Finding out how chord sequences work
This process may be easiest to understand by seeing examples and videos <link>
There are two different ways of looking at this.
1. Understanding and testing how harmonic sequences work
One way of looking at this process is as an aid to coming up with ideas about how a chord sequence of interest gets some perceived effect. With some exceptions, these are not usually generalisable theories - they are more like heuristics, depend a lot on context, and are open to interpretation. However, they are often testable. Tests can be carried out by making predictions about the effect of some identified structure or process, then testing whether variations that share that feature have the same predicted effect. Iterated variations can be used to refine heuristics and identify the contexts they depend on.
2. Chunking harmonic structure at a higher level
Another way of looking at this process is that it makes it possible to identify high level structures in common to many songs. Crucially, each structure identified in this way typically spans several chords. With a little practice, these structures may be memorised and understood at a glance, allowing interesting chord sequences to be remembered, reconstructed and understood as a combination of just a few high level ideas, rather than having to remember dozens of chords, each containing several notes. This makes it relatively easy to memorise a large number of songs, and to recognise diverse overlapping relationships between songs. This can be helpful for many purposes, including scholarship, analytical insight and ideation for song writing.
Open-endedness
Both approaches are open ended. The aim of the representation is to assist in visualising, identifying and articulating harmonic relationships as different analysts see fit - not to claim superiority of particular interpretations.
Practicalities
Harmony space contains two different libraries of songs, songs from the web and curated songs. These libraries have been produced in two different ways using two different representations, different editors and different mechanisms. They also have different purposes. Songs from the web can be played immediately and automatically graphed by an approximate heuristic algorithm.
By contrast, curated songs need to be created by playing them spatially by hand (and optionally recording and editing them). Some 100 songs have already been spatially graphed by hand and recorded in the curated songs library. Creating songs in this way is more laborious but far more likely to yield enlightenment about how the harmony works, and to allow deeper memorisation.
Songs from the web have been imported from the Polifonia Choco Online Library of chord sequences. They are recorded as a timed sequence of chords and keys. The assumption is build in that not just the chords, but also the key (or keys) have been correctly identified. Based on this assumption, the chord sequences are heuristically spatial plotted. It is possible to ask for different heuristics to be applied. While this can save a lot of work, there are several limitations, which can limit the immediate suitability of this material for the two approaches outlined above. However, there are tools that can allow these limitations to be considerably mitigated.
The limitations are as follows:
• the chords may be wrong
• keys may be misidentified
• modes beyond the major and minor are typically not identified
• analytically useful extensions to modes such as picardian modes and extended harmonic modes are not identified
• the spatial mapping is algorithmic rather than hand crafted
The mitigations are that harmony space has an editor for the songs from the web, which allows keys and chords to be edited, and spatial plots to be modified. There are also facilities for proposed corrections that can also be exported back to Choco.
Curated songs
Curated songs are created by playing them manually in harmony space, and recording the performance using either the live recorder or the step recorder. Identifying the most appropriate key(s) and mode(s) (and perhaps other settings such as chord size, inversions and chord map, etc.) and then playing the piece in harmony space is equivalent to a full functional harmony analysis. Less than 100 songs are in the library so far. Because of the nature of these recordings, they can be replayed using different settings (e.g. chord map, chord size, inversions etc). Analysing a song that you like in harmony space in this way can be very rewarding in terms of understanding how the harmony works, and in having new affordances for memorising and understanding structure.
Getting started
Find a songs and pieces of music whose harmony interests you.
Functional Harmonic analysis
1/ Use the internet find the chord sequence in conventional chord notation.
2/ As a first step, trace the roots only of the given chords in harmony space, and then shift around the key window to find one or more key window positions (keys) where the sequence (or its different stages) can fit. There may be more than one such position, or there may be none.
3/ As a second step, play the full chords (not just the roots) to see if there is any sequence of keys and modes that allows all or most of the chord qualities to fit in the key window.
4/ Look for the simplest possible description that minimises the extent of roots and chord elements that do not fit any key or mode. Check that chord’s you are assigning “home” locations feel like home.
5/ The way in which the roots of chord sequences move, and the way in which they start and finish may give clues. The aeolian, dorian, phrygian and mixolydian modes all have distinctive movement patterns <examples> and distinctive ending patterns (cadences)<examples>.
6/ The simplest description will be equivalent to a functional harmonic analysis of the piece. If you make a step recording of the piece in harmony space using the key(s) and modes you have found, then set Roman numeral labelling and press “print chords” after playing back the piece, this functional analysis will be printed out.
Minor extensions to functional analysis
1/ In many genres, including recent popular music, it can be useful to take into account extended modes such as picardian and dominant V inflections of the minor modes (aeolian, minor, dorian and phrygian).
2/ The analysis process described above embodies a heuristic known as the assumption of diatonicity. This can be useful and revealing, but it’s only a heuristic. There are other insights to find and use.
3/ Common sense is also needed, the ear always needs to be used. Harmony space can be useful but it should not be used in isolation. If possible, try continually to translate insights however inexpertly onto guitar or keyboard, or other instruments, or sing, or play with other people.
4/ The aim of the above process is not prescriptive, nor to match harmony to pre-existing patterns. Rather, memorable, durable and interesting pieces of music will typically reflect existing building blocks and patterns but will come up with new twists and combinations. Following these twists and turns is insightful and can help in coming up with new musical ideas.
Spatial sketching
Background
1/ When plotting root movement spatially in Harmony Space, most intervals can be plotted as a move to an immediate neighbouring cell. The only exceptions are moves by a tone (and by a tritone) - <see page on intervals>. However, this allows for useful interpretative space.
2/ This arises because some chord sequences are resolutely tonal <examples>; others are resolutely modal <examples> ; and others balance these two kinds of movement for musical effect <examples>. Yet others gain depth by ambiguity.
3/ In the simplest case, by choosing whether to plot a root move of a tone on the dominant axis, or on the scalar axis, visual appeal can be made to established tonal or modal patterns of movement, or alternative readings can be used to show ambiguity <example>
4/ In more subtle cases it can be useful, for example to plot root movement of a major or a minor third or a fourth on the scalar axis to show up an underlying modal pattern <example>
Test analyses by making predictions
<link>