Rhyme books

Rhyme books (yun shu 韻書), also called sound books (yin shu 音書) are books that record Chinese character pronunciations. Compiled mainly for the purpose of facilitating the writing of rhymed compositions (such as poetry, lyrics, etc.), they are continually updated to keep pace with the evolution of the pronunciations of Chinese characters. Despite the complexity of speech sounds due to dialectal variations and the evolving nature of language, rhyme books from specific historical periods still largely capture the general phonological features of the time. Organized into character groups based on shared phonological features, they cover most characters or at least the frequently used ones in the language.

Character embeddings

Word vectors, or embeddings, represent words as multi-dimensional numerical arrays, capturing the semantic properties of words based on their usage in texts to facilitate text processing by machines. They can be applied in numerous machine learning tasks, ranging from semantic analysis to emotion intensity prediction. Word embeddings can be divided into three categories depending on how they are generated, namely traditional frequency-based word embeddings, static word embeddings, and contextualized word embeddings [27]. The static ones are often used for the computation of semantic similarity between words through metrics such as cosine similarity, which measures the cosine of the angle between two vectors in space. The most widely adopted methods for training static word embeddings include the statistical model GloVe [28] and the neural network-based Word2Vec model, which uses either the Continuous Bag of Words (CBOW) or Skip-gram architecture [29,30].

As mentioned above, many Chinese characters are monosyllabic morphemes that directly combine sound and meaning. Even when a character is part of a multi-character word, character embeddings still capture its semantic contribution. Therefore, we prioritize character embeddings over word embeddings to maintain the character-level focus of this study and to examine the unique sound-meaning relationships intrinsic to individual Chinese characters. The selection of embeddings to represent character meanings is of paramount importance to our methodology. Due to the unavailability of period-specific embeddings for each of the four rhyme books, we opted for two primary sets of embeddings from the same source named Chinese Word Vector (https://github.com/Embedding/Chinese-Word-Vectors) [31]. The two embedding sets were trained using the Skip-Gram with Negative Sampling (SGNS) model [29,30] and a ngram2vec [32] toolkit. The basic settings for the SGNS model included a window size of 5, dynamic window enabled, a sub-sampling rate of 1e-5, a low-frequency word threshold of 10, five iterations, and negative sampling set to 5. The vector size was set to 300. The consistency in training methods and settings ensured that the embeddings were methodologically comparable. The first set of embeddings was trained on Siku Quanshu 四庫全書 (complete library in four sections, hereinafter Siku), the largest collection of texts in pre-modern China. Two versions of Siku embeddings were provided in the Chinese Word Vector dataset, and we opted for the one trained with individual Chinese characters instead of bigrams as context features. The second set of embeddings was trained on Baidu Baike (https://baike.baidu.com/, Baidu encyclopedia), which serves as a representative corpus for training modern Chinese word embeddings because of its comprehensive and contemporary content. Using this corpus, the developers [31] trained embeddings for various target and context units, based on different co-occurrence statistics, such as Word → Word, Ngram (1–2) → Ngram (1–2), and Word → Character (1). Since we needed character representations, we adopted the character vectors developed from the “Word → Character (1)” type, with characters as the context units. A key factor in selecting these two sets of embeddings is that they were trained on two extensive, comprehensive, and representative corpora, ensuring their capacity to accurately capture the semantic relationships between characters.

The Siku embeddings were used for the first three rhyme books GY, PSY, and ZYYY while the Baidu embeddings were applied to ZHTY. We assumed that the Siku embeddings, derived from classical texts from the recorded history of China up to the mid-Qing dynasty, were generally applicable to the three pre-modern rhyme books, and the Baidu embeddings, which reflect contemporary language usage, were suitable for the rhyme book ZHTY compiled to guide poetry creation in modern times. As posited by Wang [33], semantic shifts were typically gradual rather than abrupt. That is, semantic evolution is continuous, and consequently, the language used in earlier periods remains mostly comprehensible to speakers in later periods. Although the meanings of some characters in the texts of Siku may slightly vary across time, the embeddings trained on Siku can still generally represent these meanings, especially regarding the semantic relationships between characters. However, significant changes in the Chinese vocabulary occurred during the two to three decades following 1919 [33], making it beneficial to adopt a new set of embeddings.

To further check whether the findings based on Siku embeddings were valid to ensure the robustness of our conclusions, we trained three more sets of embeddings and conducted a focused study on GY. The decision to train additional embeddings specifically for GY, rather than PSY and ZYYY, was driven by several factors. First, PSY covers a broad spectrum of materials that are challenging to gather and verify. Second, while ZYYY is primarily relevant to Yuan Qu, GY is extensively utilized in Tang poetry composition, which places significant emphasis on sound—an essential element of poetry. Additionally, the contemporary materials for GY are readily accessible online. Therefore, to optimize the effectiveness of our study, it is reasonable to concentrate on GY for verifications. Specifically, considering that GY was widely used to guide poetry creation in the Tang dynasty, we used Quan Tang Shi 全唐詩 (complete collection of Tang poems, hereinafter QTS) to train a set of character embeddings. In case the QTS corpus is not large enough or is limited by text genres to generate reliable meaning representations, we trained two more sets of embeddings, one using Quan Tang Wen 全唐文 (complete collection of Tang proses, hereinafter QTW), and the other using a combination of QTS and QTW. A similar SGNS model to the one mentioned above was used to train these three sets of embeddings. However, due to the relatively smaller corpus sizes, the model was slightly adjusted with the following parameters: vector_size = 100, min_count  = 1, and sample = 1e-3.

Semantic similarity measurement

Cosine similarity is a widely used metric in natural language processing to quantify the similarity between two non-zero positive vectors by measuring the cosine of the angle between them [34]. Mathematically, cosine similarity between two vectors A and B is defined as:

where represents the dot product of the vectors, and ||A|| and ||B|| are the magnitudes of the vectors. This measure focuses on the direction of the vectors rather than their magnitudes, making it particularly useful for applications where the relative orientation of vectors is more important than their lengths. It can be used to measure “the similarity between a query and a document, between two documents, or between two terms” [35], and therefore is widely adopted in information retrieval and document clustering. In this study, with characters converted to vectors, we adopted cosine similarity as the metric to measure the semantic relatedness between two characters. We utilized the “cosine_similarity” function from the scikit-learn library in Python to compute these similarities.

The process of obtaining semantic similarities of phonological groups is illustrated in Fig 1. Specifically, the characters in a rhyme book were divided into phonological groups, each group G_i (i ∈ [1: m]) being composed of characters C₁, C₂, …, C_x, which were vectorized into V₁, V₂, …, V_y. Since the training materials for the embeddings were comprehensive and large-scale, they covered most of the characters in the rhyme book. However, some characters, particularly rare ones, might still be missed, resulting in x ≥ y. This was acceptable because the missed characters were typically rare, constituting only a small portion of the total characters. At least two items were required in a phonological group to calculate the pairwise cosine similarity, so only when y ≥ 2 was the “cosine_similarity” function applied to a group to obtain its pairwise similarity matrix. Then, to extract the unique similarity values between different items, only the upper-triangular part of the matrix for all unique pairs, excluding the diagonal, was retrieved and flattened into a 1D array, resulting in a list of cosine similarities, such as S_{1_2}, S_{1_y}, … in the figure. Averaging all these pairwise cosine similarities yielded the group semantic similarity, represented as (i ∈ [1: n]), where n ≤ m since some groups with y < 2 were excluded. The characters covered by the final groups constituted a population, and the average cosine similarity over all pairs of characters in this population was taken as the overall semantic similarity of the rhyme book.

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Fig 1. Workflow of obtaining semantic similarities of phonological groups in a rhyme book.

https://doi.org/10.1371/journal.pone.0322044.g001

Visualization of semantic similarities and statistical significance testing

We compared the semantic similarity of each phonological group with the population mean to determine if it is greater than average. Additionally, to evaluate whether the high similarities occurred by chance, we created comparison groups by randomly sampling from the population, with each group containing the same number of characters as the original to eliminate possible effect of group size on the group semantic similarity. To examine how the semantic similarities of phonological groups and comparison groups were distributed, we utilized violin plots for a comprehensive overview of data distribution, including density, range, and central tendency. Comparing the median line and the population mean of each violin plot would give a straightforward answer to whether the group semantic similarity tend to be greater than expected.

Statistical testing was employed to assess the significance of the divergence, if any. We used the non-parametric one-sample Wilcoxon signed-rank test, which involved calculating the difference between each group’s semantic similarity and the population mean, and then testing if the median of the differences significantly differed from zero. In a similar task of determining phonesthemes, Abramova and Fernández [21] conducted independent-samples one-tailed Welch’s t-tests, comparing the pairwise similarity of a phonestheme to that of the corresponding baseline cluster. We did not follow this to use Welch’s t-test because, unlike the carefully selected phonestheme groups, many of our naturally formed groups in rhyme books are too small (containing fewer than 30 samples) to meet the assumptions required for Welch’s t-test, particularly normality or sufficient sample size. The non-parametric one-sample Wilcoxon signed-rank test does not require these assumptions, making it a more appropriate choice for our analysis. We used the “stats.wilcoxon” function from the “scipy.stats” Python package for this calculation.

However, the Wilcoxon signed-rank test requires at least five groups, making it unsuitable for examining the four tonal groups. Therefore, we adopted a Monte Carlo simulation approach similar to the one used in [19] to assess the semantic coherence of tonal groups. This approach is feasible because, unlike some other phonological groups with very few characters, the four tonal groups each contain a sufficient number of characters to allow for robust statistical analysis.

Dimension reduction and visualization of character vectors

In this study, high-dimensional character embeddings were adopted to represent the semantics of characters. To show how characters sharing common phonological features might be distributed in a two-dimensional semantic space, dimension reduction was required. Principal Component Analysis (PCA) [36] and t-distributed Stochastic Neighbor Embedding (t-SNE) [37] are two widely adopted dimension reduction methods, while Uniform Manifold Approximation and Projection (UMAP) [38] is a recent manifold learning method. PCA reduces dimensionality by projecting data onto directions of maximum variance but struggles with nonlinear relationships common in language data. Non-linear methods like t-SNE and UMAP address this issue. While t-SNE preserves local structure, UMAP excels at maintaining both local and global structures [39]. Since our goal was to visually confirm whether characters from the same phonological group would cluster together in the plot, we adopted UMAP for its flexibility and excellent performance in capturing and visualizing both local and global structures of high-dimensional data.

To ensure that our data met the conditions for using UMAP, we conducted a series of analyses based on the three primary assumptions outlined by Allaoui et al. [39]. Specifically, we applied PCA for a preliminary check on the data to ensure their uniformity. We then calculated the coefficient of variation based on the mean and standard deviation of the k-NN (k-nearest neighbors) distances, obtaining a low value of approximately 0.296. Finally, we constructed a k-NN graph and found out that the data points were locally connected. The above procedures ensured the validity of our dimensionality reduction results with UMAP.

We employed the UMAP algorithm from the “umap-learn” library in Python to reduce the dimensionality of our data and used matplotlib to visualize the results, enhancing the plot with color-coded groups and annotated centroids for clarity.

Sound symbolism across diachronic rhyme books

Different rhyme books exhibit varying levels of granularity in how characters are grouped. For example, in GY, characters within the same small rhyme group are listed together; several of these small rhymes then collectively form a rhyme heading group, which in turn is part of an even broader inclusive rhyme group. In contrast, PSY is only roughly divided into 106 rhyme categories based on the final and tone. When comparing the four rhyme books GY, PSY, ZYYY, and ZHTY, to ensure comparability, we selected the phonological unit generally referred to as yunbu 韻部 (rhyme category), which is primarily determined by the final and tone.

We created comparison groups each containing the same number of characters as the respective rhyme categories. To assess the semantic similarities of the rhyme categories and the comparison groups, we constructed the violin plots for them in Fig 2. As can be seen, in all four subplots for different rhyme books, the semantic similarities of the rhyme categories (left violins) are more vertically extended above the dashed reference line that represents the average semantic similarity of the rhyme book, resulting in taller, more peaked profiles compared to the denser and shorter distributions of comparison groups (right violins) around the reference line. This indicates generally higher semantic similarities of the rhyme categories across all four rhyme books. In the subplots, the medians of the left violins are apparently and consistently above the reference lines, while those of the right violins are very close to them, further indicating the semantic congruence of characters within the rhyme categories. This visual evidence confirms that the structured phonological groupings in these rhyme books do exhibit stronger semantic coherence.

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Fig 2. Violin plots showing the semantic similarities of rhyme categories and comparison groups across four rhyme books.

Each subplot contains a left and a right violin, representing the distribution of semantic similarities of the rhyme categories and their respective comparison groups. The sample size (“n=”) indicates the number of rhyme categories in a rhyme book. The dashed line shows the average semantic similarity of the book, while the purple line within a violin marks the median of the group semantic similarities.

https://doi.org/10.1371/journal.pone.0322044.g002

We employed a one-sample Wilcoxon signed-rank test to examine the rhyme categories within a rhyme book. Specifically, the group-level semantic similarities, calculated as the mean of pairwise cosine similarities of characters in each rhyme category, served as the data points for the test. The book-level semantic similarity, calculated as the mean of pairwise cosine similarity across all characters covered by the book, was used as the reference value. This test assessed whether the median of the group-level semantic similarities was significantly higher than the book-level semantic similarity. We applied this test to the rhyme categories (Observed) and their respective comparison groups (Random) in all four rhyme books. We adopted a nominal significance level set at p = 0.05. However, to account for the eight comparisons in this study, we applied a Bonferroni correction, adjusting the significance threshold to 0.05/8 ≈ 0.0063. The statistics of these tests are presented in Table 1.

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Table 1. Wilcoxon test statistics for the four rhyme books.

https://doi.org/10.1371/journal.pone.0322044.t001

The results indicate that for all four rhyme books, the rhyme categories exhibit significantly higher semantic similarity than the book-level semantic similarity, suggesting a strong phonosemantic structure encoded in the historical classification of Chinese characters in the rhyme books. In contrast, the comparison groups fail to show any significant difference from the reference values, confirming that the observed coherence in the historical categories is not an artefact of random grouping. In all cases, the W statistic for rhyme categories is notably larger than that for comparison groups, indicating greater internal semantic similarity within the rhyme categories. These statistical results reinforce the patterns observed in the violin plots, where the medians of the rhyme categories are visibly above the dotted reference lines, indicating stronger semantic coherence of these categories. The combined evidence provides compelling support for a profound correlation between sound and meaning, which is central to sound symbolism. In contrast, the comparison groups, with higher p-values, exhibit the expected randomness and lack of semantic coherence. This distinction proves that the sound-meaning connections are prominent only in the genuine rhyme categories, not in any randomly assembled comparison group.

As mentioned above, to overcome the limitations of solely using Siku embeddings for the pre-modern rhyme books, we further trained QTS, QTW, and QTS + QTW embeddings for supplementary tests on GY as a robustness check. To account for the eight comparisons using these four sets of embeddings, we applied a Bonferroni correction, adjusting the significance threshold to 0.05/8 ≈ 0.0063. The earlier Wilcoxon tests on the four rhyme books addressed a separate hypothesis—validating baseline semantic coherence within phonological groups—and were treated as an independent analytical stream with its own error control. This separation is to ensure that corrections for exploratory supplementary analyses do not conflate with confirmatory tests of core hypotheses, which is assumed to be the best practice for our partitioned statistical workflow. The corresponding statistics are presented in Table 2.

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Table 2. Wilcoxon test statistics for the four embeddings on GY.

https://doi.org/10.1371/journal.pone.0322044.t002

For all four embedding sets, the rhyme categories show very low p-values (far below 0.0063), consistently indicating their significant semantic coherence. In contrast, the comparison groups, given their high p-values, show no significant semantic congruence, which aligns with the randomness in their composition. This finding reaffirms the sound-meaning connections observed in Table 1, despite the possible limitation of the character embeddings in use.

Sound symbolism across phonological features in GY

A growing body of evidence indicates that phonological elements, including vowel sounds, consonant clusters, and tones, possess inherent semantic properties that influence language perception and usage [40]. Considering this, we seek to systematically explore the symbolic capacity of various phonological units, including initials, finals, small rhymes, etc. within GY. For each of these phonological units, we calculated the semantic similarities of both the original phonological groups and corresponding comparison groups using the Siku embeddings and plotted the results in Fig 3. The number of observations incorporated in each violin may be smaller than the original count due to exclusions during the calculation process.

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Fig 3. Violin plots showing the semantic similarities of phonological groups and comparison groups for GY.

Each pair of violins represents the distribution of semantic similarities of the phonological groups and respective comparison groups, with the latter labeled with the suffix “_c” (for comparison) and displayed in a more transparent shade of the same color. The sample size (“n=”) indicates the number of phonological groups or comparison groups in a violin, where a solid purple line shows the median of the group semantic similarities. The horizontal dashed line across the whole plot marks the average semantic similarity of GY.

https://doi.org/10.1371/journal.pone.0322044.g003

For the first five phonological units under study, the left violin of each pair, which represents the original phonological groups, consistently shows a median line that is distinctly higher than the dotted reference line, indicating that these groups exhibit greater semantic similarity than the whole GY. Meanwhile, these violin shapes are primarily skewed above the reference line, suggesting that a majority of the phonological groups have semantic similarities above the GY average, reinforcing the notion of sound-driven semantic coherence. In contrast, the median lines of the right violins for the comparison groups align closely with or just slightly deviate from the dotted reference line, further confirming that the observed deviation in the left violins is not an artifact of the data but a true reflection of sound-meaning associations. The distribution of the randomized comparison groups serves as a control, illustrating the random variability of group semantic similarities when a phonological relationship is absent. The stark contrast between the distributions of the original and the comparison groups substantiates the hypothesis that phonological structures in GY contribute substantially to semantic meanings.

For each of these five phonological units, Wilcoxon tests were conducted on the semantic similarities of the phonological groups (Observed) and those of the comparison groups (Random) against the overall average cosine similarity of GY, and the results are presented in Table 3. A Bonferroni correction (α = 0.05/10) was applied to account for the 10 comparisons (5 phonological units × 2 test groups: Observed and Random), ensuring strict control of the family-wise error rate.

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Table 3. Wilcoxon test statistics for different phonological units in GY.

https://doi.org/10.1371/journal.pone.0322044.t003

The tests reveal statistically significant results for all five phonological units under study. In contrast, the comparison groups show no significant results. All these align with the visualization in Fig 3, confirming that sound-meaning association is evident across various phonological units. Notably, sound symbolism is significant not only in smaller phonological units such as initials and finals but also in broader ones like inclusive rhymes, each of which covers a wide range of characters. Its consistent presence at different phonological levels demonstrates that sound symbolism is a pervasive and integral aspect of the linguistic system.

For the tones, the Wilcoxon signed-rank test used for other phonological units is not applicable due to the limited number of groups (4 tones). Instead, we followed Otis and Sagi [19] to conduct 100 independent two-sample Welch’s t-tests for each tonal group. Each t-test compared the pairwise cosine similarities of 50 randomly sampled character pairs within a tonal group to those of 50 randomly sampled pairs from the overall population of valid characters. To ensure robustness, this process was repeated three times, and the median number of significant t-tests (uncorrected per-test α = 0.05) across runs was retained. To evaluate whether the observed number of significant t-tests exceeded what would be expected for random chance, we applied a binomial test. Under the null hypothesis (no systematic clustering), the number of significant t-tests should follow a binomial distribution with parameters n = 100 (number of t-tests) and p = 0.05 (baseline chance of a false positive per t-test). In order to test four tones, we applied a Bonferroni correction to account for multiple comparisons, adjusting the family-wise significance threshold to α = 0.0125 (0.05/4). Using exact binomial calculations based on the corrected significance level, we established the following thresholds for interpreting the results: ≥ 11 significant tests for strong evidence of clustering, 10 for marginal evidence, and ≤ 9 for no evidence. This approach balances sensitivity to tonal semantic clustering with rigorous control over family-wise error rates across all four comparisons, ensuring that the results reflect systematic patterns rather than chance fluctuations.

The statistical evaluation of the four tones revealed marked differences in their semantic coherence. We found that only the entering tone demonstrates strong evidence of systematic semantic clustering. Across three independent runs, this tone exhibited a median of 20 significant t-tests, far exceeding the precomputed threshold of 11 significant tests, suggesting that its characters share non-random semantic relationships. In contrast, the level, rising, and departing tones show no statistical support for semantic clustering, with median significant test counts of 6, 7, and 8, respectively, falling below the marginal evidence threshold of 10 significant tests. The distinctiveness of the entering tone highlights its unique role in organizing semantic information, a sound-symbolic capacity that can well account for its prominence in classical Chinese poetry. Both its distinctive phonetic profile (e.g., abrupt stops) and its semantic consistency enhance its effectiveness in the tonal patterning of pingze 平仄 (level and oblique tones) verse structures.

Exemplary illustration

To achieve an intuitive demonstration of the relationship between sound and meaning, we examined homophonic characters within the same small rhyme groups in GY. We selected those groups containing at least 10 characters, ranked them by group semantic similarity, and chose the top 10 groups for demonstration. The character vectors then underwent dimensionality reduction with UMAP for visualization on a scatterplot as shown in Fig 4, wherein characters from the same group were color-coded identically to highlight group affiliations.

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Fig 4. Visualization of ten top-ranked small rhyme (homophone) groups in a dimension-reduced semantic vector space.

Characters from the same small rhyme group are shown in the same color. Each character is represented by a dot, and each group’s centroid by a cross, annotated with its representing character.

https://doi.org/10.1371/journal.pone.0322044.g004

In Fig 4, homophonic characters in the same color appear close to each other and tend to form a cluster. For instance, characters in the ɣwœŋ 宏 group, colored in light blue, form a dense cluster near the upper right corner of the plot. This clustering phenomenon indicates that homophones are semantically close to each other.

Taking a closer look at the characters of the ɣwœŋ 宏 group, namely 宏, 紭, 嵤, 耾, 翃, 浤, 竑, 宖, 鈜, 吰, and 彋, we learned that they generally convey the meaning of “large” or “expansive”, often connected with the size of physical objects or the intensity of sounds, according to their descriptions in GY. For instance, 宏 literally means “large”. 紭 refers to a type of net, implying expansiveness and inclusiveness. 嵤 describes high and steep mountains, and 浤 refers to the surging and powerful movement of water. 彋 means opening and spreading out. 竑 means “measurement”, which is also size-related. 翃 refers to the flight of insects, suggesting the opening of their wings. Meanwhile, the rest characters of the group are directly related to sounds, especially loud or reverberating ones: 耾 means “whispering” according to GY but also often refers to thunderous sounds, 宖 refers to an echoing sound within a room, 鈜 denotes a metallic sound, and 吰 represents the sound of a bell. These characters all connect to the core theme of largeness and expansiveness, either through their literal meanings or through their associations with size and volume.

In terms of the phonetic features of the ɣwœŋ 宏 group, the initial ɣ is a hou yin (喉音 throat sound) produced with a strong airflow, conveying a sense of depth, power, fullness, and/or vastness. The medial w results in a hekou hu 闔口呼 (rounded articulation), where the lips are rounded during pronunciation, creating a strong resonance. This resonance complements concepts like “broad” and “full”. The open front vowel œ is articulated with the mouth open, and when combined with the medial w, it enhances the rounded quality, evoking a sense of openness and expansiveness. The nasal coda ŋ produces an echo effect, extending and expanding the sound. Additionally, the level tone of this group is characterized by a longer duration and extended sound [41], which further enhances the effect of opening, expansion, and force. Together, these phonetic features create a sense of grandeur and openness, directly connecting to the meanings of the characters as recorded in GY.

The above connection between sound features and meanings of characters in the ɣwœŋ 宏 group involves both corporeal and imitative symbolism [42]. The former is reflected in 宏, 紭, 嵤, 浤, and 彋, as their pronunciations resemble physical expansiveness, evident in the rounded w and the mouth opening œ. Concurrently, the characters 耾, 宖, 鈜, and 吰 exemplify onomatopoeia, as their pronunciations naturally mimic the loud or reverberating sounds, directly linking sound to meaning. This dual symbolism extends into more abstract terms such as 竑 (“measurement”) and 翃 (“insect flying”), illustrating how phonetic properties evolve from concrete sensory experiences to broader, more abstract concepts, effectively using physical and auditory mimicry to enrich linguistic expression and semantic depth. This shift from immediate to mediated symbolic relationships reflects the theoretical framework of mediacy versus immediacy as discussed by Jakobson and Waugh [43].

Through this exemplary analysis, we can see how the sound properties of characters in a phonological group connect to meanings, further illustrating and affirming the presence of sound symbolism. It also provides a glimpse into the underlying cognitive mechanisms driving the sound-meaning relationship of this kind, including corporeal and imitative symbolism, and their extension into more abstract concepts.