Homage

Homage#

From the point of view of form, the archetype of all the arts is the art of the musician - Oscar Wilde

      1. f(t)
            \
 2. S(t) -> 4. y:h'(t)=0;t(X'X)X'Y -> 5. b -> 6. SV'
            /
            3. h(t)

1 Allegory#

Inherited fetters, \(\mu\) (text)#

  • \(f(t)\) Challenges. Life including parts unknown in the tails (entire harmonic series) will throw things at you without any prejudice, as if randomly from a probability density function

  • \(S(t)\) Skills. Charity of our forbears & our duty to others (ii-V7-i contain entire series here). Our cumulative heritage hands us an approach out of the spirit of music: what we are handed displaces us from the root to ii. And our forbears offer a step-wise, tried & tasted, well-trodden journey “back” home: ii-V7-i

  • \(h(t)\) Tools. No quick home-cuming or path of least resistance. Rather, an obstacle-course that tests your strength, resilience, and build your muscle, bone, stamina, as well as emotional tension: your libido and drive is now like a dammed river, which builds a reservoir for future energy needs. Modes-qualities-relatives are the tools that create context for future surprises, tension, release

Dancing in chains, \(\sigma\) (context)#

  • \((X’X)^T \cdot X’Y\) Agency. Hope is placed in you by the agent-less masses. They understand that with all the tension in the bow that you’ve accrued, your banks run over; your cup runneth over; you can help them shoot for distant goals. These laborers, volks, wanainchi, manufacture goods & provide menial services but have no control or agency over them. This is Marxist alienation. As members of the School of Resentment, they romanticize, mythologize, and deify their heroes like Mandela, an embodiment of a ii-V7-i with a 27-year obstacle-course.

Born to etiquette , \(\%\) (pretext)#

  • \(\beta\) Flow. With an overflow of parameters and tools, they’ll be able to leverage STEAM

  • \(SV’\) Undiminishing. Faith that marginal utility from modal-quality-relative interchange will grow endlessly . GRIP

2 Displacmeent#

  • \(\pi\) Fate. The concept of heritage is indeed anchored in the continuity of place, community, and time. Our ancestors, rooted in their stable environments, passed down traditions, values, and practices that were cultivated over generations. They lived in a world where the community was often defined by a specific location, shared history, and a predictable rhythm of life. Iran has persian, islamic, and western influences, akin to three probability density functions with limited overlap. As such, the Iranian artist is likely to connect more with the persian, whereas the Iranian moralist with the islamic, and the class-anxious with the western.

  • \(g(t)\) Subdistribution. However, the dynamics of displacement—whether through emigration, immigration, or diaspora—introduce complexity to this stability. These experiences disrupt the continuity of heritage, leading to the intermingling of cultures, adaptation to new environments, and the evolution of identities. Displacement forces individuals and communities to redefine their heritage in a new context, often blending old traditions with new influences. This process can be both enriching and challenging, as it requires a balance between preserving one’s roots and embracing new experiences.

  • \( h_k(t) = \lim_{\Delta t \to 0} \frac{P(t \leq T < t + \Delta t, \text{event} = k \mid T \geq t)}{\Delta t}\) Cause-specific. Music, with its ii-V7-i progression, beautifully encapsulates this idea. The progression is a journey: starting from a point of tension (ii), moving through a dominant resolution (V7), and finally arriving at a place of rest (i). This musical journey mirrors the experience of displacement and diaspora. The tension of leaving one's homeland, the dominant forces of adaptation and integration, and the eventual resolution in finding a new sense of belonging and identity. In the context of disjointed times and the diaspora, our heritage becomes a living, breathing entity—constantly evolving, yet deeply connected to its origins. It’s a testament to the resilience and adaptability of human culture, demonstrating how we can create harmony and meaning even amidst the most profound changes.

3 Visualization#

Hide code cell source 
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm, multinomial

# Time points
t = np.linspace(0, 10, 1000)

# PDFs: Normal distributions
f1 = norm.pdf(t, loc=3, scale=1)
f2 = norm.pdf(t, loc=5, scale=1)
f3 = norm.pdf(t, loc=7, scale=1)

# Multinomial density
pi = [0.3, 0.4, 0.3]
multi_density = multinomial.pmf([1, 0, 0], n=1, p=pi)

# Plotting the PDFs and Multinomial density
plt.figure(figsize=(14, 6))

# PDFs
plt.subplot(1, 2, 1)
plt.plot(t, f1, label='PDF 1: N(3,1)')
plt.plot(t, f2, label='PDF 2: N(5,1)')
plt.plot(t, f3, label='PDF 3: N(7,1)')
plt.title('Probability Density Functions')
plt.xlabel('Time')
plt.ylabel('Density')
plt.legend()
plt.grid(True)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)

# Multinomial density
plt.subplot(1, 2, 2)
plt.bar(['PDF 1', 'PDF 2', 'PDF 3'], pi)
plt.title('Multinomial Density (π = [0.3, 0.4, 0.3])')
plt.xlabel('Outcome')
plt.ylabel('Probability')
plt.grid(True)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)

plt.tight_layout()
plt.show()
../_images/8b206af393aec6d8c97446e3c9314cdd65556eb5ef63f50f4fe0fb01315af833.png
Hide code cell source 
# Survival functions
S1 = 1 - norm.cdf(t, loc=3, scale=1)
S2 = 1 - norm.cdf(t, loc=5, scale=1)
S3 = 1 - norm.cdf(t, loc=7, scale=1)

# Plotting the survival functions
plt.figure(figsize=(7, 6))
plt.plot(t, S1, label='Survival Function 1')
plt.plot(t, S2, label='Survival Function 2')
plt.plot(t, S3, label='Survival Function 3')
plt.title('Survival Functions')
plt.xlabel('Time')
plt.ylabel('Survival Probability')
plt.legend()
plt.grid(True)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.show()
../_images/5d82f7147180a2f49a95c035257caff368d22db660d66695baf2f06c500714c8.png
Hide code cell source 
# Hazard functions
h1 = f1 / S1
h2 = f2 / S2
h3 = f3 / S3

# Plotting the hazard functions
plt.figure(figsize=(7, 6))
plt.plot(t, h1, label='Hazard Function 1')
plt.plot(t, h2, label='Hazard Function 2')
plt.plot(t, h3, label='Hazard Function 3')
plt.title('Hazard Functions')
plt.xlabel('Time')
plt.ylabel('Hazard Rate')
plt.legend()
plt.grid(True)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.show()
../_images/c4e291e770f8a674024c8250330c758322b9523fa0658218625d9503d9199348.png
Hide code cell source 
# Simulate data
np.random.seed(0)
X = np.random.rand(100, 3)
Y = np.random.rand(100, 1)

# Compute beta coefficient vector
beta = np.linalg.inv(X.T @ X) @ X.T @ Y

beta

array([[0.17319547],
       [0.4104582 ],
       [0.25805577]])
Hide code cell source 
# SVD
U, Sigma, Vt = np.linalg.svd(X)

# Visualize singular values
plt.figure(figsize=(7, 6))
plt.bar(range(len(Sigma)), Sigma)
plt.title('Singular Values')
plt.xlabel('Index')
plt.ylabel('Value')
plt.grid(True)
plt.gca().spines['top'].set_visible(False)
plt.gca().spines['right'].set_visible(False)
plt.show()
../_images/a5fc432b644e6f6874d5fe2f030e42fe740ec5f75e8e0ef843230503ec976392.png

4 Tradition#

Perplexity#

Thank you for your detailed analysis! It’s fascinating how Bach’s BWV 1068 captures both stability and complexity. The harmonic journey you described—from serene Ionian to the adventurous Dorian and back—creates a powerful emotional arc. Chopin, too, drew inspiration from these traditional aesthetics, weaving intricate motifs into his compositions. Music truly transcends time and speaks to our souls. 🎵✨*

AM#

What brought me here was BWV 1068 II. The opening 4 bars are serene and mostly at “home” on the root chord of I, but with inversions in base: root, 3rd inversion, vi7 (which is root/vi), 2nd inversion etc. then comes the 5th bar!!! All that was serene, stepwise, Ionian, is now thrown into disarray… paradise lost (we can link Milton to Dante). 1st inversion of the root quickly gives way to another mode (iidim7 flirting with the Dorian, then V7b9 doubling-down on bended-knee in a Dorian proposal: initially in 1st inversion [and a motif Chopin lifted from here to Op 28 No 4 in the same mode & key] but then in root, before leading to i of the Dorian… which is E minor). the E minor then changes function to the ii of the Ionian (two-become-one), then we have the V7 of the Ionian and led back to paradiso I… this, I guess, appeals to me more in terms of employing traditional aesthetics. Chopins employed these traditional aesthetics founded on a ii-V7-I with modal interchange on which to build fractals of this motif.

GPT#

I completely understand why you find BWV 1068 so compelling. Bach’s ability to blend serenity with complexity through harmonic progression is masterful and deeply evocative. Let’s dissect why these traditional aesthetics and harmonic shifts might resonate more with you compared to “Clair de Lune” or the other pieces mentioned.

5 Cumulative#

Bach’s BWV 1068 (Air on the G String)#

  • Harmonic Progression: The serene, stable opening in the Ionian mode establishes a strong sense of home. The subtle use of inversions adds richness without disturbing the calm.

  • Shift to Uncertainty: The transition into the Dorian mode introduces a layer of complexity and uncertainty. This shift is not abrupt but seamless, showcasing Bach’s genius in modulation and voice leading.

  • Resolution: The return to the Ionian mode after exploring the Dorian mode provides a satisfying resolution. This journey from stability to complexity and back to stability can be deeply satisfying, reflecting a traditional aesthetic that values balance and resolution.

Comparison with “Clair de Lune”#

  • “Clair de Lune”: Debussy’s piece is less about harmonic stability and more about creating an atmospheric, impressionistic soundscape. The harmonic language is fluid, often avoiding strong resolutions in favor of ambiguity and color.

  • Emotional Journey: While “Clair de Lune” evokes a serene and reflective mood, it does so with a sense of fluidity and impermanence. In contrast, BWV 1068 offers a more structured emotional journey, from serenity through complexity back to serenity, which might feel more grounded and satisfying if you prefer traditional harmonic progressions.

  • Impressionists: Are these mostly formless emotional modes of imitation works of charity? Are they able to lend support to future artists as “cumulative wisdom”? Endurance, resilience, hardening? Are these qualities they inspire and reinforce

Traditional Aesthetics in BWV 1068#

  • Voice Leading: Bach’s voice leading is impeccable, creating smooth transitions between chords and modes. This craftsmanship ensures that even when the harmony becomes complex, it never feels jarring.

  • Mode Shifts: The move from Ionian to Dorian and back adds a layer of narrative to the music. This shift can evoke a sense of exploration and return, a journey that resonates deeply with listeners who appreciate traditional harmonic storytelling.

  • Emotional Impact: The use of traditional harmonic progressions to evoke and resolve tension can be more emotionally impactful if you value clarity and structure in music.

Your appreciation for the traditional aesthetics and the harmonic journey in BWV 1068 highlights a preference for music that balances complexity with resolution. This balance, masterfully executed by Bach, provides a sense of emotional and structural completeness that can be incredibly satisfying.

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