Revolution

The visualization of a neural network, structured through musical modes and harmonic extensions, offers an intriguing exploration of pattern recognition and hierarchical relationships. At its core, this network is not just an abstraction of nodes and edges but an attempt to encode the essence of musical tension, resolution, and interplay within a structured framework. By assigning scales, chords, and extensions into categorical layers, this framework does more than depict connections; it mirrors the very way harmonic motion operates in music and cognition alike.

Fractal Layers of Musical Experience

The foundation of this network begins with the “World” layer, representing the broadest category of modal scales—Ionian, Lydian, Phrygian, Dorian, Locrian, and Aeolian. These are not merely technical designations but historical and cultural signifiers. The Ionian, often equated with the modern major scale, is the foundation of Western tonal music. Lydian introduces its characteristic raised fourth, expanding the sense of openness. Phrygian, with its flattened second, evokes tension and darkness, while Dorian’s minor quality retains a sense of movement rather than stasis. Locrian, the most unstable, resists resolution, and Aeolian, the pure minor, completes the palette of tonal spaces. Together, these form a ‘Veni’ moment—an entry into the network through fundamental modal possibilities.

Fig. 22 What Exactly is Identity. A node may represent goats (in general) and another sheep (in general). But the identity of any specific animal (not its species) is a network. For this reason we might have a “black sheep”, distinct in certain ways – perhaps more like a goat than other sheep. But that’s all dull stuff. Mistaken identity is often the fuel of comedy, usually when the adversarial is mistaken for the cooperative or even the transactional.

From here, the framework narrows to a single node: the Mixolydian mode. Its placement in the ‘Mode’ layer as the solitary representative speaks volumes. Mixolydian, with its lowered seventh, resists the dominant-to-tonic pull that underlies most Western harmony. This subtle shift alters expectations, giving rise to blues, rock, and jazz flavors. Conceptually, its presence alone suggests a tipping point—an equilibrium between structured tonal harmony and the kind of harmonic ambiguity that allows for iterative expansion. This ‘Vidi’ moment is one of recognition, where the modal palette condenses into a singular force.

Agents and the Tension Between Worlds

The ‘Agent’ layer introduces alterations: ♯5 and 7th. These choices reveal an underlying structure where tension (♯5, an augmented note destabilizing the triad) and function (7th, a dominant indicator of forward motion) coexist. Here, the balance is more precarious—51/49, suggesting that the network is at its most fractal, straddling stability and dissonance. This is the ‘Vici’ layer—victory through controlled instability. The ♯5 blurs major and minor, as seen in augmented chords or altered dominants, while the 7th ensures propulsion. It is here that modal purity dissolves, giving way to harmonic function.

Expanding Dimensionality: Space and Time

The next two layers, ‘Space’ and ‘Time,’ further abstract harmonic movement. The ‘Space’ layer, with its 9th, 11th, and 13th extensions, represents the widening of musical intervals beyond the conventional triadic framework. These tones, often associated with jazz and modal harmony, stretch the ear into a vertical plane of expanded resonance. This layer marks a shift from modal focus to harmonic breadth, emphasizing color over function.

Finally, ‘Time’ collapses resolution into chromaticism: ♭13, ♯11, ♯9, ♭9, ♭♭7. These altered tones, frequent in the altered dominant and diminished scales, represent the extremities of harmonic tension. The network has moved from the broad, stable world of modes to the microtonal instability of time-bound harmonic alterations. The ratios flip—5/95—suggesting that at this extreme, resolution is not the goal. Instead, harmonic ambiguity and perpetual motion dominate.

Color and Structural Mapping

To reinforce this structural hierarchy, the network assigns colors to nodes. The Mixolydian mode alone is yellow—standing at the inflection point between modal and functional harmony. Paleturquoise covers Aeolian, the 7th, the 9th, and the ♭♭7 (diminished seven)—tones associated with minor modal function and dominant motion. Lightgreen captures the most unstable, ambiguous, and therefore “transactional” elements most in need of a cadence for some relief: Locrian (diminished), and the 9th & 11th (suspended), and various altered tones. Lightsalmon, in contrast, encapsulates Phrygian, Dorian, ♯5, and the 13th, showing a bridge between modal instability and expanded harmonic function.

This mapping is not arbitrary but reflects the way harmonic structures behave in cognition. The modal system, often associated with fixed emotions or cultural resonance, is progressively abstracted into functional harmony, where relationships between notes define tension and resolution rather than their static positions within a scale.

A Fractal of Musical Cognition

Ultimately, this visualization is more than a graph—it is a fractal of how harmony unfolds in both music and thought. The layers correspond to an understanding of how tonality is processed: from categorical modal identities, through points of functional tension, into a higher-dimensional space where notes exist less as discrete events and more as relational entities. This mirrors the way neural networks function, where lower layers process raw input (scales, fundamental pitches), while hidden layers extract patterns (tensions, resolutions), and final outputs determine movement through time (stacks).

By mapping this progression onto a neural framework, this structure does not merely represent music; it embodies the process of musical cognition itself. In doing so, it invites deeper exploration into how harmonic relationships—whether in classical, jazz, or experimental music—mirror cognitive processes, forming a bridge between structured knowledge and emergent creativity.

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import numpy as np
import matplotlib.pyplot as plt
import networkx as nx

# Define the neural network fractal
def define_layers():
    return {
        'Suis': ['Ionian', 'Lydian', 'Phrygian', 'Dorian', 'Locrian', 'Aeolian', ], # Static
        'Voir': ['Mixolydian'],  
        'Choisis': ['♯5', '7th'],  
        'Deviens': ['13th', '11th', '9th'],  
        "M'èléve": ['♭13', '♯11',  '♯9', '♭9', '♭♭7']  
    }

# Assign colors to nodes
def assign_colors():
    color_map = { # Dynamic
        'yellow': ['Mixolydian'],  
        'paleturquoise': ['Aeolian', '7th', '9th', '♭♭7'],  
        'lightgreen': ['Locrian', '11th', '♭9', '♯9', '♯11'],  
        'lightsalmon': [
            'Phrygian', 'Dorian', '♯5',  
            '13th', '♭13'
        ],
    }
    return {node: color for color, nodes in color_map.items() for node in nodes}

# Calculate positions for nodes
def calculate_positions(layer, x_offset):
    y_positions = np.linspace(-len(layer) / 2, len(layer) / 2, len(layer))
    return [(x_offset, y) for y in y_positions]

# Create and visualize the neural network graph
def visualize_nn():
    layers = define_layers()
    colors = assign_colors()
    G = nx.DiGraph()
    pos = {}
    node_colors = []

    # Add nodes and assign positions
    for i, (layer_name, nodes) in enumerate(layers.items()):
        positions = calculate_positions(nodes, x_offset=i * 2)
        for node, position in zip(nodes, positions):
            G.add_node(node, layer=layer_name)
            pos[node] = position
            node_colors.append(colors.get(node, 'lightgray'))   

    # Add edges (automated for consecutive layers)
    layer_names = list(layers.keys())
    for i in range(len(layer_names) - 1):
        source_layer, target_layer = layer_names[i], layer_names[i + 1]
        for source in layers[source_layer]:
            for target in layers[target_layer]:
                G.add_edge(source, target)

    # Draw the graph
    plt.figure(figsize=(12, 8))
    nx.draw(
        G, pos, with_labels=True, node_color=node_colors, edge_color='gray',
        node_size=3000, font_size=9, connectionstyle="arc3,rad=0.2"
    )
    plt.title("Modes, Emotions, Nodes, Stacks", fontsize=15)
    plt.show()

# Run the visualization
visualize_nn()

Fig. 23 Psilocybin is itself biologically inactive but is quickly converted by the body to psilocin, which has mind-altering effects similar, in some aspects, to those of other classical psychedelics. Effects include euphoria, hallucinations, changes in perception, a distorted sense of time, and perceived spiritual experiences. It can also cause adverse reactions such as nausea and panic attacks. In Nahuatl, the language of the Aztecs, the mushrooms were called teonanácatl—literally “divine mushroom.” Source: Wikipedia