Scales and melody

As already mentioned, most melodic music uses some limited set of pitches repeatedly (see Absolute pitch). We introduced relative pitch and intervals by establishing how to specify two such recurrent pitches and the interval between them (see Relative pitch).

In most music, however, there are more than two recurrent pitches, and the intervals between them are not all the same. We therefore need to be able to represent a set of recurrent pitches and to differentiate the intervals between them.

The set of pitches used repeatedly in a given piece of music is called the “scale” of that piece, and the individual pitches in the scale are called “scale degrees.” The scales used in the world’s music vary widely in the number of scale degrees and the intervals between them.

Global Notation aims to be able to represent any scale equally accurately. To do this, the first step is to consider whether the piece has an identifiable “tonic,” or “keynote,” a “home” pitch that seems to anchor the music and bring a sense of closure at the end. The tonic is the “do” of “do-re-mi.”

If a tonic can be identified, it is taken as the “reference pitch” against which all the other pitches will be specified in terms of relative pitch (i.e., intervals). If no clear tonic can be identified, the lowest pitch can serve as the reference pitch. Sometimes the tonic is the lowest pitch, but by no means always; see Extended scales.

The tonic pitch (if any) is drawn into the graph as a pitch line slightly bolder than the others and extended at each end to make it more prominent. If desired, the absolute pitch of the tonic can be specified (see Absolute pitch).

After determining the tonic or reference pitch, we need to determine the other scale degrees and the intervals between them. If we don’t already know what these are, computer software can help with identifying and measuring them.

The other scale degrees are then drawn into the graph as additional pitch lines, vertically spaced in proportion to the intervals between them. A wide interval between adjacent scale degrees will appear as a wide gap between adjacent pitch lines; a narrow interval as a narrow gap. 

Because we are specifying relative pitch rather than absolute pitch, the sizes of the gaps between pitch lines are set by a vertical measuring scale in cents, not Hertz. The pitch represented by each pitch line is specified as an interval in cents above the reference pitch, as before (see Relative pitch). For any scale degrees lower than the reference pitch, see Extended scales.

We then have a set of pitch lines representing all the scale degrees used in the music we are going to notate. If desired, this grid of scale degrees can be shown in comparison to the notes on a conventional keyboard. Once more, symbols for sounds of either specified or unspecified duration can be positioned on the pitch lines.

We are now ready to notate our first actual melody. To start with something simple, we will use the well-known tune sung as either “Mary Had a Little Lamb” or “Merrily We Roll Along.”

"Merry Has a Little Lamb" nursery rhyme written in global notation

As this tune might be sung in any key and at various different speeds, absolute pitch and tempo are not specified.

In this case, the tonic is the lowest pitch, as one can tell from the sense of finality and completeness produced by this pitch at the end.

As the tune uses four different pitches, there are four pitch lines. The lowest two intervals are the same - 200 cents - but the highest one is wider, so the gap between the top two pitch lines is also wider than the other two gaps.

Note that only the pitches actually used are represented in the notation. These four scale degrees also form part of both a “major scale” and a “pentatonic scale,” and some might interpret the melody as being “based on” one or other of those scales; but this would involve assuming that pitches which don’t appear in the melody somehow form part of its scale, and Global Notation does not require us to make any such assumption.

A collection of pitch lines functions as a single layer, since a given melodic “part” will move across different pitch lines. The beat and bar lines therefore extend unbroken through all the pitch lines in a layer.

Beat lines normally extend only from the lowest to the highest pitch line, while bar lines extend beyond both. Beat lines can also be extended beyond the pitch lines if they would otherwise be obscured by onsets, but even then they don’t extend as far as the bar lines.

Any scale can be represented in the same way. For a scale using intervals that could not be played on a keyboard, we might turn to the traditional music of the Middle East.

An example of scales being represented in global notation using layer lines for "Melodic instruments"

Here, since several instruments play the melody more or less in unison, individual sound sources are not specified. The meter has ten beats to a bar, with each bar occupying one “system” of the notation, but that does not present any particular difficulties. The melody is accompanied by percussive sounds of indefinite pitch which have not been notated here, but they could easily be added in a separate layer following the principles already covered for sounds of unspecified pitch.

The tonic is again the lowest pitch, but this time (in the excerpt notated) there are six scale degrees and three different sizes of interval: 100 cents, 150 cents, and 200 cents. All these are specified the same way as any other scale.

Notice, incidentally, how the alignment of the three systems makes it easy to compare the melodic phrases in each bar, showing how each phrase follows the same overall descending contour while starting on a different scale degree and adding ornamental elaborations each time. This kind of comparison is facilitated by the way Global Notation uses a consistent spatial scale of time (e.g., 1cm = 1 beat) throughout a piece or section.

If the fast-moving ornamental notes look a bit fussy with so many rotated T symbols packed close together, they can be depicted in a smoother way (see Articulation and melisma).

Like all other information in Global Notation, specifying interval sizes in cents is optional. If preferred, pitch lines can also be labelled with the scale degree terms used by musicians within the relevant tradition, such as the “do-re-mi” of Western music, the “sa-re-ga-ma” of Indian classical music, or the scale degree numbers 1–7 used in China and Indonesia. 

Leaving interval sizes unspecified may be preferable when the interval sizes are not fixed. For instance, in Balinese gamelan gong kebyar, the pélog scale has five intervals in the order small-small-large-small-large, but the exact sizes of the intervals vary between one gamelan orchestra and another. The contrast between large and small intervals could be indicated by the spacing of the pitch lines without specifying exact interval sizes.

In its approach to notating melodies, Global Notation broadly resembles the “piano roll” notation used in MIDI applications, in which thick horizontal lines represent the pitch and duration of sounds. But in MIDI notation, these thick lines are placed in the spaces between the lines of the grid, and the pitches that can be represented are limited to the twelve notes per octave available on the piano keyboard. 

By specifying pitch with the lines of the grid rather than the spaces, an unlimited range of pitches can be represented accurately through spacing the grid lines in proportion to the intervals used in the music we wish to notate. The pitch organisation of the music can then be presented in its own terms and not through a framework derived from a different kind of music.

So far our examples have been limited to melodies that cover a fairly narrow range of pitch with the tonic at the bottom. But the same principles can be extended to music covering any pitch range.

Sources of audio

“Sama’i Bayyati” from Salah ‘Arram and Firquat al-Awtar al-Dhabiyyah, Classical Instrumental Music of the Middle East: A Performance from Egypt, Global Village CD ASIN: B003DSXSKK (2010), track 3.