An analysis of chord progressions in 680,000 songs reveals common patterns and some surprising trends. The most frequent progressions are simple, diatonic, and often found in popular music across genres. While major chords and I-IV-V-I progressions dominate, the data also highlights the prevalence of the vi chord and less common progressions like the "Axis" progression. The study categorized progressions by "families," revealing how variations on a core progression create distinct musical styles. Interestingly, chord progressions appear to be getting simpler over time, possibly influenced by changing musical tastes and production techniques. Ultimately, while common progressions are prevalent, there's still significant diversity in how artists utilize harmony.
Mathematicians have finally proven the Kakeya conjecture, a century-old problem concerning the smallest area required to rotate a unit line segment 180 degrees in a plane. The collaborative work, spearheaded by Nets Katz and Joshua Zahl, builds upon previous partial solutions and introduces a novel geometric argument. While their proof technically addresses the finite field version of the conjecture, it's considered a significant breakthrough with strong implications for the original Euclidean plane problem. The techniques developed for this proof are anticipated to have far-reaching consequences across various mathematical fields, including harmonic analysis and additive combinatorics.
HN commenters generally express excitement and appreciation for the breakthrough proof of the Kakeya conjecture, with several noting its accessibility even to non-mathematicians. Some discuss the implications of the proof and its reliance on additive combinatorics, a relatively new field. A few commenters delve into the history of the problem and the contributions of various mathematicians. The top comment highlights the fascinating connection between the conjecture and seemingly disparate areas like harmonic analysis and extractors for randomness. Others discuss the "once-in-a-century" claim, questioning its accuracy while acknowledging the significance of the achievement. A recurring theme is the beauty and elegance of the proof, reflecting a shared sense of awe at the power of mathematical reasoning.
Terry Tao's blog post discusses the recent proof of the three-dimensional Kakeya conjecture by Hong Wang and Joshua Zahl. The conjecture states that any subset of three-dimensional space containing a unit line segment in every direction must have Hausdorff dimension three. While previous work, including Tao's own, established lower bounds approaching three, Wang and Zahl definitively settled the conjecture. Their proof utilizes a refined multiscale analysis of the Kakeya set and leverages polynomial partitioning techniques, building upon earlier advances in incidence geometry. The post highlights the key ideas of the proof, emphasizing the clever combination of existing tools and innovative new arguments, while also acknowledging the remaining open questions in higher dimensions.
HN commenters discuss the implications of the recent proof of the three-dimensional Kakeya conjecture, praising its elegance and accessibility even to non-experts. Several highlight the significance of "polynomial partitioning," the technique central to the proof, and its potential applications in other areas of mathematics. Some express excitement about the possibility of tackling higher dimensions, while others acknowledge the significant jump in complexity this would entail. The clear exposition of the proof by Tao is also commended, making the complex subject matter understandable to a broader audience. The connection to the original Kakeya needle problem and its surprising implications for analysis are also noted.
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https://news.ycombinator.com/item?id=43723020
HN users generally praised the analysis and methodology of the original article, particularly its focus on transitions between chords rather than individual chord frequency. Some questioned the dataset's limitations, wondering about the potential biases introduced by including only songs with available chord data, and the skewed representation towards Western music. The discussion also explored the subjectivity of music theory, with commenters highlighting the difficulty of definitively labeling certain chord functions (like tonic or dominant) and the potential for cultural variations in musical perception. Several commenters shared their own musical insights, referencing related analyses and discussing the interplay of theory and practice in composition. One compelling comment thread delved into the limitations of Markov chain analysis for capturing long-range musical structure and the potential of higher-order Markov models or recurrent neural networks for more nuanced understanding.
The Hacker News post titled "I analyzed chord progressions in 680k songs" sparked a discussion with several interesting comments. Many users engaged with the methodology and findings presented in the linked article.
A recurring theme in the comments is the challenge of accurately extracting chord progressions from audio. Several users pointed out the difficulties in distinguishing between different inversions of the same chord, and the potential for errors in automatic chord recognition software. One commenter highlighted the issue of key modulation within a song, suggesting it could skew the analysis if not handled properly. Another user questioned the reliability of the dataset itself, wondering about the source of the chord progressions and the potential for biases in the selection of songs.
Some commenters expressed skepticism about the novelty of the findings. One user argued that the prevalence of common chord progressions is well-established in music theory, and the analysis simply confirms what musicians already know. Another commenter suggested that the focus on chord progressions alone overlooks other important aspects of music, such as melody, rhythm, and timbre.
Despite these criticisms, several commenters found the analysis intriguing. One user appreciated the visualization of the chord progression network, finding it a helpful way to understand the relationships between different chords. Another user expressed interest in exploring the dataset further, suggesting potential applications for music generation and analysis. A commenter also raised the question of cultural influences on chord progressions, wondering if certain progressions are more common in specific genres or regions.
Several users discussed the limitations of using only harmonic information to analyze music. They pointed out that melody, rhythm, and instrumentation play crucial roles in a song's overall impact. One commenter argued that while common chord progressions might be prevalent, they can be used in vastly different ways to create unique musical experiences.
A few commenters also shared their own experiences with music analysis and composition. One user mentioned using Markov chains to generate melodies, while another discussed the importance of understanding music theory for aspiring composers. These comments added a personal touch to the discussion and highlighted the practical applications of music analysis.