Where is home?
This part of the story is told like a fable, rather than as scholarly musical history. When musicians first started using triads, their roots sometimes roamed around somewhat wildly. Pieces could start or end more or less anywhere within the key window, treating anywhere as ’home’, and could move around so that notes in the chord fitted a melody without apparently worrying too much about how the chords themselves moved (this is a cartoon version of music history and musicology - but useful in any case). There were many magnificent composers playing with this kind of thing, some highly adventurous, like Guillame de Marchant, and some more restrained, like Palestrina. But then composers started developing a more evolved sense of where points of rest and tension were located and how different paths could fulfil or play against expectations.
A key insight was that musicians noticed (intuitively) that the major triads had a definite central triad, and similarly the minor triads had a well defined central position. This relationship, seen in the diagram below, reflects the emergence of the major and minor tonal centres respectively, and is an important part of the reason why the major and minor modes became more important than modes based on the five other possible home positions within the key window.
This can be most easily appreciated in this very short video clip, or see below for a rough explanation with diagrams and words.
Using harmony space, we can click on any of the notes in a key window to play a triad. The notes marked red in this diagram produce major triads, the blue ones minor triads, and the green one a diminished triad These shapes were shown in the previous section
But since there are only really 12 notes in the plane, with the pattern repeated like wallpaper, as discussed in the previous section, we can readily move the D in the previous diagram to the position in this diagram instead, helping to make clear that the minor triads have a middle position, just like the major ones.
This is much easier to see in the video. This exploded diagram, at the risk of overcomplicating something that is actually very simple, attempts to show the shape and location of each triad produced by each of the seven possible positions of the root in any key window (The problem is that showing all of the roots and all of the chords at once in a single key window, which is trivially easy in a video, is difficult in a static diagram due to the multiple overlaps). Consequently we have scattered the chords and roots graphically over the harmony space field so that each can be seen clearly. This makes no musical difference, because as already noted, the harmony space plane shows just twelve notes, but the pattern is repeated like wallpaper, because that way many higher level structures will later become visually apparent.
It is worth noting that while the physically and perceptually central position of the major and minor key centres gives musicians all sorts of resources (some of which we will explore in detail) for playing games of movement, chase and location, it is always possible to treat other locations in the diatonic key window as home, as we will see - you just have to work harder to make them feel like home for listeners.