Identifying and Tuning Lateral and Torsional Modes in Marimba barsPart Two - Identifying and Measuring the ModesJeff La Favre
|
In the graph above, we can identify a number of potential problems. For most of the bars between C2 and C4, the ratios for the first lateral mode and the third transverse mode are very close. On the left side of the graph, the second torsional mode is also close to the third transverse mode, while on the right side it approaches the second transverse mode. The third torsional mode approaches the third transverse mode on the right side of the graph. The first torsional mode may also appear to be close to the fundamental, but this is not a problem, as I discuss on a page dedicated to the first torsional mode. Now that we have identified some potential problems, we must investigate further in order to establish which bars, if any, have problems (we have already discussed the problematic A2 bar). Primarily, we must establish whether or not the potentially problematic bars vibrate with a significant lateral or torsional mode under performance conditions. In order for a problem to exist, the lateral or torsional mode must vibrate with enough intensity to interfere with a tuned transverse mode. When these conditions are found, a tuning of the offending mode should be considered. In order to determine if the lateral or torsional mode of concern does or does not cause a problem, audio recordings of the bars struck at different positions were analyzed by FFT. The wave traces of the recordings were also examined with the purpose of finding any beating patterns in the traces.
Finding the problem barsThis portion of the study is not complete at this time. Nevertheless, some helpful data are presented below. In the lower register (C2 to C4) the second torsional mode does not cause any problems with the third transverse mode. The C2, D2 and E2 bars have second torsional modes and third torsional modes that are separated by less than 1.1 times the critical bandwidth. However, the peak amplitudes of the second torsional modes are below 20% of the respective third transverse mode amplitudes. Therefore, no retuning of the second torsional mode is needed. The second torsional mode of the F2 bar does not meet the tuning standards and a retuning is indicated in the table. However, the third transverse mode for the F2 bar is relatively low, indicating a possible problem with the mallet blow. Further testing is needed before condemning the second torsional mode in the F2 bar. When we reach the G2 bar, the interval between the second torsional and third transverse modes is greater than 1.1 times the critical bandwidth. The interval continues to grow in the A2 and B2 bars. Therefore, past the F2 bar, there is no need to retune the second torsional mode on the basis of critical bandwidth (paired with the third transverse mode).
The first lateral mode does cause a number of problems in the range of C2 to C4, as is evident in the table below. All bars in the range are listed in the table if their spectra had a peak for the first lateral mode when struck at the center-edge or the bar center. Bars D2, E2, F3, A3, B3 and C4 did not have a peak in their spectra for the first lateral mode. However, that does not mean that the first lateral mode is never active in these bars during a performance. Further testing is needed to confirm that these bars never vibrate to any significant degree during a performance of the instrument.
|
First Lateral and Third Transverse Modes FFT Spectra |
|||||||||||
Bar
|
Bar struck
at center-edge
|
Bar struck
at center
|
Critical Bandwidth
x 1.1
(Hz) |
Retune?*
|
|||||||
1st Lateral
|
3rd Transverse
|
1st Lateral
|
3rd Transverse
|
||||||||
Frequency
(Hz) |
Peak Amplitude
|
Frequency
(Hz) |
Peak Amplitude
|
Frequency
(Hz) |
Peak Amplitude
|
Frequency
(Hz) |
Peak Amplitude
|
By CBW
|
By Amplitude***
|
||
C2 |
790 [786]
|
140
|
666
|
1012
|
NP
|
NP
|
666
|
4285
|
136
|
yes
|
no
|
F2 |
904 [907]
|
159
|
888
|
398
|
908
|
490
|
888
|
2881
|
162
|
yes
|
no****
|
G2 |
980 [991]
|
695
|
1000
|
1314
|
MP?
|
MP?
|
999
|
3115
|
176
|
yes
|
yes
|
A2 |
1091 [ND]
|
826
|
1121
|
617
|
1090
|
1400
|
1121
|
1982
|
194
|
yes
|
yes
|
B2 |
1213 [1219]
|
134
|
1261
|
232
|
1213
|
131 |
1261
|
876
|
214
|
yes
|
yes
|
C3 |
NP
|
NP
|
1335
|
378
|
1265 [1279]
|
279
|
1335
|
1038
|
223
|
yes
|
yes
|
D3 |
1410 [1410]
|
69
|
1510
|
171
|
1408
|
149
|
1499
|
234
|
248
|
yes
|
yes
|
E3 |
1610 [1604]
(1645)** |
59
(85)** |
1693
|
237
|
1645**
|
232
|
1693
|
555
|
277
|
yes
|
yes
|
G3 |
1960 [1965]
|
104
|
2016
|
487
|
NP
|
NP
|
2019
|
198
|
328
|
yes
|
yes
|
*The decision to retune is based on the critical bandwidth and the relative peak amplitude of the first lateral mode compared to the third transverse mode. A retune is not needed if either the critical bandwidth or the peak amplitude indicate no need for retuning. **This frequency does not match the frequency found for the first lateral mode by striking the side of the bar. The assignment of this frequency to a mode is therefore in question, but the first lateral mode appears to be the best fit. There are two frequencies (1610 and 1645) present in the center-edge struck spectrum that might be assigned to the first lateral mode. ***Amplitude of first lateral mode must be more than 20% of third transverse mode to retune by peak amplitude ****Amplitude data for center struck bar do not indicate a need to retune NP = no peak in the spectrum ND = not determined MP? = possible merged peak, the first lateral and third torsional frequencies may be too close to separate into two peaks frequencies in brackets [ ] are the first lateral mode as determined by a strike on the side of the bar at the bar end. |
Continue to Part Three - Tuning the Modes (13 images, 0.48 MB total) Part One - Establishing Tuning Standards (36 images, 1.17 MB total) Part Four - Lateral and Torsional Modes for Bars D4 through C7 Description of some methods used in the study Last update: 3/24/07 © 2007 Jeffrey La Favre |