Chord Evaluation: Should A:maj/2 Equal A:maj?

by Alex Johnson 46 views

In the realm of music information retrieval (MIR) and music analysis, chord evaluation plays a crucial role. Accurately assessing the similarity and correctness of chord transcriptions is essential for various applications, including automatic music transcription, music recommendation, and music education. However, the way chords are encoded and compared can significantly impact evaluation results. One particularly interesting issue arises when dealing with chord inversions, specifically whether chords with different bass notes but the same basic structure should be considered equivalent under certain evaluation metrics.

The Core Issue: Bass Notes and Chord Encoding

The crux of the matter lies in how the chord.encode function in the mir_eval library handles bass notes. Currently, the implementation forces the inclusion of the bass note into the chord bitmap. This means that a chord like A:maj/2 (A major with a D bass note) is encoded as A:maj(2)/2. This encoding choice has several implications for chord evaluation:

  • Discrepancies in Triad Evaluation: Under the triads metric, A:maj/2 is considered different from A:maj. This might seem counter-intuitive because both chords are fundamentally major chords, differing only in their bass note. The current encoding does not abstract away the bass note when comparing triads.
  • Inconsistency with Ninth-Note Reduction: The encoding treats A:maj/2 differently from A:maj(9), even though the ninth note is always reduced in the encoding process. This inconsistency raises questions about the uniformity of the encoding and its impact on evaluation results.
  • Agreement with the "Correct" Answer: The encoding considers A:maj/2 equivalent to A:maj(2), which reflects the inclusion of the second interval due to the bass note. However, this equivalence might not align with the desired behavior when inversion is not a primary consideration.

The provided Python code snippet illustrates these points:

In[1]: mir_eval.chord.triads(['A:maj/2'], ['A:maj'])
Out[1]: array([0.])

In[2]: mir_eval.chord.triads(['A:maj/2'], ['A:maj(9)'])
Out[2]: array([0.])

In[3]: mir_eval.chord.triads(['A:maj/2'], ['A:maj(2)'])
Out[3]: array([1.])

These results highlight the discrepancies in how chords with different bass notes are evaluated, particularly when using metrics that focus on the basic triad structure.

Arguments for and Against Bass Note Inclusion

The inclusion of the bass note in the chord bitmap is not without justification. One could argue that the bass note is a crucial element of a chord, significantly influencing its overall sound and harmonic function. Ignoring the bass note would be a loss of important musical information. This perspective aligns with the idea that inversions are musically distinct and should be treated as such.

However, this approach creates a conflict with the concept of having separate metrics for inversion and no-inversion scenarios. If the bass note is always included in the encoding, it becomes challenging to evaluate chords based solely on their root and quality (e.g., major, minor) without considering the inversion. The current implementation makes it difficult to directly compare A:maj/2 and A:maj when the goal is to assess the similarity of their underlying major triad structure.

Furthermore, forcing bass note inclusion complicates comparisons across different datasets or research studies. If some studies focus on root and quality while others emphasize inversions, the encoding differences can lead to inconsistencies and make it difficult to draw meaningful conclusions from a meta-analysis perspective.

A Proposed Solution: Decoupling Bass Note from Chord Bitmap

One potential solution is to decouple the bass note from the chord bitmap. This would involve encoding A:maj/2, A:maj/4, and similar chords as equivalent to A:maj when inversion is not being considered. In other words, the triads metric would focus solely on the presence of the major triad intervals (root, major third, perfect fifth), regardless of the bass note.

This approach would offer several advantages:

  • Simplified Triad Comparison: It would allow for a more straightforward comparison of triad structures, abstracting away the influence of inversions when they are not relevant to the evaluation.
  • Consistency with No-Inversion Metrics: It would align better with the intention of having separate metrics for evaluating chords with and without considering inversions.
  • Increased Flexibility: It would provide greater flexibility in choosing the appropriate level of detail for chord evaluation, depending on the specific research question or application.

However, implementing this change would require modifying the encoding logic of chords in mir_eval. This could have significant implications for existing research that relies on the current encoding scheme. Published results might not be directly comparable to results obtained using the modified encoding. Therefore, any such change would need to be carefully considered and implemented with appropriate documentation and versioning.

Implications and Considerations for MIR Research

The decision of whether to consider chords with different bass notes as equivalent depends heavily on the specific application and research question. In some cases, the bass note is a critical feature that should not be ignored. For example, when analyzing harmonic progressions or voice leading, the bass line plays a fundamental role.

However, in other cases, the focus might be on the underlying chord structure, regardless of the inversion. For example, when evaluating the accuracy of automatic chord recognition systems, it might be more important to correctly identify the root and quality of the chord than to precisely determine the bass note.

Ultimately, the choice of encoding and evaluation metrics should be guided by the specific goals of the research. Researchers should carefully consider the implications of different encoding schemes and choose the approach that best suits their needs. It is also important to clearly document the encoding and evaluation methods used, so that results can be easily interpreted and compared across different studies.

Conclusion: A Call for Discussion and Standardization

The issue of how to handle bass notes in chord evaluation highlights the complexities and nuances of music information retrieval. There is no single "correct" answer, and the best approach depends on the specific context and goals.

This discussion aims to foster a deeper understanding of the trade-offs involved in different chord encoding schemes and to encourage the development of more flexible and adaptable evaluation metrics. By carefully considering the implications of different choices, we can improve the accuracy and reliability of chord evaluation, leading to advancements in music analysis, automatic music transcription, and other related fields.

The question remains: Should A:maj/2 be considered equal to A:maj? The answer, as with many things in music, is it depends. What do you think?

For further reading on music information retrieval and chord evaluation, you can visit the International Society for Music Information Retrieval (ISMIR) website.