Significance Old Italian violins are widely believed to have playing qualities unobtainable in new violins, including the ability to project their sound more effectively in a hall. Because Old Italian instruments are now priced beyond the reach of the vast majority of players, it seems important to test the fundamental assumption of their tonal superiority. A recent study found that, under blind conditions, violin soloists generally prefer new violins and are unable to distinguish between new and old at better than chance levels. This paper extends the results to listeners in a hall. We find that they generally prefer new violins over Stradivaris, consider them better-projecting, and are no better than players at telling new and old apart.

Abstract Old Italian violins are routinely credited with playing qualities supposedly unobtainable in new instruments. These qualities include the ability to project their sound more effectively in a concert hall—despite seeming relatively quiet under the ear of the player—compared with new violins. Although researchers have long tried to explain the “mystery” of Stradivari’s sound, it is only recently that studies have addressed the fundamental assumption of tonal superiority. Results from two studies show that, under blind conditions, experienced violinists tend to prefer playing new violins over Old Italians. Moreover, they are unable to tell new from old at better than chance levels. This study explores the relative merits of Stradivari and new violins from the perspective of listeners in a hall. Projection and preference are taken as the two broadest criteria by which listeners might meaningfully compare violins. Which violins are heard better, and which are preferred? In two separate experiments, three new violins were compared with three by Stradivari. Projection was tested both with and without orchestral accompaniment. Projection and preference were judged simultaneously by dividing listeners into two groups. Results are unambiguous. The new violins projected better than the Stradivaris whether tested with orchestra or without, the new violins were generally preferred by the listeners, and the listeners could not reliably distinguish new from old. The single best-projecting violin was considered the loudest under the ear by players, and on average, violins that were quieter under the ear were found to project less well.

Violinists generally agree that individual violins vary considerably in their ability to project—projection referring to how well an instrument can be heard at a distance, especially over a background of competing musical sound. The paradigmatic test for projection is the violin concerto, where a soloist is expected to carry over a full orchestra, often in a very large hall. Old Italian instruments are commonly believed to have the advantage over new ones in this regard. “What made the old instruments great was their power in a hall,” wrote the distinguished violinist Earl Carlyss (1) in response to a 2010 blind study (2). Somewhat paradoxically, Old Italian violins are also commonly described as being relatively quiet under the ear of the player compared with new instruments. According to concertmaster Frank Almond (who plays a Stradivarius), “a peculiar (and sublime) aspect of great old Italian instruments is that the sound somehow expands and gains more complexity from a distance, especially in a concert hall.” He contrasts this with many modern instruments, which seem to have a large sound under the ear but may not “carry past the sixth row” (www.insidethearts.com/nondivisi/they-blinded-me-with-science/, accessed April 10, 2017). Similarly, renowned cellist Steven Isserlis (who plays a Stradivarius cello) wrote “[a] famous (and curious) feature of Stradivarius instruments is that their tone seems to increase with distance. As a rule, if my tone sounds small to me, it means that it is travelling out into the hall…” (3).

Most celebrated violinists since the early 1800s have played instruments by Stradivari or Guarneri del Gesu, and this historical fact is often taken as evidence that these violins possess some combination of playing qualities not found in newer instruments. Over the past two centuries, numerous informal playing and listening tests have challenged the notion (4⇓–6). More recently, a pair of well-controlled studies invited players to blind test new violins against those by Stradivari and other Old Italian makers (2, 7). In both studies, the most preferred violin was new, and there was a general preference for new instruments over old. Moreover, players seemed unable to reliably distinguish between new and old.

These studies focused on judgments made by violinists while playing. Because projection must by definition be judged by listeners at a distance, many questions remained unanswered. Do Stradivari violins, in fact, outproject high-quality new instruments? Are better-projecting instruments typically quieter under the player’s ear? Are the instruments that soloists prefer to play the ones that are found to project best in a hall? Can listeners tell whether a soloist is playing an Old Italian violin rather than a new one?

To answer these questions, we ran two experiments in which neither players nor listeners knew the identity of the test instruments. Projection and preference were taken as the broadest criteria by which listeners might meaningfully separate two violins in a hall: which violin is heard better, and which is preferred? The first study was held in 2012 in a small concert hall near Paris, France immediately after the above-cited preference test (7). The second was held in 2013 in a larger hall in New York City. These studies, referred to here as the Paris and New York experiments, involved 55 and 82 listeners, respectively. In each case, three new violins were tested against three by Stradivari. In Paris, the violins were tested with and without orchestral accompaniment. In New York, all tests were unaccompanied.

Materials and Methods General Methodology. In each experiment, a group of listeners was presented with a series of pairwise comparisons. Each pair consisted of a new violin and a Stradivarius (the selection of the instruments is detailed below) and was played by a soloist behind an acoustically transparent screen. Players used their own bows, which they typically would when evaluating instruments in real life. Modified welders’ goggles together with much-reduced ambient lighting made it impossible for players to identify instruments by eye. The Paris experiment was conducted in the 300-seat concert hall A coeur de ville in Vincennes (a hall well-regarded for its acoustics), and the New York experiment was conducted in the 860-seat Great Hall at the Cooper Union building. Listeners were free to sit anywhere in the halls, although in Paris, the first five rows were excluded. Seven internationally renowned soloists (named soloists 1–7 in Table S1) took part in the Paris experiment, six of whom participated in the player preference experiment (7) conducted in the preceding 2 days. In New York, one soloist from the Paris experiment was joined by another distinguished violinist (Table S1). In both tests, the number of soloists who normally performed on an Old Italian instrument was about equal to the number normally performing on a new one (Table S1). Table S1. Information about the players who took part in each experiment In Paris, we invited experienced listeners, by which we mean listeners with expertize relevant to our subject; they included violin makers, players, musicians, audiophiles, music critics, composers, and acousticians. The New York experiment was a public event within Mondomusica (an international exhibition of handcrafted musical instruments); listeners were people who saw the advertisement and were interested in the topic. In both experiments, listeners who returned incomplete evaluation sheets were omitted from the analysis. The distribution of the remaining listeners (55 for Paris and 82 for New York) is provided in Table S2. At the beginning of the experiment, listeners were informed orally that participation was voluntary and that all answers would be anonymized. Under these conditions, CNRS (the employer of C.F.) does not require any formal approval from a licensing committee before the experiment. Table S2. Information about the listeners who participated in each experiment Detailed Procedure for the Paris Experiment. This experiment was divided into three parts: parts 1 and 2 were concerned with the relative projection of old and new violins; part 3 tested whether listeners could tell if the violins being played were new or old. The full score sheet given to the participants is available in Dataset S1. Part 1. Testing projection. Relative projection was tested by a series of pairwise comparisons structured as follows. A soloist played a short excerpt on each violin of a pair and then did the same thing again. This so-called ABAB format ensured that listeners could hear each violin both before and after the other. The whole sequence was done twice for each pair, first using a solo excerpt and second, using a concerto excerpt accompanied by the orchestra (details about the orchestra can be found in SI Materials and Methods). It was made clear to listeners that the same pair was being played throughout. To test each of the Stradivari violins against each of the new violins, nine new/old pairs were formed. These pairs were played in random order by player 1; then, after a short break, they were played by player 2 but with the order of the violins within the pairs reversed and the order of the pairs modified. Note that, in choosing soloists for this test, we selected player 1 as one who regularly plays a new violin (soloist 1) (Table S1) and player 2 as one who regularly plays an old violin (soloist 2). To facilitate testing, a researcher placed each pair of violins in turn on a table. A large sign (legible even in the relative darkness) placed in front of each instrument indicated to the soloist whether it was violin A or violin B. To help listeners keep track, a large video screen indicated which violin of which pair was being played (e.g., pair 5, violin A). Musical excerpts were selected from the standard repertoire and well-known to all soloists. The unaccompanied excerpts were chosen to cover a good deal of the instrument’s range within about 10 s. Soloist 1 played the opening solo (bars 23–27) from the first movement of the Tchaikovsky Violin Concerto opus number (op.) 35. Soloist 2 played the opening solo (bars 90–94) from the first movement of the Brahms Violin Concerto in D major, op. 77. The accompanied excerpts were a bit longer (∼20 s) and passages in which the solo violin might easily be “covered” by the orchestra: soloist 1 played bars 187–202 from the third movement of the Brahms Concerto, and soloist 2 played bars 41–43 from the second movement of the Sibelius Violin Concerto, op. 47. Although projection is presumed to be an intrinsic quality of an instrument, it may well be affected by how good a “fit” a particular instrument is for a particular player. An experimental design allowing separation of these two factors would, however, require the audience to rate nine pairs of violins twice. The resulting 36 repetitions of the same excerpt would, we believe, have been an unreasonable challenge to listener concentration. To help avoid boredom and fatigue, the second soloist was, therefore, given a different excerpt. This tradeoff between experimental design and the capacities of the listeners made it impossible to later decouple the intrinsic qualities of the violins from the influence of individual players. For each pair of violins, listeners were required to answer the following question: “which violin projects best?” The meaning of projection was left undefined, but a questionnaire on the subject (SI Materials and Methods) was sent to participants after the experiment.† Listeners recorded their evaluations by placing a mark at the position of their choice along a continuous scale, where one end indicated that violin A was far superior to B in terms of projection. A mark at the opposite end indicated the converse, and a mark at the midpoint indicated that the two projected equally well (Dataset S1). Although it was impossible for the soloists to evaluate violins in this way while playing them, they did indicate (to C.F.) which instrument of each pair that they believed projected better or that the two were equal. Selection of test violins. In the Paris preference tests (7), 10 soloists were presented with 6 new and 6 Old Italian violins (including 5 by Stradivari), which had themselves been preselected from a pool of 9 Old Italian and 15 new violins made available by dealers, collectors, players, and makers (ref. 7 has details of the preselection process). Over the course of two 75-min individual testing sessions, the soloists were asked to (i) eliminate any instruments that they found unsuitable, (ii) choose from the remaining their four favorites and then rank these four in terms of overall preference, and (iii) select the single violin that would best replace their own violin for an upcoming concert tour. Time limits restricted the number of violins that could be tested for projection to three new and three old. The following factors were considered in selecting these from six old and six new violins that the soloists had evaluated. i) The number of times an instrument was the top choice of a soloist. Five violins were chosen by at least one soloist. Three were new (N5, N10, and N9), and two were by Stradivari (O1 and O4).

ii) Overall preference score based on soloists’ choices of favorite violins. The three top-scoring new violins were, in descending order, N5, N10, and N11. The three top-rated old violins were O1, O8, and O4.

iii) Measured acoustical output. Acoustical measurements were made of all instruments (SI Materials and Methods and Fig. S1). Preliminary results were used for a quick measure of the relative sound output of each instrument per unit force at the bridge. The three new violins with the highest output were (in descending order) N5, N11, and N10. The three old violins were O6, O4, and O1. Fig. S1. Difference in averaged sound output level (per unit force at bridge) for each test violin relative to violin O3 for the 200- to 6,400-Hz frequency band (represented in decibels). Based on the data in Table 1, we chose the following violins: N5, N10, N11, O1, O4, and O6. The inclusion of O6 needs justification, because it was not chosen by any soloist and was rated 9 of 12 for preference. It was selected mainly on the basis of its acoustical output, which was the highest of all of the old violins. Moreover, unlike the well-liked O8 (also a strong contender), it was a Stradivarius and therefore, of most direct relevance to our hypothesis. Table 1. Data used in the selection of three new and three old violins for the listening experiment Part 2. Would the violins most frequently chosen by soloists in preference tests outproject those that the soloists most often rejected? We had listeners compare the two most frequently chosen violins (N5 and O1) with the two most often rejected (N2 and O12). The resulting four new/old pairs were tested as in part 1, with players and listeners being asked the same questions. The solo excerpts were as above, but to increase musical variety, different orchestral excerpts were used: player 1 (soloist 3) (Table S1) played a 20-s excerpt from the second movement of the Brahms concerto (bars 93–98), and player 2 (soloist 4) played a 16-s excerpt from the third movement of the Sibelius concerto (bars 254–262). Part 3. To test whether listeners could distinguish old violins from new violins, they were presented with a succession of seven concerto excerpts, each played (with orchestra) by a different soloist (soloists 1–7) (Table S1). Unbeknown to listeners, the soloists played their own personal violins, thus forestalling concerns that they might be insufficiently acquainted with the test instruments to fully exploit their individual qualities. Each soloist had prepared a three-minute excerpt from the Mendelssohn, Sibelius, or Beethoven concerto. After each performance, listeners were asked the following questions. “Do you think the violin is old or new? Why?” Detailed Procedure of the New York Experiment. Testing projection and preference. The New York experiment tested how well the listeners’ judgments of projection correlated with judgments of preference. It was structured in much the same way as part 1 of the Paris experiment, with three Stradivari and three new violins yielding nine new/old pairs. Listeners were not asked to judge projection and preference at the same time: such a task would be cognitively challenging; moreover, the answer to the first question might influence the answer to the second, creating artificial correlations. Instead, listeners were randomly divided in two groups: group 1 was asked first which violin of a pair they preferred and why, and group 2 was asked which violin projected better. After player 1 (soloist 8) (Table S1) had played the nine pairs, the questions were switched for player 2 (soloist 9), so that the first group now judged projection and the second group judged preference. Both projection and preference were reported on continuous scale as in Paris. Unlike Paris, listeners were asked to define what projection meant to them by means of a multiple choice questionnaire (Dataset S2). As in Paris, the soloists were asked to estimate projection on a simpler scale: A, B, or equal. All tests were done without orchestral accompaniment. Selection of test violins. We would have liked to use the same old and new test violins as in Paris, but just two of them were available: the new violin N5 and the Stradivari O6. Two additional new violins were chosen by a preselection process (SI Materials and Methods) from 15 violins submitted by violin makers. The two additional Stradivari were the only ones made available to us at the time.

SI Materials and Methods Information About the Soloists and the Violins That They Played During the Experiment. Information about the soloists and the violins that they played during the experiment is provided in Table S1. Information About the Listeners. Listeners who turned in incomplete data sheets were excluded from the analysis. The distribution of the remaining (55 in Paris and 82 in New York) is described in Table S2. Information About the Orchestra. The Sorbonne Universités student orchestra was supplemented by several professional players and conducted by Vincent Barthe. In all, there were 10 violins, 5 violas, 3 cellos, 1 double bass, 2 flutes, 2 clarinets, 1 oboe, 1 bassoon, 2 horns, and timpani. To allow players to read their parts on the darkened stage, small directional lamps were attached to the music stands. Acoustical Measurements. The acoustical output (sound pressure per unit force at bridge) for each violin was measured using an impulse hammer and microphone. The bridge was tapped both horizontally and vertically, and the sound pressure was measured at 12 equatorial microphone positions 20 cm from the center of the violin in the plane of the bridge (10). These measurements yielded 24 frequency response functions (FRFs) for each violin. The real average for all 24 FRFs was calculated and then reduced to a single average (in decibels) for the frequency band spanning 200–6,400 Hz. This single average is provided for each violin in Fig. S1. The three new violins with highest levels are, in descending order, N5, N11, and N10, and the three old violins with highest levels are O6, O4, and O1. Selection of the Violins for the New York Experiment. New violins were chosen from a pool of 15 violins (including N5) submitted by their makers. A preselection took place in the same venue as the experiment. J.C. and the distinguished violin maker Sam Zygmuntovicz played the violins under blind conditions and selected what they considered the best eight violins. The selection of three new instruments was made by a blind test similar to the preselection in Paris (7). Three blindfolded soloists (the two participating in the experiment along with Karen Gyomo) each played eight violins behind an acoustically transparent screen for a small audience (J.C., F.-C.T., Sam Zygmuntovicz, and the two soloists who were not playing). Three violins (including N5) were chosen via an informal discussion of the player and listener preferences. There was good agreement among all parties. Score Sheet Used in Paris. The score sheet used in Paris is in Dataset S1. Questionnaire Sent to the Listeners After the Paris Experiment. i) What is your definition of projection (i.e., the one that you used to evaluate the different violins)?

ii) Were there one or more musicians for whom the evaluation was easier/harder? Were there one or more excerpts for which the evaluation was easier/harder? Score Sheet Used in New York. The score sheet used in New York is in Dataset S2.

Results In this study, some Bayesian statistical procedures supplement traditional frequentist inferences using LePAC software (8, 9). They assume an uninformative prior distribution (i.e., no information is used other than that contained in the data, and no particular hypothesis is favored a priori). Hereafter, Bayesian statements are notated Pr*. They are naturally conditional on the data at hand, but conditional notation is omitted for the sake of brevity. Paris Experiment. Relative projection of three new violins and three Stradivarius (part 1). Fig. 1 shows the relative projection of the nine new/old pairs tested in Paris. Fig. 1, Left shows results for unaccompanied violin, and Fig. 1, Right shows violin with orchestra. N10 was about equal to O1 and O4 in terms of projection, but in all other pairings, the new violins outprojected the old. The spaces between the blue and red error bars in Fig. 1 (which are especially wide for N11) suggest that projection depends somewhat on the player. However, no firm conclusions can be drawn, because the two players used different excerpts. Fig. 1. Relative projection of the nine new/old pairs tested in Paris. (Left) Results for unaccompanied violin. (Right) Results for violin with orchestra. Listeners scored projection on a continuous scale between zero and one. The charts show the average of their scores for each of two players—P1 in red and P2 in blue. Error bars correspond to the SEM. The two players were asked to choose one of the following for each pair: (i) violin A projects best (indicated by a mark at the left edge of the graph, (ii) violin B projects best (mark at right edge), or (iii) the two violins project equally well (mark at center line). P1’s judgements are shown in red, and P2’s judgements are shown in blue. Do violins that project well when played alone also project well over an orchestra? We find a striking consistency across the two conditions. Averaging the evaluations of all listeners and both players, the observed effect is −0.002 [solo − orchestra; t(52) = −0.25; P = 0.40]. Furthermore, we can state that Pr*(|true effect| < 0.02) = 0.95 (on a 0–2 scale): given these data, there is a 95% probability that the true effect (i.e., the effect in the whole population of experienced listeners) is between −0.02 and 0.02. Although nonnull, the zero to one scale means that its value is very small, and a conclusion of negligibility can be drawn. In other words, very similar results are obtained whether testing projection with or without orchestra. Do listeners from different professional backgrounds evaluate projection differently? By design, the entire audience consisted of experienced listeners, but they came from various professional backgrounds and included musicians, violin makers, and acousticians. All groups produced rather similar results. The observed rms of the differences between groups is 0.04 [F(2,52) = 1.75; P = 0.18; Pr*(|true effect| < 0.08) = 0.95 (on a 0–2 scale)]. Given the consistencies described above, we felt justified in averaging the data from all listeners with and without orchestra. Fig. 2 shows the differences in projection between each new violin and all three old violins and then, between each old violin and all three new violins. Again, we see a large new/old effect, with new violins judged to project better than old. The observed difference in projection is 0.19 [t(52) = 15.14; P < 10−4; 95% confidence interval (95% CI): (0.16; 0.21)]. Pr*(true effect > 0) > 1–10−4, and Pr*(true effect > 0.17) = 0.95 (on a 0–1 scale). The apparent effect of the player is moderate (0.13) but clear as t(52) = −5.82, P < 10−4, and 95% CI: (0.09; 0.18). [In this case of a 1-df comparison with exactly the same assumptions as in the frequentist theory, the frequentist 95% CI and the standard Bayesian 95% CI coincide, so that we can state Pr*(0.09 < true effect < 0.18) = 0.95. Therefore, for similar cases in the following, we report only the 95% CI limits.] Again, we cannot know whether this is because of the player or the use of different excerpts. Fig. 2. Differences in projection between each new violin and all three old violins (top three rows) and between each old violin and all three new violins (bottom three rows) tested in Paris. Results are averaged for all listeners with and without orchestra. Error bars correspond to the SEM. Relative projection of two preferred and two rejected violins (part 2). In part 2 of the Paris experiment, the two most preferred violins (N5 and O1) were compared with the two least preferred (N2 and O12). Fig. 3 shows that N5 clearly outprojected N2 and O12 and that O1 was about equal in projection to N2 and O12. There is good agreement between player and listener evaluations. Fig. 3. Difference in projection between the two most preferred violins and the two most rejected violins. Error bars correspond to the SEM. The players’ evaluations are single points at either zero or one (left or right) with the same color code as for the audience. Because the soloists gave the same answer with and without orchestra, there is no distinction between the two conditions as in Fig. 1. Comparison between soloist and listener evaluations of projection. Violinists generally believe that loudness under the ear is not directly related to projection and that a violin’s projection cannot be reliably estimated simply by playing it. During individual sessions that took place before the experiment (7), we asked each soloist to estimate projection and loudness under ear for three violins: their own, their favorite, and their next favorite of the opposite new/old category. This task was done in a rehearsal room and again in the concert hall (Table 2). Because of the selection method, only a few violins—N5, O1, and N10—were rated by five or more soloists. Table 2. Mean (SD) of the loudness and projection ratings for soloists’ own, old, and new violins averaged across the two conditions—rehearsal room and concert hall Although the soloists gave their own violins (seven of which were old) a slightly higher rating for projection than for loudness (8.2 vs. 7.9), when it came to the test instruments, the old got the same averaged rating (7.9) for both loudness and projection as the new (8.6). Because the new violins did, in fact, outproject the old, loudness under ear may be more closely related to actual projection than is generally believed. Table 3 shows the averaged projection and loudness ratings for the three most preferred violins: N5, O1, and N10. The projection estimates wrongly suggest that O1 projects better than N10. The loudness ratings, however, at least get the ordering correct: N5, N10, and O1 (in order of decreasing projection). The spread between projection and loudness seen in O1’s ratings (8.8 vs. 7.6) can be attributed to the four players who chose it as their favorite. Their ratings were (for projection and loudness) 10 and 6, 9 and 7, 9 and 8, and 9.5 and 9, respectively. By contrast, the two soloists for whom O1 was not the favorite violin rated it very similarly for the two criteria (8 and 8; 7.5 and 7). Given the small sample size, no firm conclusion can be drawn, although the data does suggest that the widely held belief that a Stradivari can project well despite sounding quiet under the ear may lead some players to overestimate projection for instruments that they like to play but find relatively quiet under the ear. There is indeed considerable anecdotal evidence that players and makers consider projection and loudness as two well-separated concepts. The distinction between projection and loudness is illustrated in the analysis of the questionnaires filled in by participants in the New York experiment (73% of whom were makers and musicians). They were asked to select which of seven possible definitions best captured what projection meant to them (Dataset S2). Table 4 summarizes the results. The question referring to loudness was selected far less often than all but one of the others. More research is needed to investigate whether listeners do indeed evaluate projection and loudness differently and if so, what the underlying acoustical parameters for each might be. Table 3. Averaged estimates for projection and loudness under ear for three violins rated by at least five soloists during their private sessions in the Paris experiment Table 4. Number of times each possible definition of projection was chosen during the New York experiment Distinguishing old from new (part 3). We asked listeners to guess whether each of seven violins was old or new; 39 of 46 subjects made a guess about all seven violins. (Incomplete evaluation sheets were discarded from the analysis.) The distribution of their correct guesses is shown in Fig. 4. It shows a unimodal distribution centered between three and four. In all, just 122 of 273 (or 44.7%) of the guesses were correct. Fig. 4. Distribution of correct guesses about the age of seven violins by 39 subjects. It is interesting to see how the correct guesses were distributed among violins. For all but two instruments (one old and one new), the 95% CIs (SI Results) include 50%, and therefore, the chance hypothesis cannot be ruled out. For the other two violins, there is a systematic error: listeners guessed that the old violin was new and that the new one was old. A supplementary analysis built on the hypothesis that the guesses were entirely governed by chance is available in SI Results. New York Experiment. The Paris experiment left at least one important question unanswered. How do listeners’ evaluations of projection relate to their evaluations of preference? It is easy to imagine, for example, that violin A is found to project better than violin B but that violin B is preferred for its tone quality. Exploring the relationship between projection and preference was the principal objective of the New York experiment. Fig. 5 shows relative projection (Fig. 5, Left) and preference (Fig. 5, Right) for each of nine new/old pairs. Looking first at projection, results are very similar to those of the Paris experiment. New violins are found to project better than old, although in this case, the difference happens to be even larger: observed difference = 0.27; t(80) = 14.55; P < 10−6; 95% CI: (0.23; 0.31); Pr*(true effect > 0) > 1–10−6; and Pr*(true effect > 0.24) = 0.95 (on a 0–1 scale). The better projection of the new compared with the old, therefore, seems robust across a change in halls, listeners, players, and violins. The observed effect of the player/order/excerpt is 0.03 (on a 0–2 scale), thus smaller than the effect of the player/excerpt in Paris (0.13 on a 0–2 scale). However, little can be inferred about the player effect, because it cannot be separated from the effect of the excerpt (in Paris and New York) and the order (in New York only). Fig. 5. (Left) Relative projection and (Right) preference for each of nine new/old pairs tested in New York. Listener scores are on a continuous zero to one scale. The charts show the average of their scores for each of two players—P1 in red and P2 in blue. Error bars correspond to the SEM. The two players were asked to choose one of the following for each pair: (i) I prefer violin A (x at the left edge of the graph), (ii) I prefer violin B (x at right edge), or (iii) I like them equally (x at center line). P1’s judgements are shown in red, and P2’s judgements are shown in blue. Looking at preference (Fig. 5, Right), listeners clearly preferred new violins over old: observed difference = 0.27; t(80) = 14.67; P < 10−6; 95% CI: (0.23; 0.30); Pr*(true effect > 0) > 1–10−6; and Pr*(true effect > 0.24) = 0.95 (0–1 scale). Fig. 5 shows slightly different results for the two players, but we cannot conclude that there is a player effect, because it is inseparable from the possible effects of different excerpts and testing order (i.e., testing preference first rather than projection first). We can, however, conclude that, if there is a player/order/excerpt effect on preference, it is rather limited: the observed value is 0.07; t(80) = 1.87; P = 0.07; and Pr*(|true effect| < 0.13) = 0.95 (on a 0–2 scale). There is an almost 90% agreement between soloists and listeners about preference, at least when testing them together in a hall. Consider that player/listener agreement was just 70% when the soloists were asked to estimate projection under similar conditions in Paris. Given that listeners generally preferred new violins over old and found them better-projecting, one may ask whether the new violins were preferred precisely because they projected better. Because the listeners were asked to explain their preference choices, we look to the explanations for insight; 58 of 82 listeners used words related to projection in at least one case (SI Results). meaning that just 158 of the total of 548 collected statements refer to projection. (Listeners evaluated nine pairs, but many listeners did not provide any explanations or else provided them for just a few of the pairs.) Among these 158 statements, some were of the kind “I preferred violin A because of its tone quality, despite it being less loud/projecting than violin B” rather than “I preferred violin A, because it projects better.” Consider, too, the extra definitions of projection given by two participants: “Doesn’t always mean the best sound but one that cuts through noise, fills a room, and allows the musician to be heard” and “full and loud, but not necessarily beautiful; sometimes harsh.” All of which to say, listener explanations do not suggest any obvious link between preference and projection.

SI Results Statistical Analysis for the Old/New Guesses (Paris Part 3). For each of seven violins, the numbers of correct guesses over the total number of guesses are presented along with two intervals, the first one being the 95% Clopper–Pearson CI and the second one being the Bayesian Credible Interval with Jeffreys’ prior. Violin 1 (old): 7/45 (6.49; 29.46%), (7; 28.13%)

Violin 2 (new): 11/46 (12.59; 38.77%), (13.42; 37.57%)

Violin 3 (new): 27/45 (44.33; 74.30%), (45.43; 73.33%)

Violin 4 (new): 26/45 (42.15; 72.34%), (43.24; 71.35%)

Violin 5 (old): 24/43 (39.88; 70.92%), (41.00; 69.88%)

Violin 6 (new): 22/44 (34.56; 65.44%), (35.62; 64.38%)

Violin 7 (old): 23/46 (34.90; 65.10%), (35.92; 64.08%) What if the guesses were governed entirely by chance, as if the subjects were in fact tossing coins? All guesses would then be independent one from each other—both from one subject to the next and among each subject’s guesses. In this case, the number of correct guesses would be distributed as a binomial distribution, with parameter n being the total number of guesses (273) and parameter π = 0.5 being the probability of a correct guess. Then, the 95% Clopper–Pearson CI would be 38.7; 50.8%. It includes 50%, meaning that the hypothesis that chance entirely governed the guesses cannot be ruled out. Nonetheless, given these data, it could be stated that Pr*(40.9% < true proportion < 48.6%) = 0.80, just as if the subjects were using a biased coin with less than 50% chance of success. However, that argument rests on the assumption of every subject performing independent guesses, which is far from plausible. Explanations Provided by the Listeners in New York to Justify Their Preferences. Only the explanations related to projection and loudness were taken into account here. The terms that we considered associated with projection are the following terms: project(ion), loud, quiet, power(ful), muted, big sound, small sound, direct sound, carrying power, strong, weak, present, and full. Clear was added to this list for the listeners who selected “which comes through to your ears more clearly” as a possible definition for projection.

Conclusions and Discussion This study compares Stradivari and new violins principally from the listener’s perspective. Projection and preference are taken as the broadest criteria by which listeners might meaningfully separate violins in a hall. Which violins are heard better, and which are preferred? Also explored is the relationship between evaluations made by listeners and those made by players. Two separate experiments were conducted: one in the suburbs of Paris and the other in New York City. In Paris, violins were played with and without an orchestra by blindfolded soloists behind an acoustically transparent screen. The same was done in New York but without an orchestra. The results are unambiguous: listeners found that new violins projected significantly better than those by Stradivari. Moreover, listeners preferred new violins over old by a significant margin. Although the listeners came from various professional backgrounds (they included musicians, violin makers, and acousticians), very similar results were obtained from all backgrounds. We find a strong correlation between projection with and without an orchestra. This correlation seems fortunate for both players and researchers, in that an orchestra is evidently not required to meaningfully test projection. Projection estimates made by players during private sessions (7) did not agree very well with judgments made later by listeners in the hall. When playing for an audience in a hall, however, about 70% of player estimates of projection agreed with listener judgments. Put another way, players were wrong about 30% of the time, confirming the wisdom of bringing a trusted listener along when trying out instruments. However, when players in the New York experiment were asked, after playing each new/old pair, which violin they preferred, their preferences were in strong agreement with those of the audience. During private sessions in Paris (7), 4 of 10 soloists chose a Stradivari as the instrument “best suited to replace their own violin for an upcoming tour.” We find here that these four soloists chose violins with significantly less projection than the two best-projecting new instruments. The most preferred Stradivari barely outprojected the least preferred Stradivari and the least preferred new violin. The New York results suggest that the most preferred Stradivari in Paris would also be less preferred by listeners than the better-projecting new violins. The most preferred new violin in the Paris experiment was considered louder under the ear than the most preferred old violin—and indeed, than every other violin that was rated for loudness. Soloists who chose a Stradivari may have preferred a violin that was less loud under the ear, at the same time believing that it would project well, because the three players who chose the most preferred Stradivari rated it notably higher for projection than loudness. Previous studies (2, 7) indicate that, under blind conditions, violinists readily separate violins that they like from those that they do not but are unable to reliably distinguish new from old. We show here that listeners (including violin makers and musicians) are no better at telling whether a soloist’s violin is new or old. The test violins were necessarily few in number, and there is no way of knowing how representative they are of the larger population. Although there is every reason to believe that there are Stradivari violins with outstanding projection, we find little reason to suppose that players would find them quiet under the ear. Violins (old or new) that (i) are relatively quiet under the ear and (ii) outproject apparently louder violins would be worthy subjects for future research. To date, we have found no evidence for their existence. A player’s requirements for projection are clearly dependent on musical context. Even a relatively quiet violin will be heard when played unaccompanied in a small hall, and a good conductor will do everything possible to ensure that a soloist with a relatively quiet violin can still be heard over an orchestra. In auditions and playing competitions, however, jurors listen to one player after another, making apparent the relative projection of their instruments. Although it is common for gifted young players to borrow Old Italian violins for such occasions, our results suggest that they would be better served by good new violins—at least so long as the identity of the instruments remains unknown to those judging. Note that this study relied on soloists, whose primary need is to be heard over an ensemble. The vast majority of violinists, however, are required to blend into ensembles. Research is needed to clarify the relationship between projection and “blendability.” Less projecting violins could have the advantage in this regard. A belief in the near-miraculous qualities of Old Italian violins has preoccupied the violin world for centuries. It may be that recent generations of violin makers have closed the gap between old and new, or it may be that the gap was never so wide as commonly believed. Either way, the debate about old vs. new can perhaps be laid aside now in favor of potentially more fruitful questions. What, for example, are the physical parameters determining the playing qualities of any violin, regardless of its age or country of origin?

Acknowledgments We thank all dealers, makers, players, and collectors for their kindness and trust in making available these valuable instruments. Special thanks to the soloists for their participation and enthusiasm and the numerous audience members for their dedication and patience. Special thanks as well to the Sorbonne Universités student orchestra players, their conductor Vincent Barthe, and their administrators Agnès Puissilieux and Lucie Paladino for their kindness and professionalism. We thank Philip De La Croix and Stéphane Agasse for the use of the Vincennes auditorium and their logistical help and Kojiro Yamada and Nippon Hōsō Kyōkai (Japan's national public broadcasting organization) for their amazing support in New York. We also thank the Lutheries–Acoustique–Musique team (particularly Indiana Wollman and Laurent Quartier), the Borsarello family, David Griesinger, Stefan Avalos, and Suzanne Ortmeier for their kindness and help throughout the Paris experiment. Also, we thank the CNRS and Université Pierre et Marie Curie for funding this experiment and the Violin Society of America for additional financial support.