Microtonal Musical Robot

<Trumpeter>

 

a robotic Bb trumpet designed and made to the order of Alain Van Zeveren

dr.Godfried-Willem RAES

2021

Robot: <Trumpeter>

When starting the design and construction of this musical robot, we could build further on the experiences gained through the realization of quite some automated brass instruments build since 1999: <So>, a sousaphone, <Korn>, a cornet, <Heli>, a helicon, <Bono>, a valve trombone and <Horny>, a French horn, <Bug>, a fluegelhorn and <Hunt>, a hunting horn.. This new robot, an automated trumpet, was designed and constructed to the order of Alain Van Zeveren. Musically speaking the cornet, the trumpet and the flugelhorn are very similar instruments, differing only in the timbre they produce. The flugelhorn is said to sound more mellow than the trumpet, the cornet finding a place in between. The ambitus, for Bb instruments, is the same.

Thus it made sense to start the design of this robot by examining the <Korn> and <Bug> robots and improving over them where ever possible. Main improvements we envisaged here were the sound volume, the attack characteristics and the speed of response, in particular for the valves. Again we used a membrane compressor directly coupled to the trumpet via a capillary comprised in one of the original mouthpieces that came with the instrument. The mouthpiece we first selected was one made in the Soviet Union designed specifically to facilitate sounding the highest registers of the trumpet. However, the metal alloy is was made from, caused it to explode into pieces in turning it on the lathe. That was the end of it. So we reverted to a standard completely orthodox trumpet mouthpiece. The motor driver causes resonance in the trumpet tubing, but in this case there is no unidirectional windflow through the instrument. When a note is requested from the trumpet, the firmware will calculate the optimum valve combination -including non orthodox fingerings- for the requested pitch. Thus a resonant standing wave in the instrument can be produced. Microtonal pitches are implemented such that the instrument is capable of performing quartertone music, as well as a wide range of different tunings and temperaments with great perfection. The relatively low Q-factor of the horn (compared to strings...) as an acoustic resonator renders this very well possible. The signal generated in the motor was shaped after a physical model of the air pressure waveform in the mouth cavity of a player. (Beauchamp, 1975,1980). Since there is no loop coupling from the resonator to the generator, the sound generation mechanism is a hybrid somewhere between synthetic/electronic and natural/acoustic. The advantage being that the reliability of the robot becomes very high, but this is obtained a bit at the detriment of realism, in particular with regard to the onset of the sounds, A dynamic formant filter was added using analogue electronic circuitry, in this case a pair of germanium diodes in series with a resonant LC circuit Thus the sound color will be to a certain extend a nonlinear function of loudness, conform to acoustic reality.

The valves are used in this instrument to tune the fundamental frequency of the instrument. The valves can be controlled independently from the mouth driver frequency. They are mechanically driven by unipolar push solenoids (Banggood types made in China, to save on cost) and use the return springs provided in the pistons in addition to the spring on the solenoids. Furthermore we mounted the trumpet upside down such that gravity also helps improving fingering speed. The notes that are normally produced using different valve combination, following theory are: Note that this is untransposed, so in reality everything will sound a full tone lower on a Bb instrument. However, we found out that using the valve combinations entailed by this system, does not lead to optimum resonance in the instrument. Thus we used the optimal valve combinations based on empirical acoustic measurement. A deficiency we encountered in our <Korn> robot was that the buildup of a sound pressure wave in the instrument was anticipating the valve movement. The valves take about 10 ms to take position, thus here we delayed the driver signal with the same amount in all cases where changes of fingering are involved. This introduces some latency but makes the sound quite a bit more realistic, in particular for the attack portion of the envelope. This idea was first implemented and fully tested on the <Bug> robot.

As we had to save as much as possible on cost, we dropped all movement from the design. Thus the construction was a lot less involved than that of the <Bug> robot.

The electronic circuitry -in overview- consists of only two 'intelligent' PC-boards:

Overview:

1. Midi-hub board: This board, using a Microchip 18F2620 controller, takes care of the Midi I/O handling and communication as well as the control of the three valves. The circuit for the pulse/hold function here follows a recipe we applied nearly one hundreth times by now: The PCB board, is a completely new design and can in principle be applied for just about any brass instrument to be automated.

2. Sound generator board: This board steers the 75 Watt motor compressor horn driver via a digital audio amplifier module. A 16-bit processor is used to generate the required waveform and two analog multipliers are used for envelope shaping and amplitude modulation. Thus we could maintain audio resolution even at the lowest soundlevels. Handling this in the full digital domain would have required a 32-bit processor. The analog dynamic formant filter also found a place on this board.

The power amp is a pure analogue design, using a high quality but by now obsolete LM12 power opamp, in a 5-pin modified TO3 package, rated for 150 Watt: We designed it back in 1991 (in fact to be used as a powerfull ac source for tape-recorder motors), but copies of it were used also for robots such as <So> and <Hunt>.

A note on the compression driver:

The longer we make the capilary and the smaller its diameter, the more will the mechanism reveal the true resonances and timbre of the instrument driven. However, the more we do that, the more power is required from the driver, and obviously only drivers with finite power are available... The compression ratio ought to be 1:50 at least. In no case should the diameter of the capilary be larger than the smallest diameter internal in the original mouthpiece of the instrument. A compression plate, as drawn, is not present in all makes of compression drivers. The Padu driver we favor to use, has one. Here is a picture: And, on the following picture it can be seen with the membrane and the voice coil in place: Note that making these internal guts visible this way, is a deadly operation for the compressor. The capton membrane with voice coil is glued to the front assembly. We did it on a burned out compressor that we took apart for close examination.. The construction with the compression plate helps a lot in suppressing own resonances occuring in the compression chamber. No physical air distance inside the compressor is larger than a half wavelength of the soundwaves corresponding to the highest frequencies the driver can produce. Here is a frontal view on the capton membrane: The voice coil is on the other side.

Power supply voltages and currents:

 

Midi Mapping and implementation:

Midi channel: 12 (fixed in the firmware)
Midi note range: 52 to 94. (Optimum sound in the range 66-89) Note on, velocity is implemented and steers the level of the sustain phase in the adsr. We may implement the pedal notes as well, in which case the range would get the extra notes 40 to 46, with a gap between 46 and 52.

Note Off commands are required, but can be dropped for pure legato playing. Note off with release is implemented and can steer the release phase of the envelope. Note Off commands for notes that were not sounding are disregarded.

Controllers:

Controller 1: Noisiness of the sound [default = 20]

Controller 3: FM modulation depth (vibrato depth). Large values can cause audible artifacts, due to the modulation of the sampling frequency.

Controller 4: FM modulation speed. (vibrato speed)

Controller 5: AM modulation depth (tremolo depth)

Controller 6: AM modulation speed (tremolo speed)

Controller 7: used as a general volume controller. Note that timbre will change as the volume is changed. On high settings, the formant frequency becomes more dominant. [default = 100]

Controller 13: allows changes of valve fingering during sounding notes. Bit 0 corresponds to the 1/2 tone valve, bit 1 to the 1 tone valves, and bit 2 to the 3 semitone valve. Using this controller it is also possible to change the fingering for a sounding note whilst it is sounding, thus rendering some sound coloration possible without changing the actual pitch.

The table below gives all details:

Ctrl 13 Value -1/2t -1t -1 1/2t
0 off off off
1 on off off
2 off on off
3 on on off
4 off off on
5 on off on
6 off on on
7 on on on


Controller 15: ADSR-period [default 40]
Controller 16: used to control the duration of the attack phase in the ADSR cycle. [default 16]
Controller 17: set the level of the attack of the sound defined as the extra boost above the sustain level set with the velo byte.[default 127]
Controller 18 is used to control the duration of the decay after the attack, the time required to reach the sustain level of the sound. [default 18]
Controller 19 steers the duration of the release decay (from sustain level to zero) starting after reception of a note off command. Release will we canceled or interrupted with a new note on command if such a command comes within this time. [default 64]

The interdependencies of these controllers together with the velo byte is shown in the graph below:

Controller 20: Tuning. To be implemented.

Controller 20 - tuning for the trumpet. By default equal temperament and A = 440 Hz for value 64. Acceptable values for this controller are limited to:

 

Controller 26: This controller steers the time the valves stay in their position after reception of a note-off command. This implements some resonance in the instrument after the excitation from the mouthpiece has stopped. It also avoids unnecessary mechanical noise from the valves, in particular on repeated notes or notes that can be produced with the same valve combination.

Controller 66: Power on/off switch (0 = off, any other value is on). Power off also resets all controllers to their default startup values. Also resets the program change to the default startup setting.

Controller 80: Dynamic range mapping. The default is 64, resulting in a 40dB dynamic range.

value mapping
0-30 20dB
31-62 30dB
63-94 40dB
95-126 50dB
127 60dB
Note that increasing the value of controller 80 and thus the dynamic range does not make the sound volume at its maximum any higher! The dB mapping steers the dynamic range, starting from the absolute maximum. So, if set to 64, corresponding to 40dB, the loudest and the softest volume levels will relate to each other as 100. Or, dynamic value 1 will be at -40dB compared to the maximum value 127. Here the maximum value is defined as 0dB.

Controllers 100, 101, 102, 103: parameters for waveshape. Program change must have been set to Parametric1 in order for this to work. It is mandatory that Ctrl100 < Ctrl101 < Ctrl102 < Ctrl103. After reception of controller 103, the wave table will be recalculated. Following graph describes the waveform and its parameters:

Controller 104: parameter for setting the symmetry when Program Change has been set to Smoothsquare prior to setting the controller value. Value 64 makes a symmetric square. Valid values are between 1 and 126.

Controllers 105 and 106: parameters for the minimum and maximum points of a triangle wave. Program Change must have been set to sawtooth prior to sending these controller values. The parameters will be clear from following waveform graph: The wave tables will be recalculated after reception of the second parameter.

Controller 107: parameter for the pulsewidth: range 2 - 126. The graph illustrates the parameter:

Controller 108: parameter for setting the symmetry when Program Change has been set to Assin prior to setting the controller value. Value 64 makes a symmetric sinewave. Valid values are between 1 and 126. The graph illustrates the parameter:

Controller 109: parameter for setting the symmetry when program change has been set to DirtAssin prior to setting the values of the two controllers.

Controller 110: parameter to set the level of noisiness in the waveform. The wave table for the DirtAssin program will only be recalculated after reception of this controller.

Controller 123: switches the sounding note off, unpowers the steppers, dims all the lights.

Program change: implemented to change the wavetable in use for the sound excitation. Following waves are implemented, using the lowest 4 bits of the value.:

Values > 15 (using the 3 highest bits) are used to change the lookup tables in use for the valve combinations. So far following programs are implemented:

Program change commands take some time as the microcontroller recalculates them on the fly. Therefore they should not be issued whilst the robot is playing notes as audible glitches in the sound may occur.

Pitch bend: The <Trumpeter> robot can be used in any tuning system. In the drawing below we give the coding example for a quartertone scale:

Most good sequencer software (such as Cakewalk or Sonar) uses the signed 14 bit format. Note that one unit of the msb corresponds exactly to a 0.78 cent interval. To convert fractional midi to the msb only pitchbend to apply follow following procedure: if the fractional part is <= 0.5 then msb= 63 + (FRAC(note) * 128), if the fractional part is larger than 0.5, we should switch on the note + 1 and lower the pitch with msb= (1-FRAC(note)) * 128. Note off does reset the pitch bend for the playing note! The resolution implemented on <Trumpeter> for pitch bend (and vibrato) is limited to 1/10th of a semitone.

 

Technical specifications:

Design, research and construction: dr.Godfried-Willem Raes (2021)

Collaborators on the construction of this robot:

Music composed for <Trumpeter>:

 

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Last update: 2021-06-12 by Godfried-Willem Raes

The following information is not intended for the general public, but is essential for maintenance and servicing of the robot.

Technical drawings, specs and data sheets:

Compression driver unit: Model PADU 100, power rating 100W, impedance 16 Ohms. (Made in China) We have measured this component carefully when making <Asa> and found the impedances in function of applied frequency as follows:11.4 Ohms @ 100Hz, 23.68 Ohms @ 1kHz, 26.7 Ohms @ 10kHz and 45 Ohms @ 25kHz. The acoustic load does influence the measured impedance at 1kHz over a 1:2 range: with the mouth completely closed it measures 32.8 Ohms and with the mouth completely opened but without any resonator, 15.35 Ohms. This phenomenon does not occur for the very low neither for the very high frequencies. The measurements were performed in 2016 with our Hameg LCR meter, model HM8018. The frequency response is 100Hz to 10kHz. The thread for mounting is 1 3/8"-18 TPI.

Valve lookup tables (according to acoustic theory)

Power supply:

Circuit drawing for the valve control and MIDI hub board:


Firmware for the hub board:

PCB for this hub board designed for 3 or 4-valve brass instruments:


[scale 200%]

Power supply modules for this board:

Compressor driver board (monophonic synth with acoustical modelling)::

Circuit drawing:

PCB for this circuit: [scale: 200%]

Soldered board:

 

References:

Beauchamp, J.W. "Analysis and Synthesis of Cornet Tones Using Nonlinear Interharmonic Relationships". In: j-aes, volume 23, number 10, pages 778--795, 1975.

Beauchamp, J.W., "Analysis of Simultaneous Mouthpiece and Output Waveforms of Wind Instruments" . In: j-aes, 1980, Preprint No. 1626,

Benade, Arthur .H., "Fundamentals of Musical Acoustics". Ed.: Oxford University Press, 1976.

Fletcher, N.H. & Tarnopolsky, A. "Blowing pressure power and spectrum in trumpet playing" In: J. Acoust. Soc. Am., volume 105, number 2, part 1, 1999.

Martin, Daniel W., "Lip vibrations in a Cornet Mouthpiece", In: J.Acoust.Soc.Am. vol13 . 1942

Raes, Godfried-Willem, "Kursus Akoestiek", Ghent University College 1982/2014, Internet: http://www.logosfoundation.org/kursus/4023.html

Raes, Godfried-Willem, <Bug> an automated Fluegelhorn, 2016.

Raes, Godfried-Willem, "Expression control in musical automates", 1977/2021,

Raes, Godfried-Willem, "Logos @ 50, het kloppend hart van de avant-gardemuziek in Vlaanderen", ed. Stichting Kunstboek, 2018

Rose,Nicholas and Holloway, Damien, "Finite element modeling of brass musical instruments', in: Proceedings of Acoustics, Fremantle, Australia 2012.

Smith, Bob H., "An Investigation of the Air Chamber of Horn Type Loudspeakers", in: The Journal of the Acoustical Society of America 25, 305-312 (1953); https://doi.org/10.1121/1.1907038


Cost calculation for <Trumpeter>:

1. Parts and components

Bb trumpet made in GDR (German Democratic Republic)
p.m.
Steel 2 Euro/kg  
Solenoids 3 Banggood 12V, 1.5 Ohm
99.00
Trumpet mouthpiece, Maheu 1
38.00
Membrane Compressor 100W 1 (Padu driver, 1 3/8" 18TPI mounting thread)
210.00
35 mm nut (1 3/8" - 18 TPI) 1 (for tightening with a 35-50 mm hook wrench)
27.00
Brass staff-material 100 mm
3.00
Soft PVC endcaps 3
0.60
M4 shock absorbers MF 12
36.00
M4 x 8 cilinder bolts 15
9.50
LM12 amplifier 150W sine 1
150.00
Mean Well SMPS 7.5V 20A 1
75.00
Mean Well SMPS 5V 20A 1
75.00
Polo, PCB-films 2  
Mirargent, silver paint 1 small jar
6.80
Blue polyacrylate, plexiglass 1 piece
2.50
     
     
M3 x 20 cilinder bolts and nuts 10
9.00
M3 x 35 cilinder bolts and nuts 10
10.00
M4 x 20 cilinder bolts and nuts 10
7.00
M4 x 16 hex bolts and nuts 8
6.00
M 4 x 35 hex bolt and nut 4
4.00
M5 x 10 cilinder bolts and nuts 2
1.00
M5 x 25 cilinder bolts and nuts 8
8.00
M4 x 10 hex bolts and nuts 8
5.00
M6 x 45 countersunk bolts and nuts 10
15.00
M6 x 16 hex bolts and nuts 5
4.00
M6 x 25 hex bolts and nuts 2
1.00
M6 x 120 hex both and nut 1
3.00
M8 x 25 cylinder bolts and nuts 4
8.00
M8 x 30 cylinder bolts and nuts 10
10.00
M8 x 40 cylinder bolts and nuts 10
11.00
M12 x 35 cylinder bolts and nuts 3
4.00
Cyanoacrylate glue 1 (Loctite 401, 3g)
4.00
PCB Hub board 3 analog in, 4 pulse/hold outputs, 3 outs, midi-in, differential thru, TTL midi out PIC 18F2620, 5V power supply module, Weidmueller connectors
355.00
PCB Generator board 2 16 bit PIC 24EP128MC202, 3 op amps, 2 multipliers, Weidmueller connectors, 1% precision resistors, 4 inductors
435.00
IEC Mains power entry Schaffner FN-372 6 (230V - 6A)
7.00
Toggle switch power on/off 230V / 3A
5.00
Faston connectors, blue 35, power supply wiring
11.00
Wire 25 m, 0.75 mm2, 1.5 mm2
6.00
Waco connectors, snap in 2 5-contacts
3.00
Wiring 30 m of mounting wire in coded colors
18.00
Heatshrink tube Polyolefine 1 m
6.00
Felt for mounting and dampening
2.00
     
Subtotal:  

2. Consumables

Cobalt 3mm drill bits 1
3.50
Cobalt 4mm drill bits 1
3.80
Cobalt 5mm drill bits 1
4.00
Cobalt 8mm drill bits 1
9.00
TIG welding materials Argon gas and Tungsten electrodes
50.00
Cutting disks 12 (A60 T-BF41 125 x 1.0 x 22.2
40.00
Sanding disks and paper  
18.00
Grinding disk 1
5.00
TIG welding nozzle, nr.5 1
12.00
Cutting oil (spray can) 1
1.00
Solder Pb/Sn 40/60 5 m
5.00
Steel welding electrodes 10 3.2 mm
8.00
Aceton 0.5 l
4.00
Etching baths Fe2Cl3 1 liter
5.00
Methanol 0.25 l
2.00
NaOH sollution 0.5 l
1.00
Subtotal:  

3. Depreciations on tools and equipment used (calculated over 1 month)

Tool Value Depreciation percentage / month
Tektronix TDS2024C 3500 2.77%
97.00
TIG welding equipment 2000 2.77%
55.00
Contimex Lathe 2500 2.77%
69.50
Cobalt saw 2800 2.77%
77.50
Soldering equipment 1000 2.77%
27.50
Proton+ Laptop & ICD 1800 2.77%
25.00
Lab power supply 380 2.77%
5.00
Odin column drill 6000 0.92%
27.50
Welding table 2500 0.92%
11.50
Subtotal:    
395.50

4. Labor and design (45,-/hour)

02.06.2021 8 h
360.00
03.06.2021 3 h
135.00
04.06.2021 3 h
135.00
05.06.2021 7 h
315.00
06.06.2021 3 h
135.00
07.06.2021 30'
22.50
08.06.2021 30'
22.50
09.06.2021 2 h
90.00
10.06.2021 30'
22.50
11.06.2021 4h
180.00
Subtotal:  
xx.00

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