Computational determination of transition times using the measured mouthpiece pressure from soprano and bass clarinet players

The clarinet has been studied in the musical acoustics community for quite some time; however, the less commonly known bass clarinet (BCL) has not been awarded the same attention. While the basic acoustics of the instrument seem similar, playing techniques can be quite different. Not all clarinet players will study and perform on the BCL. One specific difference is the size of the mouthpiece and reed. As the body of the BCL is much larger, it requires more breath support and air to move through the instrument to sound as the musician intends. All aspects of the instrument are larger: keys and tone holes, mouthpiece and reed, instrument body, and bell. Due to these physical differences, playing techniques are varied between the two instruments. This paper will define a metric that can be useful in describing differences in articulation between the BCL and B $♭$ soprano clarinet (SCL) qualitatively and quantitatively. This metric is called the transition time and will be defined herein. We will show that with this method of analysis, numerical comparisons are possible for a range of different musical contexts, musicians, and instruments.

Section 2 will offer the relevant and recent literature defining this problem. Section 3 will describe the experimental methods employed to collect data from the two instruments and musicians as well as detail the analysis method used to find the transition time. Section 4 will then detail the results of the tests and transition times of the two instruments in different playing scenarios. Finally, Sec. 5 will offer the conclusions and thoughts on future work.

The SCL plays in the frequency range of about 150–2000 Hz, whereas the BCL plays around 70–700 Hz. The differences between the SCL and BCL are not often studied, especially not from an acoustical standpoint. Many of the discussions come from The Clarinet, a quarterly journal for practicing musicians and teachers. In his popular clarinet handbook, renowned clarinet teacher and past journal editor James Gillespie¹ emphasizes attack, dynamics, tone shading, etc. and briefly discusses the use of the BCL for instrument doublers (musicians educated on more than one instrument). Palanker² offered an anecdotal comparison from an instructor's perspective, and a more specific treatment of the BCL technique and literature is given on his website.³ To the authors' knowledge, there is only one recent conference paper involving the acoustics of the BCL, written by Mallinger et al.⁴ Their paper focuses on the extended techniques of the instrument and the evolution of reed motion and mouthpiece pressure during performance.

Otherwise, many of the articles discussing clarinet and BCL technique are more subjective,⁵ using clarinet professors' vast experience and knowledge to describe the problem. As for many studies in musical acoustics, a goal of this work is to be able to describe the technique and resultant playing using quantitative measures. Eventually, the method could be used by performers to track their own playing progression and offer a quantitative measure of a players' articulation technique.

This study began as a way to add to the body of work on the BCL; however, it resulted in the discovery of a new metric that will be useful in studying a wide range of reed instruments. To aid in describing the importance and usefulness of this discovery, this paper will (1) define a new analysis metric called transition time (ΔT), (2) show how this computational technique can be used to compare transitions between notes for the SCL and BCL played in different musical styles, and (3) offer perspectives on how this technique could be used for further analysis of clarinet playing.

To measure playing parameters, a sensor-equipped mouthpiece (SEM) similar to that used by Li et al.,^6,7 Coyle and Gabriel,⁸ and Pámies-Vilá et al.⁹ for the clarinet and Munoz et al.¹⁰ for the saxophone was utilized. A Buffet (Mantes-la-Ville, France) R13 Festival B$♭$ SCL and a Selmer (Mantes-la-Ville, France) 1430LP B$♭$ BCL were used for all tests. Signals were read to the computer via an acquisition box [National Instruments (Austin, TX) NI-6212] at a sampling frequency of 40 kHz. For the SCL, a Vandoren (Paris, France) soprano reed (strength 3) was used with a Yamaha (Hamamatsu, Japan) 4C SCL mouthpiece. For the BCL, a Vandoren BCL reed (strength 3) was used with a Yamaha 4C BCL mouthpiece. Each mouthpiece was fitted with two Honeywell (Charlotte, NC) SCX05DNC microstructure pressure sensors connected with small tubes to the mouthpiece measuring P_b (blowing pressure) and P_mp (pressure inside of the mouthpiece).

Three musicians, experienced in clarinet doubling, participated in this series of measurements and were allowed a 5 min training period with each SEM before tests began. Each musician self-reported their playing ability at the amateur level, each with over 18 years of playing experience and at least 2 years of university level instruction. A total of 80 measurements were recorded for each musician. These tests are described fully in Table 1. The musician was asked to play a specified task with given tempo, dynamics, and articulation style. Two tempo markings [60 and 120 beats/min (bpm)], two dynamics (piano and forte), and one type of articulation [portato (articulated legato—gently separated notes, by the tongue)] were employed. Further, all measurements were taken in the first playing register of the instruments. The two passages played were sequential notes played chromatically (ascending only) and non-sequential notes (in the scale) played as an arpeggio, ascending and descending. The purpose of the measurements was to compare duration of transitions (ΔT) for the two instruments when played by the same musicians in similar conditions. This metric will be further described in Sec. 3.2. All tests were repeated five times.

Using the technique from Coyle and Gabriel,⁸ the measured pressure signals, P_b and P_mp, were analyzed to determine the articulation style for each note separation. Figure 1 shows a 2 × 2 plot of representative data for one musician playing one trial of four of the tests described on the BCL. In each case, the player was asked to play the test with a portato articulation between notes. For Fig. 1, the plots are as follows—Chro-60-f [Fig. 1(a)], Chro-120-f [Fig. 1(b)], Arp-60-f [Fig. 1(c)], and Arp-120-f [Fig. 1(d)]. In each subplot of Fig. 1, the orange line is the root mean square (RMS) of the mouthpiece pressure (P_RMS), and the blue line is the second derivative of the RMS mouthpiece pressure (⁠$P¨RMS$⁠). The black, unfilled circles are centered on the local minima surrounding each transition. The RMS envelope is computed using a 1 ms window coupled with a Gaussian-weighted moving average with a 40 ms window as done in previous studies concerning transients.^8,11,12

While the musician was asked to use a portato tonguing technique for each transition, there are, of course, small differences, depending on which notes are being played. Nevertheless, wherever the algorithm detected a viable transition (⁠$P¨RMS$ with two peaks, a non-slurred transition), a transition time, ΔT, was calculated in the following way. After each note-to-note transition was analyzed and deemed a tongued transition (portato/separated), two minima (valleys) surrounding the transition (as shown in Fig. 1 by the black, unfilled circles) were located. The value of ΔT for that particular transition is defined to be the time between these two minima. The use of minima and maxima of derivatives of $PRMS$ as reference points for the three segments of a note—attack, or opening transient, sustain, and release—was first proposed by Jensen.¹¹ Bergeot et al.¹² defined the end of the opening transient as the minima of $P¨RMS$⁠, and Coyle and Gabriel⁸ used maxima of $P¨RMS$⁠, representing the end and start of the release and attack, respectively, to automatically distinguish portato and slurred transitions. With ΔT defined in this work as the time between the start of the release of the preceding note and the end of the attack of the following note, it follows from the literature that the minima of $P¨RMS$ are suitable reference points for determining ΔT. While this method would likely be valid for defining a transition time for slurred notes, as they also exhibit two minima surrounding the transition (as seen in Coyle and Gabriel⁸), this paper focuses on the application to tongued transition times.

The important focus of the current work is the introduction of this analysis technique and metric, ΔT, as a means for comparing tonguing or articulation duration between players, tasks, and reed instruments (in this study between the SCL and BCL but eventually other reed instruments as well). Using only the mouthpiece pressure signal and the described analysis technique,⁸ a time between notes can be determined computationally and objectively. Section 4 will offer a selection of the results from comparison playing tests between the clarinet and BCL (and other tasks from Table 1) for one of the three players.

In this section, we comment on the use of the ΔT metric for making comparisons for different combinations of tempo, dynamic, task, and instrument (the tests described in Table 1). A number of example plots are shown, each with the y axis representing the transition times, in seconds (ΔT). For reference, the ranges of absolute ΔT values measured for the SCL were between ΔT = 20 ms and ΔT = 400 ms. For the BCL, the values ranged from around ΔT = 40 ms to ΔT = 300 ms. While the upper ranges of these transition times seem high, there were no musician surveys conducted to gauge the usability or “goodness” of the transition performed. All data were kept and analyzed for this study.

Tempo markings in musical compositions can range from extremely slow, 20 bpm (Larghissimonth), to an impressive 200 bpm (Prestissimonth). The tempo marking will inevitably affect the note-to-note transitions of any player and will likely have a great impact on the transition time as defined in this work.

Figure 2 shows transition times for one player, playing BCL, chromatic scale, with a forte dynamic. The blue dots represent the transition times when playing 60 bpm, and the orange dots are for 120 bpm. As shown, the transition times in this example ranged from 0.1 to 0.14 s. Until further studies are conducted, there is no way to know if a difference in absolute transition times measured would be interesting or significant enough for players to concern themselves with. Nevertheless, in each of the plots, a y axis result approaching a higher value would represent a longer (slower) transition time, whereas values approaching zero would represent a shorter transition time (faster).

Figure 2 shows the data for this test and leads to the conclusion that for this player, in this situation, playing at a faster tempo results in faster transition times (orange dots, numbers approaching zero on the y axis) compared to playing at a slower tempo (blue dots). This result is not surprising, as a musician would expect their tongue motion to be faster as the tempo increases.

An interesting question that could be posed about this data set is “How does a change in dynamic affect the player's resulting transition time?” Figure 3(a) shows the transition times for one player, playing BCL, chromatic scale, 60 bpm, and Fig. 3(b) shows the transition times for a different player, playing BCL, chromatic scale, 120 bpm. In each case, the blue dots represent the transition times when playing piano, and the orange dots are for a forte dynamic. For this test, both players showed that, despite the change in tempo, the notes played at a softer dynamic would exhibit longer transition times. The trend, though it is impossible to say concretely, seems to be showing an increase in transition time as the players reach the middle of the first register chromatic scale and then a slight decrease for the last note. Further studies could be performed to understand which transitions cause the most problems for players, based on the measurement of ΔT.

While experienced clarinetists will have a high level of comfort playing the different instruments in the clarinet family, it is expected that their technique will not be identical on each instrument due to the physical differences each exhibits. The transition time will likely change based on which instrument is being played by a musician due to the tongue-reed interaction for different sized reeds and mouthpieces.

Figure 4 shows the transition times for one player, playing the chromatic scale, 120 bpm, with a forte dynamic. The orange dots represent the transition times when playing the SCL, and the blue dots are for the BCL. For all the transitions shown for this player, the transition times are longer for the BCL than for the SCL. However, this was not the result across all players and all trials. This result and the variability of these results could be based on player experience on each of the clarinets. A hypothesis, to be tested with more players and more trials, would naturally be that the larger the instrument (the BCL, with larger mouthpiece and reed and requiring more breath support), the longer the transition time—in any of the different situations being tested.

Using only the mouthpiece pressure signals and the analysis technique from Coyle and Gabriel,⁸ reed instrument players can now compare different articulation styles and techniques in regard to their transition times from note to note. An analysis method using a SEM for BCLs has also been developed. This will make it possible to study the clarinet family more comprehensively. A potential use for this technique is for musicians to analyze their own playing and, with practice, arrive at their ideal transition times based on the task at hand. The musicians could also use the technique to test different instruments and accessories (reeds, mouthpieces, etc.) to decide which are best for their needs. The transition times could also allow composers to better understand musician limitations when articulating for instruments in the clarinet family in different musical settings involving extreme tempos, dynamics, or modern playing techniques. Future work is planned to further investigate the effect of player experience and specific tempo markings in relation to the limits of transition times as well as a deeper study of how ΔT results compare to other metrics in the literature, such as the tongue contact time defined by Pámies-Vilá et al.⁹ 

This work was supported by Grant No. PHY-160749 from the National Science Foundation and the Rollins College Student-Faculty Collaborative Scholarship Program. The authors would like to thank A. David-Sivelle, and T. Moore for initial experimental advice and Q. Fuse for preliminary data organization.