In musical notation, frequency intervals are implicitly expressed in the relative vertical position of notes on the stave. For those who are skilled readers of music, this may be sufficient. However, as a more general solution, it has a number of problems. First off, the actual physical spacing of notes on the stave is not a linear reflection of the actual breadth of an interval, since a note in a physical position may represent one of 3 different frequencies depending on the key signature and any incidental sharps and flats that may be present. Secondly, the interval, as represented on the score names the interval, but doe not give us any further indication of its quality. Unless we have an internal mapping between the name of an interval, and how that interval is experienced, this does not help.
Some simplified notation methods are used by computer sequencing software. Usually, in this case, notes are presented as vertical lines expressing the duration of the note horizontally and the position on the scale vertically. These may use the physical spacing of the piano keyboard, or may simply allot one unit of vertical space to one semitone difference in pitch. In some ways this is more directly descriptive of the actual size of an interval. On the other hand, because we no longer have the key signature and incidentals, we lose other information that bears on the quality of the interval in the context of the current key.
Colour may be used to code individual notes in the scale. There is probably sufficient expressive range in the colour spectrum to represent the notes in the octave robustly. We cannot express the intervals by mixing the colours because colour mixing destroys information. When two colours are mixed, they create a new colour which may be indistinguishable from the colour representing another single note. Grouping patches of colour solves this problem, however in this case the quality of interval is still coded in a language which is arbitrary, and must be learned.
Another possibility is shape. Adding harmonically-related pitches together results in a wave with a specific shape, so at the simplest level, intervals will have characteristic wave-shapes.
| octave |  |
|---|---|
| perfect fifth |  |
| perfect fourth |  |
| major third |  |
| major sixth |  |
| minor third |  |
| minor sixth |  |
On the other hand, the signature differences between these wave-shapes does not always register quickly, especially where the shape is similar and the difference in in the number of ripples.