances where repetition, resulting in familiarity, paves the way.
After a leap in either direction, a melody usually turns in the opposite direction but an augmented interval will continue in the direction of the chromatic alteration before resolving. The requirement to turn in the opposite direction will obviously be ignored in ‘real’ music where a composer wishes to create an intensely dramatic feeling of unusually high upwards energy by defying the ‘rule’ and allowing the melody to continue upwards. Augmented intervals in melody can give rise to awkwardness but where a melody clearly describes an arpeggiated form, e.g. going from the seventh to the third in a dominant seventy type of chord – f > b in C7 – or when it occurs in an augmented chord, many situations are ‘allowed’, although they are best suited to instrumental music. Vocalists find some intervals difficult to pitch (and they’ll usually still sound wrong, even if sung well except, possibly, in a jazz context).
It might be worth pausing, here, to consider that this problem isn’t all one-way. A musically aware, experienced listener will be more tolerant.
Traditional rules regarding note-doubling are too simplistic in an orchestral setting. Apart from the obvious fact that they would place too many constraints on a composer, sections of instruments of a similar tone-colour tend to cohere and are heard as elements of the picture in their own right.
Having learned the basics of harmony, the next important step is to consider the vertical placement of chordal functions. The lowest note practicable in music is c = 16 vibrations per second (two octaves below the bottom c on my bass trombone). Referring to the harmonic series we find that e doesn’t occur until the fifth harmonic, which takes us to the e below the bass clef, the third of the chord of C major. Placing the the third of any chord below this level will imply the existence of a fundamental that doesn’t exist in performable music. Although our systems of harmony evolved independently, especially with the adoption of equal temperament, the vertical structure of harmony must comply with the arrangement of the harmonic series, with wider spaces low down and closer intervals higher up. (Colouristic effects are likely to use any distribution, of course.) Other, similar, considerations involve the avoidance of placing higher chordal extensions below the seventh. ‘Clustered’ jazz voicings are another matter, of course.
In one of the textbooks I own the chord f-a-c-e in open harmony is given as a C thirteenth chord in a musical example, even though the f (the eleventh!) is just below the bass clef. This cannot be unless, of course, you’re happy with abstract examples that only exist according to ‘root theory’.
High tension chords will benefit in terms of clarity if the octave placement of the bass is correctly chosen. For example, both the natural fifth and the altered fifth may be used at the same time if these considerations are exercised and the ‘offending’ notes are kept well away from each other. The raised or lowered fifth then become the lowered thirteenth or the raised eleventh, respectively.
Isn’t life complicated? Well, not necessarily, when you understand how things really work.
* The riff is one of those terms that has changed its meaning over the years. A riff is a repeated phrase or motif that continues under (or over, or in between) the other parts even in cases where, technically, it doesn’t always fit. It was a characteristic of jam sessions. Nowadays, it is a term often used to describe those memorable heavy rock phrases. Similarly, cool referred to a deadpan style that was characteristic of modern jazzmen seeking to escape the hotter styles of the past. Nowadays it’s used as a sign of approval. Un-cool means it sucks (it’s a lemon, in US parlance).
Footnote: I haven’t used the numeric description of octave placement in this blog because there isn’t really much standardization. Mostly, the octaves are numbered from the bottom up but I prefer the scheme where ‘middle’ c is the starting point and notes above this are numbered with superscripts and notes below with subscripts. Subscripts move downwards numerically.