REVERSE PERSPECTIVE IN JAZZ HARMONY

Tonality, Linear Perspective and Reverse Perspective

As opposed to the art forms from Renaissance until Modern Art, a multi-centric design is a leading quality in Medieval art. Understanding how these art forms came into being and how they were perceived requires a historical insight not only from a sonic perspective but also from a visual one. Linear perspective could be called a counterpart of tonal center, whereas reverse perspective could be called a counterpart of the multi-centric modal approach in the Middle Ages. The perception of center had started to change during the Medieval times and, by the Renaissance, a linear perspective gained its position as the prominent driving force for visual representation. Pavel Florensky who was an art historian and intellectual that lived between 1882-1937 described reverse perspective as such:


Dimensions in Reverse Perspective

“The closest dissemination of the methods of reverse perspective to be noted is the use is the use of polycenteredness in representations: the composition is constructed as if the eye were looking at different parts of it, while changing its position.” (Florensky,2006)
In linear perspective, the point where the lines are crossing exists as the center for visual perception. The same thing happens in tonal harmony. The tonic is perceived as the center in relation to the subdominant, subdominant minor, tonic minor and dominant regions which are created by necessary and sufficient conditions in tonal harmony. In next figure each line in linear perspective could be labeled as regions in tonal harmony to see how three-dimensional structures are constructed in visual art and tonal composition. Julian Johnson describes the parallel form between linear perspective and tonality as such “Tonality is to music what linear perspective is to painting-it organizes time towards a central point of perception within the listener the way that, in painting, space converges on the eye/ I of the viewer. Tonality, in short, is the means by which musical modernity invests time with spatial dimensions, a process both constitutive and expressive of the modern subject.” (Johnson,2015)


Dimensions in Linear Perspective

Dimensions in Tonal Harmony by Visual Representation of Linear Perspective

Diatonic Chords

Cmaj7    D-7    E-7    Fmaj7    G7    A-7    B-7b5
Imaj7     II-7    III-7    IVmaj7   V7   VI-7    VII-7b5

Tonal Harmony – Necessary & Sufficient Conditions
1. Major-Minor Scales
2. Functional (Distance to the center)
3. Structural Progressions based on 4ths and 5ths

When we transpose the relationship between the primary dominant and the Ist function to the other diatonic functions, we get non-diatonic dominant chords which we call secondary dominant chords. The progression II-7 V7 IMaj7, being the most powerful progression in tonal harmony, has almost become a stereotype. That is why it is called a Primary Tonal Progression.



Chords From the Subdominant and Dominant Areas:

Up to this point we have examined chord relations of the diatonic chords and the related secondary dominants. Now we will start to discuss non-diatonic chords that do not appear as secondary dominants. These deeper level analyses will deal with the areas that relate to the centre by the structural relationships of 4ths and 5ths, as can be seen below. The structural progression of 4ths and 5ths, a necessary condition of tonal harmony, makes all of these relationships possible.
Since the dominant chords of minor and major keys are the same, the major and minor areas of the F subdominant area connected to the C centre, and the major and minor areas of the C centre are connected to the G dominant area through their shared dominants. The chords that result from the formation of these structurally related areas can be used in the C key as non-diatonic chords. Non-diaotonic chords from these areas lead us to hear a depth as in created in linear perspective perception.

Dimensions in Tonal Harmony
The Most Common Non-Diatonic Chords From Harmonic Regions
G Dominant Major Chords: D7 (II7) F#-7b5 (#IV-7b5)
F Subdominant Minor Chords: F-7 (IV-7)- Bb7 (bVII7) DbMaj7(bIIMaj7)- AbMaj7(bVIMaj7)
C Tonic Minor Chord: EbMaj7 (bIIIMaj7)
F Subdominant Major Chord: BbMaj7 (bVIIMaj7)


Non-Functional Harmonic Progressions: Pattern Based Progressions to Distort Centric Perception
The main purpose of non-functional harmonic progressions is to distort centric perception of functional harmony by means of pattern based chord progressions. There is no centre, namely Ist degree chord ( I maj7).

Constant Structures:

Constant structures are harmonic progressions that consist of structurally identical chords, whose movements are mostly determined by a constant interval form. In the first example, three Maj7 chords move by thirds. In the second example Min7 chords are in the same interval patterns, 4th apart from Maj7 chords. There’s no tonal relationship between the chords whatsoever. These types of harmonic structures are analyzed by explaining how the harmonic texture is woven. These types of analyses are called descriptive analyses in the academic literature.

Model- Based Chord Progressions:

In this kind of structure, the harmonic progression is created by modeling the relationship between two chords. Unlike constant structures, there are no constant parameters in model-based progressions. The model has no other function besides being copied. In the example below, you can see that the minor 3rd relationship between Cmaj7 and Ebmaj7 is determined and then copied. There are no guidelines on where the other models begin. Therefore there is no other connection besides the minor 3rd relationship between these chord pairings.



Multitonic Approaches:

The most eesential thing in tonal harmony is the hierarchy of the Ist function. In this structure, the IVth and Vth functions have secondary importance. This kind of structure creates an asymmetrical relationship. A symmetrical design lays the foundation for a non-functional relationship. Upon this foundation, we divide the octaves equally and each structure that’s formed has central value. These types of structures are called multitonic stuructures.

Down below, you can see the symmetrical forms created by equal divisions. The most well-known example for this type of approach is the harmonic progression in John Coltrane’s Giant Steps. In the second example, you can see how three tonic centres are created in the first eight measures of this piece via major 3rd divisions. Even though the centres are accentuated by dominant resolutions, the lack of any kind of tonal relationship between them implies that the piece is non-functional.



The Application of Reverse Perspective To Jazz Harmony

Inversional Symmetry:

Centricity in post-tonal music can be based on inversional symmetry. An inversionally symmetrical set has an axis of symmetry, a midpoint around which all of the notes balance. (Straus,2005)

I defined chord progressions instead of pitch class sets on the basis of this definition:
C as a midpoint to create a temporary center.



By means of this relationship I am able to attribute more than one function to chords in order to design a reverse perspective effect. Maj7 and min7 chords are the most appropriate chord qualities because dominant 7 chord has potential to resolve in dominant resolution pattern in tonal quality. In reverse perspective approach because of covering more dimensions it is possible to have different perceptions in a unified form.

An example analysis from Reverse Perspective album in 2019:

As you see in the analysis multi-functional chords and inversional symmetric chord progressions open space for more dimensions of the way we perceive and hear chord progressions. Even though non-functional chord patterns help us to hear nonconcentric space, these patterns have difficulties in presenting more than one dimension. Because these chord progressions are just defined to break functional relationships. By means of multi-functional chords that are defined in my reverse perspective context, I can create a multi-dimensional perspective for perception. This is the most crucial difference between what I am trying to do in reverse perspective chord progressions and nonfunctional chord patterns.