Chopin

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

A not-so-compelling analysis that works for the masses. What is “missing” in this analysis is quite literally everything Chopin was expressing

• Chopin asked for this piece to be played at his funeral together with Mozart’s requem

• This piece samples three openning chords from Mozart’s Lacrimosa: i/III-ii7b5-V7

• We must also acknowledge this ii-V7-i as the universal archetype alluded to by Wilde & Dante

• Mozart’s melody is infinitely richer and in counterpoint. But at one memorable point it begins on the root:

  • And consists of 8 stepwise ascending diatonic notes followed by 8 ascending chromatic notes

• Here with Chopin we have 6 hesitant descending chromatic notes

  • But the real beauty is in the archetypal chords he samples from Mozart & the bii-V7/vdim-I7 insertions

Missingness of one or all of the principle components of data, code, server, models, weights, and profiles is what is at stake (but perhaps migration represents redefining home?):

• \(f(t)\) I

• \(S(t)\) ii-V-I

• \(h(t)\) iii, IV, vi, vii, alterations: being in the moment trumps the ii-V7-I duty

  • Δ7

  • m or min

  • ° or dim

  • ø or m7♭5, -5

  • + or aug, ♯5 or +5

  • sus

  • ♭9, ♯9, ♯11, ♭13

• \((X'X)^T \cdot X'Y\) tension & release (e.g. Aiim7/E (GΔ) - iim7♭5/E Em)

• \(\beta\) m7♭5 > 7♯9 > 7♭9 > °7 > 7, etc

• \(SV'\) BWV 846 Prelude in C Major, Op 28 Prelude No. 4

While Tyler Perry’s work captures the collective unconscious via tension (bad marriage) & release (church music), the characters he creates don’t have individually compelling arcs that subsume many of the parameters of life

This is equivalent to their \(SV'\) being a vector of mostly \(zeros\) and the barriers, challenges, diversions, sirens, misfortunes, obstacles, courses, “chains” within which Tyler Perry is supposed to “dance” aren’t rich, leaving a basic ii-V-I redemption arch with perhaps one or two straightforward insersions of, say, iii and IV.

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

ii: Departure 1, 2, 3

• Sensory acuity ³¹: vision, hearing, smell, balance, glucose

• Memory & cognitive: integrity, decline, tests

• Physical activty: sarcopenia, brisk, dynamometer

V: Struggle 4

• Frailty: loneliness, isolation, usefulness

I: Return 5, 6

• Independence: ADLs, IADL

• Hard-outcomes: shuffling, reflexes, falls, hospitalization, organ-failure, death

Tip

In John Adams letter to Abigail concerning the “three generation” process of making an artist or seeker of leisure, we can reconceptualize it as a ii-V7-I chord progression.

One ancestor departs from the homeland and finds manual work (garbage collection for Kardashians). Their struggles in a new adoptive home yield a triumph: a professional second generation (trial lawyer for Kardashians).

The final generation has seen no struggle and the family has “returned” to the idealized paradise they would have wanted at their original home but found elsewhere. It’s in this light that you should read the letter to Abigail ³⁰

Letters to Abigail

                         1. Pessimism
                                     \
            2. Beyond Good & Evil -> 4. Dionysian -> 5. Science -> 6. Morality
                                     /
                                     3. Robustness

                             1. Chaos
                                     \
                        2. Frenzy -> 4. Dionysian -> 5. Algorithm -> 6. Binary
                                     /
                                     3. Energy

Activation Function \(Q\)

• Hunter-gatherer/War: humanism, spiritual teachings (I)

• Peasant/Economics: judeo (B)

• Farmer/Calculus: christian (G)

Biases \(U()\)

• Manufacturer/Philosophy: world religions (Y)

Weights \(\frac{dU()}{dQ}\)

• Energy/Musick: prophetic utterances (O)

• Deployment/Leisure: individual experience (R)

Show code cell source Hide code cell source

import numpy as np
import matplotlib.pyplot as plt

# Define the total utility function U(Q)
def total_utility(Q):
    return 100 * np.log(Q + 1)  # Logarithmic utility function for illustration

# Define the marginal utility function MU(Q)
def marginal_utility(Q):
    return 100 / (Q + 1)  # Derivative of the total utility function

# Generate data
Q = np.linspace(1, 100, 500)  # Quantity range from 1 to 100
U = total_utility(Q)
MU = marginal_utility(Q)

# Plotting
plt.figure(figsize=(14, 7))

# Plot Total Utility
plt.subplot(1, 2, 1)
plt.plot(Q, U, label=r'Total Utility $U(Q) = 100 \log(Q + 1)$', color='blue')
plt.title('Total Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Total Utility (U)')
plt.legend()
plt.grid(True)

# Plot Marginal Utility
plt.subplot(1, 2, 2)
plt.plot(Q, MU, label=r'Marginal Utility $MU(Q) = \frac{dU(Q)}{dQ} = \frac{100}{Q + 1}$', color='red')
plt.title('Marginal Utility')
plt.xlabel('Quantity (Q)')
plt.ylabel('Marginal Utility (MU)')
plt.legend()
plt.grid(True)

# Adding some calculus notation and Greek symbols
plt.figtext(0.5, 0.02, r"$MU(Q) = \frac{dU(Q)}{dQ} = \lim_{\Delta Q \to 0} \frac{U(Q + \Delta Q) - U(Q)}{\Delta Q}$", ha="center", fontsize=12)

plt.tight_layout()
plt.show()

One needs challenges, a worthy adversary, the embrace of more remote overtones of the harmonic series - Qualities to be reinterpreted as the form of the character arc: the ii-V7-I archetype that music lends to all the arts

Bellissimo

The beauty here lies in the familiar ii-V7-i eternally recurrying, but with increasingly tantalizing transformations (insertions to delay premature home coming &, deletions to avoid redundancy in repetition). The thematic coherence of the insertions is perhaps the most charming thing here: they are almost invariably ii-V7-i but drawn by the inimitable Pole from other modes (Phygian & Ionian), qualities (maj, min, dom, dim, 7, 9, 11, 13 & their extensions), and relatives (Ionian-Aeolian)

Case-study: Op 28 Prelude No. 4 ³⁵

• Em (Aelian mode)

• Largo common time

• ii-(V7sus, dom, b9, #9, b13)-i

• Interruptions of above odyssey (Mode, Quality, Relative):

A: i relative/III

• Phrygian II7, 6th, dim

• I7

B: Im7

• idim7, iim7 relative Maj/i, ii/i

• V7 relative Maj

• v7 relative Maj

• vdim relative

• im7/IV

A2: i relative/III (V deletion & other deletions)

• Phrygian ii7, iim7b5, iidim7

• I7

B2: im7 (shortest, agitato)

• idim7

Coda i minMaj7 (9)

• ii relative

• Vb9 Maj7

Marginal-utility

By offering a gradually increasing challenge-level to the listener, the audience remains very engaged and ultimately invited to hit “replay” or “loop” because the human mind is attracted to challenges we believe we can match if given the right amount oftime and tools with which to work.

Anthony Bourdain spent 28 years in New York kitchens. Now, that is a “ii” chord – away from our idealized “home”, which is invariably a tropical beach with a nearby garden with vines, grapes, wine, cheese, and friends. Over those three decades he decoded the essence of his craft in the 2000 bestseller “Kitchen Confidential: Adventures in the Culinary Underbelly” (later inspiring the Typhoid Mary fantasy), which really are all the “insertions” borrowed from ii-V7-I of other modes, qualities, and relatives, culminating in a most severe V7 tension that the only way out is “out of the kitche”.

Indeed, his next eighteen years, also the rest of his life, were lived outside the kitchen:³⁶ A Cook’s Tour (2002–2003), No Reservations (2005–2012), The Layover (2011–2013), and Parts Unknown (2013–2018). This literally involved the ii-V7-I chord sequence, where ii represents work and all the preparation with his team, V7 is the foreign trip and filming, I is returning to New York to spend some time with his daughter (or travelling to Italy to spent time with his girl friend) before heading back to work for the next session. Whether the different countries, personalities, and cuisines represents sufficiently new challenges is questionable. Diminishing marginal utility set in and this ultimate antidote to life couldn’t suffice anymore after 18 years of the same “ii-V7-I”, not at all a paradise (i.e., an ultimate I destination)

Ah, Dorian, how happy you are! What an exquisite life you have had! You have drunk deeply of everything. You have crushed the grapes against your palate. Nothing has been hidden from you. And it has all been to you no more than the sound of music.

Parts Unknown

At another time he devoted himself entirely to music, and in a long latticed room, with a vermilion-and-gold ceiling and walls of olive-green lacquer, he used to give curious concerts in which mad gipsies tore wild music from little zithers, or grave, yellow-shawled Tunisians plucked at the strained strings of monstrous lutes, while grinning Negroes beat monotonously upon copper drums and, crouching upon scarlet mats, slim turbaned Indians blew through long pipes of reed or brass and charmed—or feigned to charm—great hooded snakes and horrible horned adders. The harsh intervals and shrill discords of barbaric music stirred him at times when Schubert’s grace, and Chopin’s beautiful sorrows, and the mighty harmonies of Beethoven himself, fell unheeded on his ear. He collected together from all parts of the world the strangest instruments that could be found, either in the tombs of dead nations or among the few savage tribes that have survived contact with Western civilizations, and loved to touch and try them. He had the mysterious juruparis of the Rio Negro Indians, that women are not allowed to look at and that even youths may not see till they have been subjected to fasting and scourging, and the earthen jars of the Peruvians that have the shrill cries of birds, and flutes of human bones such as Alfonso de Ovalle heard in Chile, and the sonorous green jaspers that are found near Cuzco and give forth a note of singular sweetness. He had painted gourds filled with pebbles that rattled when they were shaken; the long clarin of the Mexicans, into which the performer does not blow, but through which he inhales the air; the harsh ture of the Amazon tribes, that is sounded by the sentinels who sit all day long in high trees, and can be heard, it is said, at a distance of three leagues; the teponaztli, that has two vibrating tongues of wood and is beaten with sticks that are smeared with an elastic gum obtained from the milky juice of plants; the yotl-bells of the Aztecs, that are hung in clusters like grapes; and a huge cylindrical drum, covered with the skins of great serpents, like the one that Bernal Diaz saw when he went with Cortes into the Mexican temple, and of whose doleful sound he has left us so vivid a description. The fantastic character of these instruments fascinated him, and he felt a curious delight in the thought that art, like Nature, has her monsters, things of bestial shape and with hideous voices. Yet, after some time, he wearied of them, and would sit in his box at the opera, either alone or with Lord Henry, listening in rapt pleasure to “Tannhauser” and seeing in the prelude to that great work of art a presentation of the tragedy of his own soul.

Dorian Gray Mode

“Because,” said Lord Henry, passing beneath his nostrils the gilt trellis of an open vinaigrette box, “one can survive everything nowadays except that. Death and vulgarity are the only two facts in the nineteenth century that one cannot explain away. Let us have our coffee in the music-room, Dorian. You must play Chopin to me. The man with whom my wife ran away played Chopin exquisitely. Poor Victoria! I was very fond of her. The house is rather lonely without her. Of course, married life is merely a habit, a bad habit. But then one regrets the loss even of one’s worst habits. Perhaps one regrets them the most. They are such an essential part of one’s personality.”

Certainty vs. Ambiguity

“Ah! then it must be an illusion. The things one feels absolutely certain about are never true. That is the fatality of faith, and the lesson of romance. How grave you are! Don’t be so serious. What have you or I to do with the superstitions of our age? No: we have given up our belief in the soul. Play me something. Play me a nocturne, Dorian, and, as you play, tell me, in a low voice, how you have kept your youth. You must have some secret. I am only ten years older than you are, and I am wrinkled, and worn, and yellow. You are really wonderful, Dorian. You have never looked more charming than you do to-night. You remind me of the day I saw you first. You were rather cheeky, very shy, and absolutely extraordinary. You have changed, of course, but not in appearance. I wish you would tell me your secret. To get back my youth I would do anything in the world, except take exercise, get up early, or be respectable. Youth! There is nothing like it. It’s absurd to talk of the ignorance of youth. The only people to whose opinions I listen now with any respect are people much younger than myself. They seem in front of me. Life has revealed to them her latest wonder. As for the aged, I always contradict the aged. I do it on principle. If you ask them their opinion on something that happened yesterday, they solemnly give you the opinions current in 1820, when people wore high stocks, believed in everything, and knew absolutely nothing. How lovely that thing you are playing is! I wonder, did Chopin write it at Majorca, with the sea weeping round the villa and the salt spray dashing against the panes? It is marvellously romantic. What a blessing it is that there is one art left to us that is not imitative! Don’t stop. I want music to-night. It seems to me that you are the young Apollo and that I am Marsyas listening to you. I have sorrows, Dorian, of my own, that even you know nothing of. The tragedy of old age is not that one is old, but that one is young. I am amazed sometimes at my own sincerity. Ah, Dorian, how happy you are! What an exquisite life you have had! You have drunk deeply of everything. You have crushed the grapes against your palate. Nothing has been hidden from you. And it has all been to you no more than the sound of music. It has not marred you. You are still the same.”