Participants

Participants (n = 47; 29 F, 18 M) were music majors recruited from the Ohio State University School of Music participant pool. The average age was 19.6 years (range 18–21, SD = 1.6). Participants reported an average of 11.3 years of regular musical practice (range 3–19, SD = 3.6).

Design

Participants listened to two-second recordings of instruments playing sustained notes and were randomly assigned to rate either notes played on the oboe or notes played on the horn. Manipulated variables included pitch, register, and dynamic level; specifically, the stimuli for each instrument included four registers (Low, Middle 1, Middle 2, and High) represented by three chromatically neighboring pitches, and each of these 12 pitches were presented at three different dynamic levels (pianissimo, mezzo mezzo, and fortissimo), for a total of 36 stimuli per instrument. Participants listen to 18 of the 36 recorded notes in a random order and made ratings of the stimuli on 20 semantic scales from Reymore & Huron (2020; see Table 1). A priori, it was decided that for the purposes of analysis, values for each register would be represented by the mean ratings of the three pitches chosen to represent that register.

Materials

Stimuli were recorded by professional musicians for the purpose of the experiment. To address the issue of the tractability of the study, stimuli were limited to a representative sample of pitches and dynamics. One approach would be to sample single pitches from different registers at varying dynamics. However, using a single pitch risks interference due to idiosyncratic timbral variations among pitches. For example, C5 on the oboe is a notoriously difficult-to-control note because it exhibits a timbre that is relatively more unfocused and nasal than any of the other instrument's pitches, a result of the physics of the instrument. While well-designed instruments minimize this timbral difference and professionals can further temper the difference, anecdotally, a timbral uniqueness to C5 is still almost always perceptible to the trained ear and may even be able to aid in absolute pitch identification (Reymore & Hansen, 2020). Were C5 to be chosen as the single pitch representing the middle range of the oboe, it is likely that ratings of dimensions such as focused/compact and nasal/reedy would better characterize this single pitch than the middle range of the register, which is in general much more focused and less nasal than C5. While such note-to-note idiosyncrasies are quite familiar to the players of a given instrument, there is little empirical information about this source of variability, though a systematic report of idiosyncratic intonation tendencies can be found in Snow (2006). Likely, intonation and timbral idiosyncrasies are in many cases related—plausibly, pitches that tend to be sharp are also brighter and/or more nasal. It is probable that timbral idiosyncrasies, like intonational idiosyncrasies, are more prominent in certain instruments than others, most likely as a function of various aspects of the physics and acoustical properties of each instrument.

To mitigate the potential idiosyncratic effects of individual notes, three neighboring chromatic pitches were used to represent each register. The selection of neighboring pitches minimizes the potentially confounding effect of pitch height on timbre but provides a method in which each register is represented by multiple pitches. Pitches were selected through consultation with the professional players who recorded the stimuli. First, we determined the lowest and highest sets of three pitches that are both comfortable to play and are reasonably common in the repertoire. The other two pitch sets for both instruments were derived by dividing up the space between the high and low sets equally. A priori it was determined that these sets could be shifted up or down by half or whole step in order to avoid particularly idiosyncratic notes (like C5 on the oboe); decisions about shifting were made in consultation with the professional musicians. As a result, four sets of three pitches were recorded to represent the high, low, and middle registers of the instruments. See Appendix A for more detail on stimuli selection. Table 2 lists the pitches recorded for the oboe and the horn; these pitch samples are visualized in Figure 1.

Figure 1. Piano keyboards illustrating pitch stimuli for the oboe (purple, top) and French horn (orange, bottom).

The professional musicians recording the stimuli were instructed to play each of the pitches at three different dynamic levels:

1. Pianissimo. Play as piano as possible without sacrificing tone quality or intonation.
2. "Mezzo mezzo." Play at a comfortable middle dynamic level for your instrument, between mezzo piano and mezzo forte. 2
3. Fortissimo. Play as forte as possible without sacrificing tone quality or intonation.

The musicians recorded 36 notes for each instrument (4 registers * 3 pitches * 3 dynamics). While neither the oboe nor the horn has specifically defined registers in the way that the clarinet does, general descriptions of high, middle, and low registers are applicable; we can consider the lowest set of pitches to represent the instruments' low registers and the highest to represent their highest register. For the purposes of discussion, I refer to the four registers with relative names: Low, Middle 1, Middle 2, and High.

Procedure

The study was implemented as an Internet survey using the Qualtrics platform; participants were tested individually in an Industrial Acoustic Corporation sound attenuation room. Instructions are included in Appendix B. Participants listened to 36 two-second recordings of either the horn or the oboe playing sustained notes. After listening to each stimulus, for each of 20 timbre qualia dimensions, they rated how well the dimension applied to each note on a scale from 1 to 7 where 1 was labeled as "does not describe at all" and 7 was labeled as "describes extremely well." Note that while shorthand terms (Table 1, column 2) are used throughout his paper for ease of discussion, participants were presented with the full semantic descriptions during the experiments (Table 1, column 1). Participants were able to listen to each sound as many times as they felt was necessary. In piloting the experiment, it was determined that rating all 36 pitches for a single instrument took about an hour. As the task is a particularly repetitive one and attention was a concern, the experiment length was reduced so that each participant would rate a subset of 18 pitches for one of the two instruments, which took about a half hour.

Oboe

The top-rated dimensions for all pitches at all dynamics on the oboe—comprising its aggregate average profile—are nasal/reedy (4.57), sustained/even (4.42), resonant/vibrant (4.22), focused/compact (4.11), pure/clear (4.07), and open (3.95). Tables 3 summarizes the top six descriptors for each pitch register combination. The dimensions that are not included in the top six descriptors in the instrument's aggregated average profile are bolded in order to highlight which features are relatively unique to certain registers, dynamics, or register-dynamic combinations. For example, oboe notes are perceived as relatively more strongly sparkling/brilliant in the Middle 2 and High registers, while woody only appears in Low and Middle 1 registers as a top descriptor. The soft/singing quale is associated relatively more with softer and middle dynamic notes in middle registers.

Complete visualizations of differences in qualia profile for each register-dynamic combination are visualized in Appendix E, using the radar plot Timbre Trait Profile format from Reymore (2021).

Means on each dimension as grouped by register and dynamics for the oboe are visualized in Figures 2 and 3. In these figures, the reported mean for each register is the average of the means of the three notes in each register set. Error bars illustrate the 95% confidence intervals. Figure 2 reports register on the x-axis, with shape/color of the points indicating dynamics. Figure 3 presents the same data, but with dynamics on the x-axis and register indicated by shape/color. Numerical data related to these figures can be found in Appendix D.

Figure 2. Qualia variation by register, oboe.

Figure 3. Qualia variation by dynamic, oboe.

Horn

The top-rated dimensions for all pitches at all dynamics on the horn (aggregate average profile) are brassy/metallic (5.21), direct/loud (3.95), rumbling/low (3.81), nasal/reedy (3.76), raspy/grainy (3.65), and sustained/even (3.60). Table 4 summarizes the top six descriptors for each register/dynamic combination. As before, dimensions that are not included in the top six descriptors in the instrument's aggregated average profile are bolded in order to highlight which features are relatively unique to certain registers, dynamics, or register/dynamic combinations. For example, horn notes were rated as relatively more strongly shrill/noisy at a forte dynamic across ranges; this descriptor does not appear in the top six for piano or mezzo dynamics. Pure/clear characterizes the Middle 2 and High registers at piano and mezzo dynamics.

Each register/dynamic combination is visualized via radar plot in Appendix E.

Figures 4 and 5 demonstrate the rating means on each dimension for the horn. As with the oboe data reported earlier, Figure 4 provides register on the x-axis, while Figure 5 presents the same data with dynamics on the x-axis. Numerical data can be found in Appendix D.

Figure 4. Qualia variation by register, French horn

Figure 5. Qualia variation by register, French horn.

Factor Analyses

Previous work engaging the 20-dimensional timbre qualia model has reported a number of analyses concerning the structure of rating data. Reymore and Huron (2020) originally derived the model using Principal Component Analysis (PCA) and other techniques from ratings on 77 categories. PCA explained 72% of the variance with 20 components, while smaller models with 3–5 components, comparable to the size of models proposed in previous literature, explained only 39–50% of the variance. The data in that study were thoroughly examined for optimal dimension reduction—details about the PCA and the rationale for choosing a 20-dimensional model are included in the paper and its Supplementary Materials. The dimensionality of the model was further assessed in Reymore (2021), using a different rating dataset, in three ways: with respect to the correlation matrix, the relative usefulness of descriptors, and Principal Component Analysis. No recommendations were made for dimension reduction on these bases. This paper also presented analyses suggesting the model to be reliable across studies for generating ratings of imagined musical instrument sounds.

Analyses reported in these papers, along with other unpublished analyses of additional datasets using the model, suggest that the underlying structure of rating data may vary with different sets of rated instruments. That is, while 20 dimensions are needed to capture reasonable variance for the entire set of Western orchestral instruments (as in Reymore, 2021), it may be the case that certain dimensions could be highly correlated among subsets of instruments. Were this the case, we might observe variation in latent structure among ratings for different instrument subsets. By extension, this may also be the case for within-instrument semantic variation, and techniques such as EFA thus may help us to better understand the semantic structure of individual instruments with respect, in this case, to register and dynamics. This possibility was addressed with the current dataset.

For both oboe and horn data, the Kaiser-Meyer-Olkin (KMO) statistic was > .75, and Bartlett's test of sphericity was significant, suggesting that EFA was appropriate. In choosing a number of factors, I considered various rules of thumb, including the eigenvalues, scree plot, and percent of variance explained (Jolliffe, 2002); as in Reymore and Huron (2020), I preferred to err on the side of "too many" rather than "too few" factors and considered the relative interpretability of the potential models. With both sets of data, while the eigenvalue > 1 guideline suggested a 4-factor model, the resulting scree plots did not demonstrate clear elbows, suggesting five, or possibly more, factors. In the case of the oboe ratings, four factors explained 69% of the variance, whereas five factors explained 76%. Within the horn ratings, four factors explained 75% of the variance, while five explained 81%. I determined from a comparative examination of 4- and 5-factor models for both instruments that 5-factor models were substantially more clearly interpretable. Taking into account both the interpretability and the 6–7% increase in variance explained with the addition of a fifth factor, I chose to report the 5-factor models here.

As summarized below in Table 5, factors in both models were named using up to three of the highest loading descriptors greater than .5; in cases where only two descriptors loaded greater than .5, only two descriptors were used to name the factor. The full models with complete loadings are reported in Appendix F.

Although the two 5-factor models demonstrate some close similarities, it is evident that the latent structure differs: that is, between the two instruments, relationships among some of the dimensions differ. Factor 1 is highly similar between the two instruments. Factor 4, for both, is primarily driven by rumbling/low, but for the oboe is also influenced by woody, while the horn sees a secondary influence of raspy/grainy. Factor 5 in both models seems motivated by material; however, as one instrument is a woodwind and the other a brass instrument, the dimensions that load onto this factor vary. Factors 2 and 3 also reveal how the structures of the ratings differ from oboe to horn; for example, direct/loud and nasal/reedy load together for the horn, but not for the oboe, and airy/breathy and nasal/reedy load together for the oboe, but not for the horn, suggesting different relationships between these dimensions for each instrument. These differences are further illustrated in the exploratory models reported in the next section.

Exploratory Modeling

In order to understand which descriptors may be significant and most relevant to changes in register and dynamics—and to lay the groundwork for hypothesis testing in future experiments—two approaches were taken toward post hoc exploratory modeling of the data. Partial proportional odds (ordinal) regression models were used to suggest which descriptors may have significant relationships with dynamics and register. Additionally, random forest classifiers were used to obtain a measure of relative variable importance for the descriptors that can be compared across instruments and parameters.

Random Forest Classification

The data were also modeled via random forest classifiers using the caret package (Kuhn, 2020). This modeling process produces a measure of relative variable importance that is helpful in assessing the findings. Performance was measured from 5-fold cross-validation, where the data were split into five folds and each fold served in turn as the testing set for the model trained on the other 80% of the data. Thus, accuracy and kappa values reported here are averaged across all five folds of the cross-validation for each of the four types of models. The models were trained using the train function with method set to "rf," where the control parameter included 5-fold cross-validation.

For the dynamics models, where chance classification is at 33.3%, the oboe model's accuracy was 52.8%, κ = .29, while the horn's accuracy was 62.3%, κ = .44. For the register models, where chance classification is at 25%, the oboe model's accuracy was 62.2%, κ = .50, while the horn model's accuracy was 58.3%, κ = .44. The confusion matrices suggest that the middle registers of both instruments were most problematic to identify and were often confused; similarly, the mezzo mezzo dynamic was consistently misclassified more often than the fortissimo or pianissimo dynamics. Relative variable importance is illustrated in Figure 6 and reported quantitatively in Tables 6–9; relative variable importance measures are taken from each model trained on the entire data set using 5-fold cross-validation.

Figure 6. Relative variable importance from random forest classifiers predicting register and dynamics for oboe and horn from semantic rating data.

Tables 6–9. Relative variable importances from the random forest classifiers and significant (p < .05) descriptors in predicting register and dynamics for oboe and for horn from partial proportional odds regressions.

Table 6. Dynamics, Oboe

	Random Forest	Partial Proportional Odds Regression
Semantic Descriptor	Variable Importance	Significance	Effect Type
direct/loud	100.0	✓	nominal: p|m, m|f
airy/breathy	75.1	✓	nominal: p|m, m|f
soft/singing	67.0	✓	ordinal
resonant	58.7	✓	ordinal
ringing/long	51.4
open	51.2
focused/compact	50.9
pure/clear	50.6
hollow	50.5	✓	ordinal
nasal/reedy	50.4
shrill/noisy	50.4
sparkling/brilliant	50.0
watery/fluid	48.5
sustained/even	47.0	✓	ordinal
woody	43.7	✓	ordinal
raspy/grainy	38.0
muted/veiled	32.7
rumbling/low	22.2
brassy/metallic	21.7
percussive	0.0

Note. Significance levels for the proportional odds regressions can be found in Appendix G along with the full models.

Table 7. Dynamics, Horn

	Random Forest	Partial Proportional Odds Regression
Semantic Descriptor	Variable Importance	Significance	Effect Type
direct/loud	100.0	✓	nominal: p|m, m|f
shrill/noisy	73.5	✓	ordinal
soft/singing	51.6	✓	ordinal
muted/veiled	30.2	✓	ordinal
raspy/grainy	28.8
brassy/metallic	27.6
open	22.6
hollow	22.4
focused/compact	22.2
pure/clear	21.4
airy/breathy	21.3
sustained/even	21.2
watery/fluid	20.1	✓	ordinal
nasal/reedy	19.6
rumbling/low	19.5
sparkling/brilliant	19.3
ringing/long	18.1
resonant	17.6
woody	10.4
percussive	0.0

Table 8. Register, Oboe

	Random Forest	Partial Proportional Odds Regression
Semantic Descriptor	Variable Importance	Significance	Effect Type
shrill/noisy	100.0	✓	ordinal
rumbling/low	95.5	✓	ordinal
sparkling/brilliant	52.9	✓	ordinal
soft/singing	49.8	✓	nominal: M2|H
woody	35.9	✓	nominal: M1|M2, M2|H
open	31.8	✓	nominal: M2|H
focused/compact	28.7
watery/fluid	28.5
airy/breathy	28.2
direct/loud	27.2
resonant/vibrant	24.6	✓	nominal: M1|M2
nasal/reedy	24.4	✓	ordinal
ringing/long	24.1
sustained/even	23.8
pure/clear	21.7
hollow	21.7
raspy/grainy	16.7	✓	ordinal
muted/veiled	16.2	✓	ordinal
brassy/metallic	8.5
percussive	0.0

Table 9. Register, Horn

	Random Forest	Partial Proportional Odds Regression
Semantic Descriptor	Variable Importance	Significance	Effect Type
rumbling/low	100.0	✓	ordinal
sparkling/brilliant	27.7	✓	ordinal
direct/loud	23.6	✓	ordinal
nasal/reedy	21.0	✓	ordinal
shrill/noisy	19.9	✓	ordinal
raspy/grainy	15.3	✓	ordinal
focused/compact	15.0
brassy/metallic	14.2
sustained/even	13.0
ringing/long	12.2
muted/veiled	7.2
open	6.9	✓	ordinal
watery/fluid	6.5	✓	ordinal
pure/clear	6.2
soft/singing	6.0	✓	ordinal
hollow	6.0
resonant	5.0	✓	ordinal
airy/breathy	4.7
woody	2.7
percussive	0.0

Comparing ratings of recorded stimuli and auditory imagery

Results of the current study can be compared to results from Reymore (2021) in order to explore how semantic characterizations of imagined "typical" instrument sounds compare to characterizations of recorded instrument sounds. To examine this relationship, I compared the aggregate average ratings in the current study (mean of all 36 pitches for a given instrument on each dimension) to values reported in Reymore (2021) for the oboe and horn.

For the majority of the dimensions, the means for the imagined stimuli tend to be slightly higher than those of the recorded stimuli. For the oboe, the average of the absolute values of the differences in mean ratings between the auditory imagery task and recorded stimuli task was 0.69. That is, on average, mean ratings for each of the dimensions using imagined stimuli and using recorded stimuli were less than one point apart relative to a seven-point scale. The maximum absolute difference (i.e., absolute value of the difference) between ratings of auditory imagery and recorded stimuli was 1.52 points and the minimum absolute difference was 0.06 points.

For the horn, the average absolute difference in mean ratings between the auditory imagery task and recorded stimuli task was 1.10, higher than the comparable value for the oboe. The maximum absolute difference was 2.47 points and the minimum was 0.02 points. Dimensions with the highest absolute differences between imagined and recorded stimuli means include soft/singing (2.47), resonant/vibrant (2.28), and sustained/even (1.97).

Notably, the differences between imagined and recorded means for the French horn are on average greater than for the oboe. One factor that might be related to this difference is the variance in timbre-implicated parameters afforded by each instrument. The oboe has a small pitch range in comparison to most orchestral instruments, spanning only about two and a half octaves. The French horn has a relatively large pitch range, spanning more than four octaves. Accordingly, although stimuli were sampled from four nearly equally spaced locations in each instrument's range, the range of pitches sampled for the oboe was two octaves plus three semitones while the range of pitches sampled for the French horn was three octaves plus four semitones. Similarly, the dynamic range of the oboe is very small and is limited by the physics of the instrument and reed, with its incredibly narrow opening, while the dynamic range of the French horn is especially impressive—a horn may play a quiet, pure, golden note or an ear-shattering roar. In Reymore and Huron (2020), participants were asked to imagine a typical sound that an instrument would make rather than an unusual one. Values from the current study represent an average over 12 register/dynamic combinations, and some of the sounds presented to the participants in the current study likely were far from what participants in previous studies deemed to be a typical sound (for example, the lowest ff notes in the horn).

In general, rating differences between imagined and recorded stimuli for both instruments are likely also related to the differences between imagined typical sounds and real instantiations of sounds that come from the recording equipment, recording space, other factors including distance from the mic and the individual tone quality of the musician making the recordings. In particular, while both instruments were recorded with high-quality equipment, the recordings took place in a small room with little resonance, and the musicians were necessarily somewhat close to the mic, given the dimensions of the room. In considering the observed differences in means in light of the recording circumstances, it seems likely that most participants in the initial study imagining the sound of each instrument as they might have heard it live or recorded in a concert hall or other resonant space. Especially if the instrument was not their native instrument, they likely imagined the sound from a distance rather than in close proximity. The close mic in the recordings from this study picked up on slight imprecisions in the sounds that would be otherwise masked in a resonant space; this may have contributed to the lower ratings of pure/clear in the current study on both instruments: the differences in pure/clear between ratings from auditory imagery and recordings were among the highest for both instruments. For the horn, resonant/vibrant and ringing/long decay were both rated particularly low from the recordings as compared to the imagined tones of the previous study, both dimensions that ostensibly are related to the acoustics of the recording space, particularly in conjunction with the big sound of the horn.

Interestingly, the data from imagined stimuli predicted much higher ratings on soft/singing for both instruments than were collected in the current study. Although participants in the initial experiment were asked to imagine a sustained single tone, the qualities included in the soft/singing dimension (soft, smooth, singing, voice-like, sweet, gentle, calm) may have been associated with the instrument not only by virtue of a particular tone that was imagined, but also with their melodic characters and with the types of sweet (oboe) or soaring (horn) melodies that are characteristic of their orchestral personalities. Some dimensions may be a part of an instrument's characteristic or stereotypical timbral qualia but may not manifest in two-second, single note clips. If this is the case, some dimensions (such as soft/singing) may have been apparent with the use of imagined prototype stimuli but not experienced as strongly by participants in the brief recordings. However, despite some of the differences in means between the two studies (the largest was 2.47 points), the overall agreement in the ratings between the imagined and recorded instruments is quite strong, especially for the oboe.

Comparative Observations

For the oboe, register appeared to consistently provide the most variance along the timbre qualia dimensions; relatively less variance occurred with dynamic level change on most dimensions. Relative to chance performance, the random forest classifiers were much more successful in predicting register than predicting dynamics, even more so for the oboe than for the horn. In general, dynamic level seems to play a more important role in timbre qualia for the French horn than for the oboe. The differences in average ratings as effects of dynamics are both more consistent and more pronounced with the French horn—that is, there are wider ranges of qualia ratings as products of dynamic change, and several clear trends are apparent across dynamics that are mostly consistent among registers.

Tables 10–11 summarize the results of the partial proportional odds regressions and random forest classifiers. Although the nuances of these results may be very important in some contexts, considering overall trends can help guide future predictions.

Tables 10–11.Overlapping and unique significant predictors for register and dynamics in the oboe and horn; results from exploratory modeling. The third and fourth columns indicate whether or not each significant descriptor from the partial proportional odds regression was among the top six most important variables in the corresponding classifier.

Regarding register (Table 7), the two instruments share eight of the same significant predictors while retaining two unique predictors each. However, which descriptors are significant in the dynamics models (Table 8) varies much more in comparison to the register models: the two instruments share only two significant predictors while the horn is associated with an additional three unique predictors and the oboe with an additional five. It is notable that despite the relatively large number of predictors and small sample size, each model still contained 5–11 significant predictors, suggesting that changes in timbre qualia in response to both register and dynamic are somewhat complex: these parameters appear to motivate multidimensional semantic change in a variety of directions and strengths. Furthermore, because the models for register contained ratings of pitches at various dynamic levels, and vice versa, they provide an overall picture of each parameter individually and do not describe potential significant interactions (for example, the mean ratings for shrill/noisy in the horn as function of register behave differently at each of the three dynamic levels).

While there are some differences in the results of the two modeling approaches, there is a significant amount of overlap in that the top 4–6 descriptors in relative variable importance for the random forest classifiers are also significant in the corresponding partial proportional odds regression (see Tables 6–9). These shared descriptors can guide future experiments; the predictive descriptors that are unique to each instrument suggest that it may be the most obvious candidates (e.g., direct/loud and soft/singing for dynamics; rumbling/low, shrill/noisy, and sparkling/brilliant for register) that have similar effects across instruments. However, the unique descriptors are arguably the most interesting from acoustical, compositional, and music analytical perspectives.

Future experiments can use these findings as the basis for hypotheses related to semantics and register and/or dynamics, suggesting which semantic dimensions to focus predictions on. Examining a reduced set of descriptors based on these results increases the tractability of rating tasks through reduced experiment length and/or rating additional stimuli. When testing hypotheses about individual descriptors, reducing the number of descriptors also reduces the necessary number of multiple tests on the same dataset.

Another consideration in future experimental design relates to the inclusion of words in the descriptors which are clearly semantically related to pitch height and loudness, including "shrill" in shrill, harsh, noisy; "low" in rumbling, booming, low, deep, thick, fat, heavy; "loud" in direct, projecting, loud, aggressive, commanding, assertive, powerful; and "soft" in soft, smooth, singing, voice-like, sweet, gentle, calm. One option would be to remove these four words in order to determine the extent to which they are explicitly driving associations.

Note-to-note Idiosyncrasies

Average ratings on individual notes from within the same register sometimes varied significantly (see Appendix C). This is likely due in part to timbral idiosyncrasies that are inherent to the instruments. It is possible that some variability could be attributed to the particular instantiation of the note that was played during the recording. The musicians were permitted to re-record each note as many times as they wanted and were encouraged to do so if they were not happy with the quality of a note. Even so, one particular recording of a note might be slightly louder than the other notes in its register set or vary on another factor, such as articulation or vibrato, which could affect timbre qualia judgments. In future studies, providing several versions of each stimulus note, with one version presented at random to each participant, may help reduce the variability introduced by using a single, instantiation of a note; however, note-to-note variations will likely still be present. Given the idiosyncrasies observed in these results, the procedure of averaging three notes to represent a register, rather than one, was a productive one, illuminating several trends among the interactions of timbre qualia dimensions with register and dynamics, and is recommended in future research.

Within-instrument timbral variability

The level of detail to which the timbre qualia of an instrument might be mapped out is potentially enormous when considering all the parameters that can affect timbre. At some point, the resources and time invested in further refinement may yield diminishing returns, depending on the purpose of the research. Even at the level of detail under consideration here, we can see that while some dimensions can vary somewhat widely within a single instrument, other dimensions remain fairly consistent. For example, in the French horn, the largest range of mean ratings for each register-dynamic combination is 5.24, on the rumbling/low dimension. Specifically, of the 12 conditions (4 registers * 3 dynamics), ff in the low register was rated the highest on rumbling/low at 6.50 and pp in the high range was rated the lowest at 1.25. With this wide range of levels for rumbling/low, the nuanced representation of this dimension resulting from this study could add important information to musical analysis, both orchestrally and in solo or chamber settings. At the other extreme, the smallest range of mean ratings observed here is in the oboe on the dimension percussive, with a difference between the maximum rating (1.52 for mm in the low range) and the minimum rating (1.08 for pp in the low range) of only 0.44. Such a difference is unlikely to be especially useful or relevant to analysis involving the oboe. Further support for this interpretation comes from the observation that percussive was not significant in any of the regression models and was consistently ranked lowest in all random forest models in terms of relative variable importance. While the dimension of percussive might prove crucial in later assessments of timbral differences resulting from variation in articulation styles, it would not be germane to an analysis accounting for timbral interactions with register and/or dynamics.

These considerations lead to the question of what constitutes a meaningful difference in variability on a given dimension for a given instrument. Thus, it is informative to look at which dimensions exhibit the highest within-instrument variability for both instruments. The five dimensions for each instrument with the highest differences between maximum and minimum means are listed below in Table 8a–b. However, while the table below and results from the exploratory modeling can provide some kind of objective criteria for answering the question of meaningful variability in general, for music analysis, meaningful variability can only be assessed in the context of a particular piece of music. Consider a piece or orchestral solo for French horn that took place entirely in the middle register of the instrument; variation on rumbling/low would not prove as relevant here as it would for a piece that made use of all registers of the instrument.

Table 12–13. Highest within-instrument variabilities for the oboe and horn.

Based on the ratings results reported here, we might frame the dimensions in Tables 12 and 13 as those for which each instrument has the most timbral flexibility, at least in relation to pitch and dynamics with stimuli played in a traditional manner (that is, excluding extended techniques). Both oboe and French horn shared three out of their five highest within-instrument variabilities: direct/loud, shrill/noisy, and rumbling/low. As these dimensions are semantically intertwined with dynamics and pitch, it would be reasonable to extrapolate these trends and predict that all instruments that can vary in intensity would show at least some variance on direct/loud while all instruments that vary in pitch would show at least some variance on shrill/noisy and/or rumbling/low. In general, the results suggest that the French horn has a higher capacity for timbral flexibility as generated through pitch and dynamics than does the oboe, a conclusion that accords with casual observation. The main source of timbral flexibility for the oboe may be generated through the manipulation of other variables not assessed here and their interactions. For example, a primary source of timbral flexibility for the oboe may involve vibrato, which is typically not a source of timbral variation for traditional horn sounds and was not manipulated for either instrument in this experiment.

Summary, Register

Based on exploratory modeling, the most clearly relevant dimensions for register in both instruments include rumbling/low, shrill/noisy, and sparkling/brilliant, though several other descriptors are implicated through either the regressions, random forest classifiers, or both (see Tables 6–9). Uniquely for the oboe (that is, not for the horn), significant relationships between register and woody and muted/veiled were demonstrated. In the horn, the nominal effect for muted/veiled between the Middle 2 and High registers was close to significance (p = .054), suggesting that this possibly may be a subtle effect that could be detected in a larger sample. Uniquely for the horn, direct/loud and watery/fluid were related to register.

Summary, Dynamics

The most clearly relevant dimensions for dynamics include direct/loud and soft/singing; intriguingly, the differences between effects of dynamics on semantic dimensions appear to be greater than for the effects of register. That is, more dimensions were related uniquely to either the oboe or horn and were not shared results. In the oboe, airy/breathy and resonant/vibrant were both significant and ranked highly in relative importance, while for the horn, this was true of muted/veiled and shrill/noisy. While watery/fluid was significant for the horn, it did not rank highly in variable importance. For the oboe, watery/fluid neither was significant nor ranked highly, though it did near significance (p = .08), suggesting again that a general relationship may hold in a larger sample, albeit a weak one.

Recommendations for Future Research

The results recommend several suggestions for consideration in future timbre semantics research, particularly in regard to research which aims to understand timbre semantic variability in response to changing musical parameters. In sum:

• In relation to timbre semantics, dynamics may interact with register. For example, for the oboe, airy/breathy increases from the Middle 2 to the High registers at a piano dynamic but decreases at a forte dynamic. Brant tests during exploratory analysis confirmed that while some descriptors can be treated as ordinal, others should be considered nominal.
• Trends between musical parameters and semantic ratings may be non-linear. Future studies will need to account for this in relation to hypothesis testing and model building.
• The range of semantic affordances may vary from instrument to instrument in relation to a given parameter—here, the horn demonstrated greater semantic flexibility for both register and dynamic as compared to the oboe. The oboe demonstrated relatively limited flexibility in response to dynamics.
• Note-to-note idiosyncrasies in timbre may significantly impact semantic judgements. This should be considered when selecting stimuli, particularly when seeking to represent register.
• The type of relationship between a given semantic descriptor and either register or dynamics may vary from instrument to instrument.
• Similarly, the latent structure of rating data may vary from instrument to instrument.

These exploratory results mark an initial step forward in understanding within-instrument timbral flexibility, an issue that has not been previously addressed in a systematic way. This question is relevant to understanding how within-instrument timbres contribute to musical expression and meaning. For example, results of this study could be applied in analysis of unaccompanied works for oboe or horn. Sandell and Chronopoulos (1996) proposed the term "macrotimbre" to describe the formal unity of timbres associated with a single source, inclusive, for example, of variation in timbre across an instrument's range. The results illustrate the timbral possibilities afforded by these instruments as a result of manipulating dynamics and register, adding dimensionality to our understanding of their macrotimbres as presented in Reymore (2021).

Future research that maps additional instruments and manipulates different parameters would deepen our understanding of timbral similarities across instruments. Soden (2020) introduces the term "metatimbre," for the purpose of describing any collection of related timbres. Definitions of metatimbre include—but are not limited to—those produced by a single instrument, so that one could speak of, for example, the metatimbre of the clarinet, a concept that overlaps with Sandell and Chronopoulos' concept of macrotimbre. However, Soden's concept of metatimbre also includes collections of timbres across instruments with similar perceptual qualities or qualia, which seeks to qualify relationships among timbres of different instruments. For example, Rimsky-Korsakov noted timbral similarities among the viola, the middle register of the bassoon, and the low register of the clarinet as well as between the bassoon and horn when played piano or mezzo-forte (as cited in Soden, 2020). The current work provides a method for quantifying timbral similarities such as these that are specific to register-dynamic combinations. For example, upon collecting data for the viola, bassoon, and clarinet, we would expect to see more similarity among the registers specified by Rimsky-Korsakov than among other registers of these instruments or of other instruments, such as the oboe. Techniques such as hierarchical clustering or rank-ordering Euclidean distances would be appropriate for mapping metatimbral spaces across instruments. It is possible that this type of information may be able to predict perceptual effects of orchestration, such as blend between instruments (as described in McAdams, Goodchild, & Soden, 2022). Such results would also likely be useful in pedagogy of orchestration and composition and may have applications in music-theoretical analysis.

Future research using these methodologies might also examine the effect of musical experience on the cognitive linguistics of timbre by collecting ratings from both musicians and non-musicians or from participants from non-Western cultures. The original model (Reymore & Huron, 2020) was derived from studies involving Western, classically trained musicians. By asking people with different types of musical experience to apply the terms of the model to instrument sounds, we can begin to develop a sense of which linguistic concepts are more or less common across groups or are culturally constrained.

The subtle timbre nuances, tendencies, and idiosyncrasies of a given musical instrument are critical to the experience of a musician who has expertise with that instrument and as evidenced by the results of this study, are often apparent to listeners. Yet, the timbral affordances of musical instruments, even in response to basic parameters such as dynamics and register, are rarely discussed. The study reported here demonstrates that not only is within-instrument timbral variability based on dynamic and register apparent to listeners, such variability may be quite complex, and interactions among parameters may play an important role. Results can inform predictions for future work addressing which dimensions of timbre qualia are unique to specific instruments or groups of instruments and which are common across many instruments as well as the types of relationships, both linear and non-linear, between timbre qualia and playing techniques.