An element is a fundamental component of music.
Composition is the process of assembling elements, or components, into a shape or form.
There is little consensus on what the elements of music are or even what they should be. Melody and harmony are often listed as basic components. Rhythm too, although it is sometimes split into two separate components, meter and tempo. There are plenty of other candidate elements. A cursory trawl of the internet yields the following: instrument, dynamics, timbre, pitch, notation, tonality and texture. There are notable omissions, noise, one of the features of this guide, is never mentioned. And no one is really sure if form itself is a component or not.
Classification issues aside, there is another problem, which is how to link components. A component should be a standalone self-contained unit which can be processed separately from other components. The order of processing should not matter. Start with whichever component is to hand, finish it, and move on to the next. Except it does not work that way. It is impossible to write a melody then add a rhythm, it already has one. Yet it is possible to do it the other way round, write a rhythm then add a melody. Order evidently does matter.
The idea of links between components begs the question: is there a fundamental element? Sound itself seems the most likely candidate. Yet sound can be broken down into frequency, amplitude and phase. If sound is not the basic component of music, then we have a problem.
This guide is titled Writing Music and not Composition because of the problems associated with the notion of component.
The guide is based on the process of writing music and structured according to the complexity of organising sound. Frequency was chosen as the starting point. It allows greater flexibility in terms of organising sound than amplitude or phase. Since frequency and pitch mean the same thing, sound is split into unpitched and pitched sound. Unpitched sound is obviously less organised than pitched sound, so the guide starts with it. Continuous unpitched sound is less organised than discrete unpitched sound so the guide starts with noise then moves on to rhythm. Melody, pitched sound, is less complex than harmony because there are fewer notes, so melody is tackled before harmony. This is why the guide is structured as it is, not in terms of components, but in terms of the process of organising sound in terms of its complexity: noise then rhythm then melody then harmony.