Filling up like water
(Building chords)
Chords in early western music
Harmony is all about what happens when you play more than one note at once. What if we are allowed two notes at once? (To grasp the ideas in this section most simply and quickly, this video may help).
One of the ideas in the middle ages was chords like this (tracking in fifths in conventional terminology). It’s a start, but every chord (with one somewhat problematic exception) is the same shape and sounds the same (apart from being higher or lower in pitch) so there is little sense of a landscape to be explored beyond the melody.
To play around with this in harmony space, select chord size two in the chord size panel and stacked fifths in the chord map panel, both on the left hand side.
Two-note chords (3rds and 6ths)
Musicians soon found a more interesting way to work with two pitches at once. To play with this idea in Harmony Space, select chord size two in the chord size panel and press the natural button next to the chord map list. Try playing (clicking on) different notes inside the key window (the white area) and look at the different chord shapes you get depending on your location within the key window (there are two different shapes). Try setting inversion 1 in the inversion panel (first inversion in traditional terminology) and see what difference this makes to how the chords sound and look compared with inversion 0.
Regardless of the inversion setting, these chords all follow a simple rule. Whatever note you click on, you get that note and the physically closest next higher note that fits in the key window. It looks a bit like you are filling the key window with water, but strictly proceeding left to right & upwards. You may find that first inversion sounds better, and in any case change of inversion allows for more variety. When you set inversion to 1, all that is happening is that the note clicked on (the lowest note) gets boosted up by an octave, so it is no longer the lowest, but still keeps the same note name. With chord size set to 2, and inversion set to 0 (no inversion) moving around in this way is called tracking in thirds. With inversion set to one its is called tracking in sixths (using traditional terminology - see here). It can sound good to alternate between the two.
If someone sings a tune, many musicians can add the second note more or less following this rule completely intuitively. Many, well-known songs and musicians use this. The Beatles, Bach, Handel, The Unthanks, Crosby Stills, Nash and Young, Pentatonix and many more artists can provide endless examples. <link>
Here we have a fragment of a medieval melody ‘Hodie Christ’s natus est’.
This melody starts: C D E E E D E F E and so on.
To harmonise this melody in one stereotypical medieval style, we set the chord map on the left hand side to ‘stack fifths’, and the chord size to 2.
As we click on each melody notes, we also get the next note diagonally upwards in the key window.
This is a very primitive form of harmonisation.
Given a simple melody starting C F G A D…….
Try setting the chord size to two in the chord size panel on the left, the inversion to 2, and press the ‘natural’ button next to the ‘chord maps’ panel on the left.
As you click on each melody note, you also get the next highest note that fits into the key window, either to the right if there is room, or upwards if not.
This is called tracking in thirds (though because of the inversion, properly speaking this is tracking in sixths)
To see a simple example of tracking in thirds, using inversions, select Pachelbel from the list of Curated songs, select chord size two from the chord size list and press play. In the trace shown below, each note in pink is the note played by mouse (the root of the chord) and the red note next to it is the additional automatically added note in the chord
To play a complete piece from the library, tracking in thirds,
Select Pachelbel from the list of Curated songs, select chord size two from the chord size list and press play.
Three note chords (Triads)
To start to get a hint of the rich structures hidden in the diatonic scale (it took 400 years for musicians to articulate some of these) it is useful to look at chords where three notes are played at once. Now, there is nothing stopping any composer or performer from playing any three notes at once, and indeed later on we will see how to exploit this to good effect. But for now, if you follow the same principle as for two notes, but extend it to three notes, interesting things happen.
To play with this idea in Harmony Space, select chord size three from the chord size panel and press the ‘natural’ button next to the chord map list (which sets chords to be built naturally, or diatonically, as it is called by musicians). Try playing different notes in the key window (the white area) and look at the different chord shapes you can get depending on your location within the key window. There are just three different shapes that can be generated naturally in this way. Try setting inversions 1 and 2 (first and second inversion in traditional terminology) and see what difference this makes compared with inversion 0 (zeroeth or root inversion).
Compared with two notes chords, it is now easier to see the idea that chord building looks a bit like you are filling the key window with water, but strictly left to right & upwards.
As a quick but informative diversion, try clicking on the same note note with chord size set to 1, 2, 3, 4 and 5 respectively to see this in action and extended.
Building chords naturally, or diatonically is also known as “stacking thirds” for reasons explained <here>.
This diagram is not a record of normal working, but just a way to try to show the different chord shapes spread out for clearer viewing. This is perhaps easier to understand by playing with the program of looking at the video.
Various three note chords (‘triads’) are shown above, highlighted in red, spread out across the screen to separate the different chord shapes visually. These are all played in first inversion. The inversion number of any (thirds-stacked) chord can be read visually straight off the diagram, by counting the number of lighter shaded (i.e. octave boosted) notes at the bottom. <footnote for experts> All of the shapes have something interesting in common: the constituent notes are as physically close together (‘maximally compact’) as they can possibly get in the key window following the ‘water filling’ rule. In particular, the three chords that are triggered by roots on the “west coast” of the key window are all the same shape (called “major triads”) and three notes triggered by roots on the “east coast” of the key window are all a different shape (called “minor triads”). The chord triggered by the note right at the top of the “east coast” is the odd man out with a chord generally held by many to sound more unsettled than the other chords. This chord has its own unique shape “diminished triad”. The isolated green notes in the diagram above are just displayed for the purposes of this diagram to show graphically to how the roots of the six major and minor chords line up.
To recap, just as a piece of terminology used in harmony generally, this approach to building chords, a bit like filling up the key window with water, is known by musicians as ‘thirds stacking’.
Due to the way the major and minor triads line up as seen in the diagrams, two wonderful pieces of structure emerge that can be perceived untutored by listeners exposed to diatonic music, as explained in the next section.
Previous Elements of Harmony
Next Where is home?