FFT Spectrum of C2 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 372 milliseconds (i.e. from the moment the bar is struck until 0.372 second later) . Notice that the third transverse mode at 666 Hz is very strong. Therefore, this mode will have a strong influence on the timbre of the bar when struck in the center. Also note that there is no peak at the position of the second transverse mode (i.e., there is no vibration of this mode) and a very weak vibration of the fourth transverse mode.

Wave trace of C2 bar hit at the center, resonator in place. The waves of the third transverse mode are clearly seen in all three traces above. Notice that the peak height of the waves reduces as time goes on (in other words, the volume is high right after the mallet blow and reduces as time goes on). At 0.360 second (360 milliseconds) the peak height of the third transverse mode waves is very small compared to the waves early in the vibration cycle. Look at the top trace in the range of 0 to 20 milliseconds. Note here that some of the peaks are split in two. The two small peaks are indicative of the fourth transverse mode. The last double peak of the fourth transverse mode can be seen at 15 milliseconds. After that point the bar ceases to vibrate in the fourth transverse mode. At the far right of the middle trace note that the peaks are starting to move up and down, which becomes more obvious in the bottom trace. This undulating pattern indicates the presence of the first transverse mode (fundamental). This undulating pattern becomes obvious near the 160 millisecond point. In other words, the fundamental is obscured by the third transverse mode until 160 milliseconds. This is due in part to the slow building of amplitude of the fundamental in the resonator and the decline in the amplitude of the third transverse mode. There is another undulating pattern that is seen in the first trace. This should not be confused with the fundamental pattern. This early pattern is the result of a cyclical variation in the peak height of the third transverse waves. The variation in wave amplitude is due to the mixing of two frequencies near each other, resulting in a mild beating. In this case the beating pattern appears to be due to the mixing of the third transverse and the 11th harmonic of the fundamental arising from the resonator itself rather than the bar. The spectrum for the C2 bar without the resonator in place does not have the beating pattern in the wave trace.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of C2 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 372 milliseconds. Note that this spectrum is much different than the first one. When the bar was struck in the center, there was no excitation of the second transverse mode. But when struck off-center at position 2, the second transverse mode is the strongest mode. When the bar is struck slightly off-center, the timbre is more consonant due to the strong presence of the second transverse mode, which is tuned to two octaves above the fundamental. In contrast, the third transverse mode is tuned to three octaves and a third above the fundamental. Therefore, a strong presence of the third transverse mode results in a timbre that is less consonant. Some performers prefer to strike the bar at position two because it yields a more consonant tone, particularly in the bass region. Also note that in this spectrum the fourth transverse mode is strong, while it was very weak in the center struck bar.

Wave trace of C2 bar hit off-center (position 2), resonator in place. In the top trace the waves of the fourth transverse mode are clearly seen. In the second trace (70 to 130 milliseconds) the waves of the fourth transverse mode are also evident, although they are not as strong. In this trace the pattern of the second transverse mode of vibration is also evident. In the region of 250 to 300 milliseconds (third trace) the last obvious vestiges of the fourth transverse mode are evident. After that point the only obvious waves are those of the second transverse mode. However, a careful examination of the bottom trace reveals a slight up and down pattern of the second transverse mode waves, indicating the presence of a weak fundamental.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of C2 bar hit off-center (position 3), resonator in place - sampled in the range of 0 to 372 milliseconds. When the bar is struck at position 3, the third transverse mode is excited to a greater degree than the other modes and this is evident in the spectrum above. In addition, the amplitude (strength) of the fundamental is the lowest (weakest) here since the mallet blow occurs near the node of the first transverse mode. As far as I know, it is not common for a performer to strike the bar in this location.

Listen to the timbre of the bar struck at position 3  (Windows Media format)

FFT Spectrum of C2 bar hit at end of bar, resonator in place - sampled in the range of 0 to 372 milliseconds. When the bar is struck on its end, all transverse modes are excited as is evident in the spectrum above. In this case the third transverse mode is strong but the second transverse mode is also relatively strong. Therefore, a strike at this position yields a timbre intermediate between a center strike and an off-center (position 2) strike. Keep in mind that the accidentals (sharps and flats) of the marimba are sometimes struck on the bar end. If you play this way, you should expect a slightly different timbre for the accidentals compared to the naturals. If you want the timbre of the naturals and accidentals to match exactly, then you will need to hit them in the same position (this may not always be possible, depending on the music you are playing).

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of F2 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 372 milliseconds. This spectrum is very similar to the spectrum for the C2 bar hit at the center. However, the amplitude of the first transverse mode for the F2 bar is more than twice the value of the C2 bar. Part or most of the amplitude increase is due to increased sensitivity of the microphone between 66 and 88 Hz (see graphic near top of page). But then, human hearing increases in sensitivity in this range as well. As far as the listener is concerned, the fundamental of the F2 bar is likely to be louder than the C2 bar. You can compare the two by using the link below, although a listening in person is the only true way to evaluate the relative intensity of each fundamental.

Listen to both bars struck at center, C2 first then F2   (Windows Media format)

Wave trace of F2 bar hit at the center, resonator in place. The FFT spectrum indicates that this bar does not vibrate in the second or fourth transverse modes when struck in the center. Therefore, only the wave patterns of the first and third transverse modes should be evident in the wave trace. That is exactly what can be seen in the trace above. The fundamental becomes evident in the middle of the second trace, around 85 milliseconds. At 245 milliseconds in the bottom trace, the third transverse mode is almost gone. Note here that the waves of the fundamental are more pronounced than in the C2 bar struck in the center, which is expected since the FFT spectrum indicates the same. There was a very weak fourth transverse mode in the C2 bar but not in the F2 bar. In the C2 bar, small peaks of the fourth transverse mode were evident during the first 15 milliseconds. There are no visible waves of the fourth transverse mode during the first 15 milliseconds in the F2 bar.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of F2 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 372 milliseconds. As in the C2 bar, the F2 bar has a strong second transverse mode when struck at position 2. However, the fourth transverse mode is weak in the F2 bar compared to a strong fourth transverse mode in the C2 bar. This is a trend that is similar for other modes as well. Moving higher on the keyboard, the higher modes diminish in strength. Additionally, the higher modes reach maximum strength early in the vibration cycle, while the fundamental reaches a maximum after the higher modes. Therefore, it is important to evaluate the relative strength of higher modes earlier in the cycle by keeping the FFT sample range shorter. This results in less accuracy in frequency determination but is necessary to get a picture of the spectrum shortly after the bar is struck. The next spectrum below is for a shorter sample range (below the wave trace).

Wave trace of F2 bar hit off-center (position 2), resonator in place. In the F2 bar the fourth transverse waves are evident but they are not nearly as obvious during the first 46 milliseconds as they were in the C2 bar. Again this is expected because the FFT spectrum indicates the presence of only a weak fourth transverse mode. Instead of a dominant fourth transverse mode during the early vibration cycle, here the waves of the second transverse mode are obvious. The second transverse mode can be seen even at the 600 millisecond point in the bottom trace.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of F2 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Note here that the 4th transverse mode is stronger shortly after the mallet blow, but still it does not have much amplitude. Therefore, at this point the 4th transverse mode ceases to contribute significantly to the timbre of the bar.

FFT Spectrum of F2 bar hit at end of bar, resonator in place - sampled in the range of 0 to 372 milliseconds. When the F2 bar is struck on its end, there is a strong mix of the first three transverse modes.

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of C3 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 372 milliseconds. At the position of the C3 bar on the keyboard, the sample range of 0 to 372 milliseconds is perhaps a bit long. Nevertheless, the spectrum is provided to allow comparison to lower bars. Now the analyses will shift to shorter sample ranges.

FFT Spectrum of C3 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 93 milliseconds. With a 93 millisecond sample range, it is evident that the third transverse mode is stronger. This is expected since the vibration of this mode damps out at a relatively quick rate after the mallet blow.

FFT Spectrum of C3 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 46 milliseconds. With the even shorter sample range of 46 milliseconds, it is evident that the third transverse mode is even stronger. Therefore, this mode contributes to the timbre of this bar only during the early part of the vibration cycle. This property holds for all of the bars. That is, the higher modes damp quicker than the lower modes. The higher the frequency, the quicker the damping of the mode. When examining a spectrum with a short sample range like this one (i.e. starting at time 0 and sampling for a short period), keep in mind that the relative strength of the higher modes decreases quickly after this sampling period, when the fundamental will dominate.

Wave trace of C3 bar hit at the center, resonator in place. Here the third transverse waves are strong during the first 40 milliseconds of the vibration cycle and thereafter quickly recede into obscurity. Unlike the C2 and F2 bars, the C3 bar has a clearly evident wave pattern of the fundamental as early as 20 milliseconds after the mallet blow.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of C3 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Here the second transverse mode is strong in the C3 bar when struck at position 2. The fourth transverse mode is also present but at low amplitude.

Wave trace of C3 bar hit off-center (position 2), resonator in place. In this wave trace the second transverse waves appear immediately after the mallet blow and die out around 170 milliseconds. The third transverse waves can also be seen, with the last vestiges between 70 and 80 milliseconds. The fundamental starts to appear around 30 milliseconds and is clearly the dominant mode starting in the zone of 60 to 70 milliseconds.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of C3 bar hit at end of bar, resonator in place - sampled in the range of 0 to 46 milliseconds. Here again there is a mix of the first three transverse modes when the bar is struck on the end.

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of F3 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 46 milliseconds. The third transverse mode continues to be prominent in the F3 bar with a center strike. However, between this point and C4, the third transverse mode fades to an insignificant role.

Wave trace of F3 bar hit at the center (position 1), resonator in place. The third transverse waves are clearly evident in this trace and dominate the spectrum during the first 20 milliseconds. Starting around 20 milliseconds the pattern of the fundamental becomes obvious. The third transverse waves drop to an insignificant role around 95 milliseconds. There is what appears to be a strong damping of the third transverse mode in the zone of 45 to 60 milliseconds followed by a recovery. The cause of this is the presence of another frequency near the frequency of the third transverse mode, which is alternately adding to and subtracting from the wave amplitudes of the third transverse mode. This is a continuation of the pattern seen during the first 20 milliseconds, where the amplitude of the waves is cycling between higher height and lower height. The source of this interfering mode has not been determined at this time.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of F3 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Notice here that there is no detectable vibration in the fourth transverse mode in this bar. Attempting to tune this mode in this bar would be a futile exercise.

Wave trace of F3 bar hit off-center (position 2), resonator in place. The waves of the second transverse mode have a strong presence immediately after the mallet blow, building to maximum amplitude between 20 and 30 milliseconds. Between 250 and 300 milliseconds the second transverse mode fades to an insignificant role and then there is mostly a weak fundamental vibration.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of F3 bar hit at end of bar, resonator in place - sampled in the range of 0 to 46 milliseconds. When the F3 bar was struck on the end the second transverse mode was clearly the dominant mode in the early vibration period. Since there was a strong third transverse mode in the center-struck bar, a significant peak should be expected here as well. But there is a very weak peak for the third transverse mode. The cause of the weak third transverse mode is unknown to me.

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of C4 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 46 milliseconds. At middle C it is clear that the third transverse mode is fading in importance.

FFT Spectrum of C4 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 23 milliseconds. Here the sample time is reduced to half the above spectrum to show that the third transverse mode is significant only during the very early part of the vibration cycle. This can also be seen in the wave trace below.

Wave trace of C4 bar hit at the center (position 1), resonator in place. In this trace the waves of the third transverse mode are clearly evident early in the vibration cycle. However, they fade to insignificance between 10 and 20 milliseconds. The fundamental becomes obvious as early as 5 milliseconds after the mallet blow in this bar. The presence of the third transverse mode over such a short period of time contributes to the low peak seen in the FFT spectrum of 0 to 46 milliseconds.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of C4 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Even at middle C the position of the mallet blow is still important. A strike off-center still results in a much stronger second transverse mode compared to a strike at the bar center. However, also note that the fundamental is starting to dominate the spectra. The very strong second transverse mode seen in the lower bars is now starting to decrease. Farther up on the keyboard the second transverse mode will no longer be a significant contributor to the bar timbre. That is the region where only the fundamental is tuned.

Wave trace of C4 bar hit off-center (position 2), resonator in place. Waves of the second transverse mode appear immediately after the mallet blow but begin to decline rapidly 20 milliseconds after the mallet blow. By the time of 70 milliseconds, the spectrum is totally dominated by the fundamental.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of C4 bar hit at end of bar, resonator in place - sampled in the range of 0 to 46 milliseconds. When the C4 bar is struck on the end the spectrum is remarkably similar to the spectrum obtained with a strike at position 2.

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of F4 bar hit at the center (position 1), resonator in place - sampled in the range of 0 to 46 milliseconds. The journey up the keyboard has reached the point where only the fundamental is present with a center strike.

Wave trace of F4 bar hit at the center (position 1), resonator in place. The nearly pure sine wave in this trace indicates as well that this bar vibrates almost completely only in the fundamental mode with a center strike.

Listen to the timbre of the bar struck at the center (Windows Media format)

FFT Spectrum of F4 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Even when the bar is struck off-center, there is very little contribution from the second transverse mode. This is the region of the keyboard where the fundamental is the only important transverse mode, regardless of the position of the mallet strike.

Wave trace of F4 bar hit off-center (position 2), resonator in place. The second transverse mode is seen early in this wave trace as humps and distorted peaks on the fundamental waves. Clearly the fundamental is the completely dominant mode.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of F4 bar hit at end of bar, resonator in place - sampled in the range of 0 to 46 milliseconds. The spectrum here is very similar to the spectrum for the off-center strike. Therefore, the timbre of this bar will essentially be the same when struck off-center and at the bar end.

Listen to the timbre of the bar struck at the end (Windows Media format)

FFT Spectrum of C5 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. The C5 and F5 bars were recorded in a separate session from the rest of the bars, using a different mallet and different player. It is apparent that these bars were struck with more force than used by the other player. Thus, the amplitudes of the waves are higher. Nevertheless, the data is important in analyzing the vibrations higher on the keyboard. The fundamental of this bar is dominant, even when struck at a position where maximum excitation of the second transverse mode occurs.

Wave trace of C5 bar hit off-center (position 2), resonator in place. The second transverse waves are stronger here than in the F4 bar. Whether this is due to the intrinsic properties of the bars or due to a stronger mallet blow is unclear. Nevertheless, it is clear that the second transverse mode has a minor influence at best on the bar timbre.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)

FFT Spectrum of F5 bar hit off-center (position 2), resonator in place - sampled in the range of 0 to 46 milliseconds. Comparing the F5 bar to the C5 bar, it is evident that the fundamental is growing in amplitude while the second transverse mode is receding. At this point the second transverse mode clearly has little or no influence on bar timber.

Wave trace of F5 bar hit off-center (position 2), resonator in place. The wave trace shows that the second transverse mode is present to a moderate degree only during the first 5 milliseconds after the mallet blow.

Listen to the timbre of the bar struck slightly off-center (position 2) (Windows Media format)