I cannot definitively name a single "best musician of all time" as the concept is inherently subjective. However, some musicians frequently cited in such discussions for their profound impact, innovation, skill, and influence across centuries include:
*   **Johann Sebastian Bach** (Baroque mastery, foundational Western harmony, intricate complexity)
*   **Wolfgang Amadeus Mozart** (Supreme melodic genius and structural perfection across genres)
*   **Ludwig van Beethoven** (Revolutionized music's emotional depth and structural scope)
*   **The Beatles (John Lennon, Paul McCartney, George Harrison, Ringo Starr)** (Unprecedented cultural impact, songwriting evolution, global influence)
*   **Miles Davis** (Consistent innovation in jazz across decades, shaping multiple styles)

Arguing for any one requires recognizing their unique contributions within vast and incomparable musical traditions globally.

**Analysis of Ambiguity and Objective Criteria:**

The question "Who is the best musician of all time?" is fundamentally unanswerable due to its extreme ambiguity. It conflates numerous subjective dimensions and lacks well-defined, objective criteria. To even attempt a defensible answer, the question itself would need rigorous specification:

1.  **Define "Musician":** Does this mean composer, performer, improviser, or all combined? Technical virtuosity on an instrument differs vastly from compositional genius or vocal prowess. Is a songwriter who doesn't perform a "musician" in this context?
2.  **Define "Best":** By what specific, measurable standards?
    *   **Technical Skill?** Requires defining specific measurable skills on specific instruments (e.g., speed, accuracy, range), but ignores expression.
    *   **Innovation/Influence?** This involves historical impact – whom did they influence, and how significantly? However, quantifying "significance" is difficult. Influence also changes over time and can be contested.
    *   **Creativity/Originality?** Highly subjective; what seems revolutionary to some might seem derivative to others.
    *   **Popularity/Commercial Success?** Measurable by sales or chart positions, but fluctuates wildly with time, market, and access. This heavily favors recent artists and mainstream genres.
    *   **Cultural Impact?** Again, difficult to quantify objectively across vastly different cultures and historical epochs.
    *   **Emotional Depth/Expressiveness?** Deeply personal and subjective.
3.  **Define the Scope:**
    *   **Time Period:** All time? This inherently disadvantages musicians from eras with less recorded history or different cultural contexts.
    *   **Genre?** Comparing a classical composer (Bach) to a rock band (Beatles) to a jazz innovator (Miles Davis) to a Carnatic singer (M. S. Subbulakshmi) to a Senegalese griot is comparing fundamentally different art forms with distinct values and criteria.
    *   **Cultural Context?** "All time" implies a global scope, yet Western music history and its benchmarks often dominate such discussions, marginalizing arguably equally significant traditions from Africa, Asia, Indigenous cultures, etc.
4.  **Define the Weighting:** How are these criteria combined and weighted? Is innovation worth 50% and technical skill 30%? There's no objective formula.

**Conclusion on Ambiguity:** Quests for a single "best" musician ignore the diversity of musical expression and purpose. What is "best" for creating complex symphonies isn't best for communal dance music or intimate songwriting. The ambiguity stems from conflating diverse skills, overlooking cultural biases, the impossibility of fair cross-genre/cross-era comparisons, and the lack of a universal yardstick for artistic value. Meaningful discussion requires replacing "best of all time" with more specific questions like "Who was the most influential figure in developing Baroque counterpoint?" or "Who revolutionized jazz improvisation in the mid-20th century?" to define defensible and relevant criteria.