Intervals 1: Traditional Notation
This tutorial explores the limitations of traditional notation when it comes to representing interval relationships between notes. Note that while the illustrations show harmonic intervals, what is being said applies equally to melodic intervals.
At first glance traditional notation seems to do a good job representing interval relationships. Thirds can be easily recognized anywhere on the staff as two notes located on adjacent lines or adjacent spaces (assuming that no accidental signs are involved). Similarly, fifths and sevenths are also two notes that are both on lines, or both on spaces. Seconds, fourths, sixths, and octaves have one line-note and one space-note. This general pattern makes it easy to identify intervals and distinguish them from each other. Seconds have a distinctly different appearance from thirds, and thirds from fourths etc. Accidental signs introduce exceptions, but otherwise this pattern is consistent across all the different keys and key signatures.
Diatonic Intervals in Traditional Notation, Key of C Major, Treble Clef
However, while traditional notation does provide this basic and important level of consistency in the appearance of intervals, things are not as consistent as they may appear. It is fairly easy to identify intervals as seconds, thirds, sixths, or sevenths, but it is impossible to tell from their direct appearance whether these intervals are major or minor. Similarly, one out of every seven intervals that looks like a perfect fourth or fifth is actually a tritone -- an augmented fourth or diminished fifth. (Fourths and fifths are "perfect" intervals that are do not have major or minor variations.) So intervals that look the same may sound quite different.
Before reading further, take a moment to look at the diagram above and see how quickly you can determine which intervals are major or minor, and which are tritones posing as fourths or fifths...
Now imagine a different key signature and see how that makes the task more difficult, and how it gets more and more difficult with more complex key signatures...
Now imagine a different clef and see how that also changes everything around...
While the immediate appearance of an interval gets you so far ("this is most likely a third and not a second or fourth") to fully identify an interval one must take into account the current clef sign, key signature, and any accidentals, going through the mental procedure of calculating the names of the individual notes before their interval relationship becomes clear.
The following diagram illustrates these inconsistencies in the appearance of intervals, as they are found even in the simplest case, the key of C major with no accidentals.
Diatonic Intervals in Traditional Notation, Key of C Major, Treble Clef
These inconsistencies keep traditional notation from fully and clearly representing interval relationships. This is especially problematic for certain important basic intervals: whole steps and half steps (the basic elements of diatonic scales and modes) and major and minor thirds (the fundamental building blocks of diatonic chord structures).
By preventing what one sees from corresponding to what one hears, traditional notation frustrates and undermines the musician's understanding and proficiency with the patterns of intervals found in diatonic (or non-diatonic) music. How might the aspiring musician's understanding, appreciation, and ability to play music change if this were not the case?
Furthermore, these inconsistencies make it much more difficult to play by reading the interval relationships between the notes (rather than reading their individual pitch values). This has implications for learning to improvise or play by ear - skills which largely entail playing by interval relationships. Not to mention basic understanding of harmony and music theory.
Continue on to Intervals 2: 6-6 Notations to see how alternative notations can improve upon these limitations of traditional notation when it comes to representing interval relationships.