PONE-D-22-20874

Convergent evolution in a large cross-cultural database of musical scales

PLOS ONE

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Additional Editor Comments:

Both reviewers were impressed with the work, both theoretically and methodologically. However, both reviewers raise some valid concerns and bring up additional perceptual-cognitive and music-theoretical work that should be included. Importantly, both reviewers were not so convinced that the results adequately provide support for convergent evolution per se, a sentiment with which I agree; rather, there could be similar constraints across cultures that gave rise to the prevalence of certain intervals in musical scales. Reviewer 2 offers a great starting list of such possible constraints. I would add that the growing literature on non-octave-based, artificial tuning systems such as the Bohlen-Pierce scale, and the relative ease with which humans in different cultures learn and represent pitch patterns in these scales, should be discussed as a limitation for studying scale evolution. 

As a very minor point: It was also noted that citation 33 references a pre-print, but the cited pre-print has now been published at Attention, Perception and Psychophysics in 2022. Please update the citation.

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Reviewers' comments:

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Comments to the Author

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Reviewer #1: No

Reviewer #2: Partly

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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Reviewer #2: Yes

5. Review Comments to the Author

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Reviewer #1: This very interesting submission presents a database of musical scales, drawn from a relatively wide range of sources representing different societies and geographical regions. This database is analyzed statistically to investigate what kinds of regularities may be found across the scales, as well as the set’s range and nature of variability. The manuscript presents some possibilities which may have given rise to both regularities and variation, across time and across geography.

The new scale database is, in this reviewer’s opinion, a fine contribution to the research literature. It appears to be larger and broader in scope than any such extant resource. Making this database, and the computational tools used to analyze it, publicly available is, to this reviewer, the greatest benefit of this study.

The analyses of the database are really quite interesting and, as the authors note, require innovative thinking as there may be no generally accepted methods for how to investigate the questions undergirding this study.

The first proposed method, comparing the database’s scales to a lognormal distribution, makes sense in some ways, but the hypotheses that scale degrees (to use the musical term) might be chosen independently from such a distribution and that that “small intervals should be uncommon” do not accord with what we know of melodic structures in general, possibly motivated by something like Fitts’ law (cf. Brinkman & Huron 2021, Ammirate & Russo 2015, Huron 2001). The notion that scales serve as organizing schemas for melodies (Dowling 1978) which are, culturally and evolutionarily, vocal in origin, would work against notions of scale degrees as independent from one another (as the authors note in a more limited way); studies of melodic entropy and other such related measures give rise to the possibility that scales arise, in part, from physiological affordances and constraints (motor, perceptual, and neurological). The second and third methods, shuffling and resampling, likewise start from assumptions which are plausible if the idealized musician involved is constructing scales as abstract entities out-of-time (perhaps as a precursor to musical composition), a view which does not seem plausible as an evolutionary mechanism. It is good to see that the authors state that “Ultimately, it is hard to say exactly how scales are chosen….”

Nonetheless, the results support what would be expected, from a multitude music-theoretic, perceptual-cognitive, and enthnomusicological crosscultural studies: “whole steps” (in the region of 200 cents), “perfect fifths” (+/- 700 cents), and octaves (+/- 1200 cents) are prounounced and notably different from what is predicted by each model. Figures 3-4 require some puzzling-through to interpret; the explanatory text is sufficiently detailed but somewhat dense.

The ”Statistics of octave scales” section was very interesting, convincing, and provocative. In the “Variation across societies…” and “Statistical analysis shows…” sections, there is much of interest, such as the clustering of equiheptatonic scales in the center of the 2D solution provided, and the quasi-circular distribution of other scales (sliced differently in the diagrams), reminiscent of spacing in 2D renderings of many phenomena (affect, musical timbre, linguistic vowel space). The lack of any interpretation of the axes of the tSNE graphs renders them opaque to much interrogation (for example, why are the Western ‘modes’ arranged as they are, given that they are rotations of the ‘same’ underlying structure?) The claim that most scales tend to be close to equidistant is tantalizing but more is needed in the way of explanation or argumentation to make the case convincingly. It’s possible that simply labelling the Y axes of the graphs in Fig. 7 would be a help in this regard.

The Discussion section begins with consideration of how diverse scales are across cultures. This section builds on two ‘case studies’, the first published (but, one expects, not widely known) on Georgian singing, and the second newly-conducted and in the supplemental information. Together, these present interesting ideas but are need expansion to sufficiently make the case; the Georgian study is itself some dozens of pages in its exploration, and the problems of dealing with pitch extraction from percussion (marimba and carillon) are nontrivial. The overall conclusion here, that “shared biases” underlie “convergent evolution”, does not seem adequately supported. One might consider neural bases (Large’s work would be a starting point, e.g. Large et al 2016) as well as cross cultural/cognitive/perceptual ones (add Dowling 1978 as a starting point) in addition to the vocal/motor approaches already mentioned in this review. “How do scales evolve over time” provides good possibilities, but is perforce speculative, as is also the case with “How are scales selected.” Many citations are given here, and the portmanteau character of the section is stimulating but could, in this reviewer’s opinion, be either greatly trimmed (reducing speculation) or expanded (to support the argument—it would take quite a bit of text to really support what’s implied here from the citation of the Partch book).

On balance, this reviewer recommends reformulating the MS to be primarily a report of a new, substantial database, and accompanying analyses, which adds to our current and widely accepted knowledge of musical scales in good ways. substantially trimming the Discussion section to reduce the speculative aspects. This is worthwhile and should be supported by publication.

However, the study’s overt goal—to set this forth as evidence for convergent _evolution_--is not supported adequately. Readers with more musical background will differ on various points as to how pitch, interval, scale, and tonality are conceptualized, defined, and utilized; readers looking for causal mechanisms—one of the key selling points for any evolutionary theory—will find references to intriguing proposals but not a convincing causal narrative. Emphasizing the rather clearer contributions of the database analysis will make for a more integrated approach, probably reduce the extremely large number of highly divergent citations to a more inter-coherent set, and allow specialists in musicology and music perception/cognition to work from the findings presented herein.

References cited

Ammirante, P., & Russo, F. A. (2015). Low-skip bias: The distribution of skips across the pitch ranges of vocal and instrumental melodies is vocally constrained. Music Perception: An Interdisciplinary Journal, 32(4), 355-363.

Brinkman, A., & Huron, D. (2021, July). Cross-Cultural Corpus Creation and Statistical Tendencies in Music. In 8th International Conference on Digital Libraries for Musicology (pp. 14-22).

Dowling, W. J. (1978). Scale and contour: Two components of a theory of memory for melodies. Psychological review, 85(4), 341.

Huron, D. (2001). Tone and voice: A derivation of the rules of voice-leading from perceptual principles. Music Perception, 19(1), 1-64.

Large, E. W., Kim, J. C., Flaig, N. K., Bharucha, J. J., & Krumhansl, C. L. (2016). A neurodynamic account of musical tonality. Music Perception: An Interdisciplinary Journal, 33(3), 319-331.

Reviewer #2: Convergent evolution in a large cross-cultural database of musical scale

This paper is clearly written, and easy to follow. It describes an analysis based on a newly assembled corpus of different types of scale data. By analyzing this data, the authors found convergence between the different types of intervals used across cultures, and also showed that scales vary as much within cultures (broadly defined) as between.

I have several broader comments, and some minor comments.

1. Section on ‘Qualitative evidence for octave equivalence’. Most of the results described in this section are evidence for the importance of (or, more precisely) the presence of octave relationships in musical scales. Evidence of the octave’s presence on musical instruments does not show that listeners perceive those notes as ‘equivalent’. Likewise, performing melodies in parallel octaves does not prove octave equivalence; many harmonies use, say, thirds in parallel, but this should not lead to the conclusion that notes separated by thirds are perceived as equivalent. I think this section could be easily re-worked to suggest that octaves are ‘important’ and/or ‘present’, but not that there is ‘octave equivalence’. Stronger evidence for octave equivalence would be that the scale system is cyclic, centered around octave transpositions, but it is not clear to me that that result falls neatly out of any of the models presented in this paper (this cyclic nature of scales was, as far as I can tell, assumed in the ‘statistics of octave scales’ section). Either way, I think the claim of octave equivalence is not necessary for the observation that octaves are a frequent interval to still be interesting.

a. The fact that the octave is equivalent is an assumption you are making to examine the statistics of ‘octave scale’. It should be stated as an assumption, rather than as a fact.

b. It could be possible to look in one octave, find what intervals are common, and see how well that predicts intervals you find in other octaves. This might provide stronger evidence for octave equivalence.

2. Page 8 – ‘humans make mistakes in discriminating intervals below ~100 cents’. There is some evidence that this threshold is precisely because (in Western listeners, the majority of those tested) sub-semitone intervals are not musically relevant. It is misleading to state this as somehow causal to how scales have developed around the world.

a. Zarate, J. M., Ritson, C. R., & Poeppel, D. (2012). Pitch-interval discrimination and musical expertise: Is the semitone a perceptual boundary?. The Journal of the Acoustical Society of America, 132(2), 984-993.

3. The high frequency of perfect fourths and perfect fifths in scales could, like octaves, be explained by tonal fusion. I think this could be mentioned earlier. Most of the introduction focuses on why the octave might be common, but most of the arguments could apply just as easily to perfect fourths and fifths, which are found in low parts of the harmonic series. This was only touched on very briefly in the discussion (page 14).

4. The relationship between melodic scales and harmony was not discussed. Conceivably harmony is a constraint on scale systems as well?

5. I did not understand the description of the database. The figure shows 931 total scales, 434 theory scales, and 497 measured scales. However, in the text a few different numbers were references (382 theory scales, 434 measured scales, etc.). Therefore, the correspondence between the figure and the text was not clear, and the relationship between the different numbers referenced in the text was likewise unclear. Potentially making a flow chart summarizing the information in the supplementary materials would avoid confusion.

6. I think the title does not match the conclusion. As the authors themselves state in the discussion, scales can be invented without referencing existing scales, and ‘evolution’ is difficult to trace with scales. I think something like ‘Convergence in a large cross-cultural database of musical scale’ would be more appropriate.

7. I think it is incorrect to say that scale evolution is relatively unconstrained (page 15). The convergence of scales around the world does give circumstantial evidence that there are constraints! The physicality of musical instruments is a constraint, for example. Ease of sung production is a constraint.

Minor comments:

8. Page 1: ‘Pitch (frequency)’ – I’d flip this and say frequency (pitch) to emphasize the measurable item (which you use in your models) rather than the percept. Why do you have ‘duration (time)’? Are you distinguishing between duration and time?

9. Page 3: ‘but is always within 10 cents’. Is there a citation for this assertion? Similar question for the statement ‘5 cents for tuning forks’ on page 8.

10. Page 2: ‘But since we perceive pitch logarithmically’ – Jacoby et al could be a useful second citation here.

11. Figure 2: Is ‘Western’ referring to South America? Or was South America included in ‘Latin America’? Either way that labeling was confusing. Maybe re-ordering the bars so they are lined up (approximately) with the appropriate area of the globe would be helpful?

12. Page 9: It was not clear initially that the first section of the result only examined measured scales. This should be stated at the beginning of the results section, not in the subsequent ‘Statistics of Octave Scales’ section.

a. Would the results of the initial section be the same if you applied the analysis to theory scales? It could be a good sanity check.

13. Figure 6: I liked this analysis and plotting!

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Reviewer #1: No

Reviewer #2: No

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PONE-D-22-20874R1Convergent evolution in a large cross-cultural database of musical scalesPLOS ONE

Dear Dr. McBride,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

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Associate Editor, PLOS ONE

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Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

Both reviewers are happy with the manuscript and indicate it is almost ready to be accepted for publication.

There are just two minor points to address. Reviewer #1 cites a recently-published paper - please feel free to comment on this paper and it's relevance. Please also address reviewer #2's concerns regarding Figure 2.

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Reviewers' comments:

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Comments to the Author

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Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

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4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The revision addresses many of the reviewers' comments and the remaining disagreements are no more than normal for scientific discourse.

I note that a recently published paper ( Anglada-Tort, M., Harrison, P. M., Lee, H., & Jacoby, N. (2023). Large-scale iterated singing experiments reveal oral transmission mechanisms underlying music evolution. Current Biology ) directly addresses material in this submission,focally but not limited to discussion on lines 472ff.

Reviewer #2: I appreciate the attention to detail and care that the authors took in addressing the reviewer comments, and I think the paper is much clearer in its current form.

I will add two minor points, one to clarify a point from my first review, and another on one aspect that is still unclear to me:

1. "The relationship between melodic scales and harmony was not discussed. Conceivably harmony is a constraint on scale systems as well?"

- There is a world in which people would use notes within a harmonic context but not use those same notes within melodies, but to my knowledge that doesn't appear to happen. So it does seem like aspects like fusion/harmony constrain (or maybe, better put, guide) individuals to use particular notes in melodies. The added comments about fusion maybe address this issue sufficiently; I'll leave that to your discretion. I hope this clarifies my point.

2. The bar labels are still unclear to me on Figure 2. I only see one country labeled in Latin America, and many South America. Why is the label 'Latin America'?

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Reviewer #1: No

Reviewer #2: No

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Convergent evolution in a large cross-cultural database of musical scales

PONE-D-22-20874R2

Dear Dr. McBride,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Reviewers' comments: