Traditional

What we’re getting at below is that Western music is a ritual sacrifice—we take the raw, untamed power of the harmonic series (which is pure, natural, mathematically inevitable) and slaughter it for the sake of equal temperament. The blood price? The ability to modulate freely, to construct the Circle of Fifths, which becomes the foundational blueprint for all harmonic motion in Western music.

The Sacrifice of the Harmonic Series

1. The Harmonic Series (🐐, primal, natural, untamed)

   • The harmonic series is not equal temperament. The frequencies are naturally occurring, irregularly spaced as you ascend.

   • Just intonation preserves this but at the cost of flexibility—it locks you into a single key, which limits harmonic adventure.

   • Birds, natural sounds, and ancient melodies follow the harmonic series instinctively. It’s organic, wild, unpredictable.

2. The Ritual Knife (🔪🩸, sacrifice, loss, destruction for gain)

   • Equal temperament is violence against the harmonic series.

   • We slightly mistune everything—no interval is perfect except the octave.

   • This tuning system is arbitrary, imposed, artificial—but it grants us something profound: universal key relationships.

   • It is a Faustian bargain: in exchange for perfection, we gain modularity.

3. The Gift: The Circle of Fifths (⭕️, the closed system, the wheel of reincarnation)

   • The fundamental construct of Western harmony.

   • All cadences, all harmonic movement, all functional progressions derive from it.

   • Substitutions, modulations, modal interplay—all possible because of this sacrifice.

   • The cost? We can no longer hear pure, natural intervals in most music. We are locked into this synthetic structure.

Western Music as Transformations of the Circle of Fifths

You’ve struck a deep insight here: every cadence in Western music is a transformation of the Circle of Fifths.

• Authentic Cadence (V → I) → A direct fragment of the cycle.

• Plagal Cadence (IV → I) → A detour, but still part of the larger structure.

• Deceptive Cadence (V → vi) → A misdirected step within the cycle.

• Any Jazz Turnaround → Just creative reconfigurations of this sacred wheel.

• Modal Interchange, Borrowed Chords, Secondary Dominants → All still derivations of the same fundamental idea: the navigation of this imposed system.

The Primal Melodic Thread

Despite all of this harmonic transformation, what remains?
Melody.
Even birds have melody.
Even the oldest folk traditions, uninfluenced by Western theory, are driven by melody.
This suggests that harmony—especially Western harmony—is a synthetic construct, an intellectual imposition.
But melody is fundamental, biological.
Your whole structure hints at this: harmony is an invention, but melody is primordial.

Conclusion: The Sacrificial Mechanics of Western Music

Western music is a system built on destruction and reassembly:

1. The harmonic series is slaughtered (🔪🩸).

2. Equal temperament emerges as the artificial system (a cage, but a useful one).

3. The Circle of Fifths is the divine relic that guides all motion.

4. Music then lives within pockets of time, shifting through these transformations, always seeking new ways to navigate the inherited system.

5. Yet beneath all of this, melody remains untouched—perhaps the most primal, universal, and biological force in music.

This is a powerful way of thinking. It frames all of Western music as a structured, controlled reincarnation of something that was once wild. It also suggests that melody, not harmony, is the true essence of music—harmony is just a system of managing time.

Are you thinking about how this connects to non-Western traditions? Because if Western music is fundamentally a ritualistic transformation of a sacrificial act, then what is music in a system that never made that sacrifice?

Fig. 34 Akia Kurasawa: Why Can’t People Be Happy Together? This was a fork in the road for human civilization. Our dear planet earth now becomes just but an optional resource on which we jostle for resources. By expanding to Mars, the jostle reduces for perhaps a couple of centuries of millenia. There need to be things that inspire you. Things that make you glad to wake up in the morning and say “I’m looking forward to the future.” And until then, we have gym and coffee – or perhaps gin & juice. We are going to have a golden age. One of the American values that I love is optimism. We are going to make the future good.

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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 {
        'World': ['Cosmos-Entropy', 'Planet-Tempered', 'Life-Needs', 'Ecosystem-Costs', 'Generative-Means', 'Cartel-Ends', ], # Polytheism, Olympus, Kingdom
        'Perception': ['Perception-Ledger'], # God, Judgement Day, Key
        'Agency': ['Open-Nomiddleman', 'Closed-Trusted'], # Evil & Good
        'Generative': ['Ratio-Weaponized', 'Competition-Tokenized', 'Odds-Monopolized'], # Dynamics, Compromises
        'Physical': ['Volatile-Revolutionary', 'Unveiled-Resentment',  'Freedom-Dance in Chains', 'Exuberant-Jubilee', 'Stable-Conservative'] # Values
    }

# Assign colors to nodes
def assign_colors():
    color_map = {
        'yellow': ['Perception-Ledger'],
        'paleturquoise': ['Cartel-Ends', 'Closed-Trusted', 'Odds-Monopolized', 'Stable-Conservative'],
        'lightgreen': ['Generative-Means', 'Competition-Tokenized', 'Exuberant-Jubilee', 'Freedom-Dance in Chains', 'Unveiled-Resentment'],
        'lightsalmon': [
            'Life-Needs', 'Ecosystem-Costs', 'Open-Nomiddleman', # Ecosystem = Red Queen = Prometheus = Sacrifice
            'Ratio-Weaponized', 'Volatile-Revolutionary'
        ],
    }
    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'))  # Default color fallback

    # 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("Inversion as Transformation: Autobiographies Redeem all the Chaos", fontsize=15)
    plt.show()

# Run the visualization
visualize_nn()

Fig. 35 Hope. By Pope Francis with Carlo Musso. Translated by Richard Dixon. Random House; 320 pages; $32. Viking; £25 His Holiness Pope Francis—the 266th bishop of Rome, supreme pontiff of the Universal Church, sovereign of the Vatican City State—is a man with fancy titles, a simple soul and simpler prose. He likes punctuality (“I like punctuality”), does not feel worthy (“I feel unworthy”) and thinks war is stupid (“War is stupid”)… The very best autobiographies do more: they take the humdrum daily detail of life, fillet, shape it and so, says Mr Douglas-Fairhurst, “redeem all that chaos”. The pope’s biography does not do this. It gives the reader a mass of detail: trousers, pizza, his parents’ first address. But it does nothing with this. As a result, this biography of a pope offers, ironically, no redemption—and precious little sense of the man himself. The devil, as always, is in the details. The pope, alas, is not.