Microtonal Musical Robot

<Cornalto>

 

a robotic Eb alto saxhorn designed and made to the order of Alain Van Zeveren

dr.Godfried-Willem RAES

2021

Robot: <Cornalto>

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, <Hunt>, a hunting horn, and <Trumpeter>, the latter also made on request for Alain Van Zeveren. Musically speaking the cornet, the flugelhorn as all saxhorns are very similar instruments, differing only in the timbre they produce. They all have a conical bore and are said to sound more mellow than the trumpet, the trombone and other brass instruments with a cylindrical bore. The ambitus of the alto saxhorn however is considered to be quite a bit more limited, the lowest notes being never used. The textbooks mention 2 1/2 octaves at the most. The alto is in fact not really a horn, although called altohorn ('althoorn' in Dutch), but a saxhorn like the tuba. Before the second world war, the alto was constructed in the shape of a horn (circular). Later on its shape became prevalent as that of the tuba, the barytone and euphonium.

Thus it made sense to start the design of this robot by examining the <Trumpeter > robot and improving over this one where ever possible. Again we used a membrane compressor directly coupled to the saxhorn via a capillary. In this case we could not use the original mouthpiece that came with the instrument as it didn't have a large enough cylindrical part that we could make fit the membrane compressor. Thus we had to turn a new one on the lathe. The internal sizing conforms to the original mouthpiece and is just a little smaller sized in the capilary section. The motor driver causes resonance in the horn tubing, but in this case there is no unidirectional windflow through the instrument. When a note is requested from the horn, 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, the return springs on the solenoids were removed. Furthermore we mounted the saxhorn 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 minor thirth higher on an Eb instrument. However, we found out that using the valve combinations entailed by this system, does not always 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. It is also implemented in our <Trumpeter> robot and in this one.

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 moving brass robots <Bug>, <Korn>, <Horny> and <Hunt>.

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 new design used for the first time for the <Trumpeter> robot. It can in principle be applied for just about any brass instrument with up to four valves to be automated.

The source code for this processor is here.

The hex-dump for programming the PIC processor using MPLAB IPE is here.

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 (introduced bij National Semiconductor in 1988), 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 <Autosax>, <So>, <Hunt> and <Trumpeter>.

A note on the compression driver:

see what we wrote on that topic on the <Trumpeter> page.

Power supply voltages and currents:

 

Midi Mapping and implementation:

Midi channel: 12 (fixed in the firmware)
Midi note range: 45 to 87. (Optimum sound in the range 54-82) Note on, velocity is implemented and steers the level of the sustain phase in the adsr. We did not implemented the acoustic pedal notes 33 to 39 as they are extremely difficult to sound. Thus the implemented range is now continuous starting from note 45.

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 (valve 2) -1t (valve 1) -1 1/2t (valve 3)
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
Controller 16: used to control the duration of the attack phase in the ADSR cycle.
Velocity byte = attack level
Controller 17: sustain level
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.
Controller 19 steers the duration of the release decay (from sustain level to zero) starting after reception of a note off command. Release will be canceled or interrupted with a new note on command if such a command comes within this time.

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

 

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

 

Controller 25: Steers the attack force for the valve solenoids.
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 33: Selects different lookup tables for the fingerings. The default value 0 corresponds to our own findings in terms of optimal resonance. This lookup table differs quite a bit from the theory-book fingerings used for an Eb instrument. Controller value 3 corresponds to the official fingering for an= high Eb alto horn. By setting this parameter to 9, the robot would use a lookup table as if it were an A-horn. With value 12, it would finger for a C-instrument . Note that we do not treat the instrument as a transposing instrument! Acceptable value for this controller are limited to the range 0 to 12. On cold boot, this controller is always set to zero.

Controller 40: Selects the waveform used for the pedal tones, notes 40 to 46. The default setting here is 6. A good alternative could be 0.
Controller 41:Selects the waveform used for the low register, notes 52 to 71. The default setting here is 6.
Controller 42: Selects the waveform used for the medium register, notes 72 to 82 . The default setting is 1. Good alternatives are 6, 0 or 11.
Controller 43: Selects the waveforn used for the high register, notes 83 to 94. The default setting is 3. Good alternatives are 0,6,1

Waveforms implemented for these four controllers:

0 Beauchamp parametric, acoustical modelling

4 parameters: CC100, 101, 102,103

the default settings are respectively 27,83,96,110

1 Wave_1, excitation wave  
2 Square Wave 1 parameter: CC104, default setting is 42
3 Wave_3, excitation wave  
4 Triangle wave

2 parameters: CC105, CC106

default settings: 42, 85

5 Sawtooth  
6 Wave_6, excitation wave  
7 Sine wave added for research purposes
8 Sinx/x tophat  
9 Squared Sine  
10 Sin3 this one tends to sound an octave lower.
11 Beauchamp textbook, acoustical modelling  
12 Pulse wave

1 parameter: CC107

default setting: 8

13 Asymetric sine wave

1 parameter: CC108

default setting: 64 (with this setting, a pure sine is produced)

14 Dirty asymetric sine wave (with noise)

2 parameters: CC109, CC110

default setting for the parameters: 20 and 64

 


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 wave tables to the default startup settings.

Controller 80: Dynamic range mapping. The default is 62, resulting in a 30dB 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. Note that changing this controller affects all amplitude related parameters, including the ADSR and the tremolo.

Controllers 100, 101, 102, 103: parameters for waveshape parametric Beauchamp. . This applies to Wave0. 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 waveform 2 is selected. 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, selectable with waveform 4. The parameters will be clear from following waveform graph:

Controller 107: parameter for the pulsewidth. This is waveform 12. The range for the parameter is 2 - 126. The graph illustrates the parameter:

Controller 108: parameter for setting the symmetry when waveform 13 has been selected. This is an assymmetric sinewave. 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 Waveform has been set to 14 (dirty assymmetric sine wave) .

Controller 110: parameter to set the level of noisiness in the waveform 14.

Controller 123: switches the sounding note off.

 

Pitch bend: The <Cornalto> 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 <Cornalto> 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 <Cornalto>:

 

Back to composers guide to the M&M robot orchestra.

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Construction & Research Diary:

 

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Last update: 2021-09-21 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%]

Soldered board:

Power supply modules for this board:

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

Circuit drawing:

PCB for this circuit: [scale: 200%]. An improved PCB for later versions is available. The placement of the formant filter components was subject to improvements.

Current drawn by this board 310mA @ 5V supply.

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

National Semiconductor Corporation, "Linear Databook 1", p.2-272 -2-285 (LM12), 1988 Edition.

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 <Cornalto>:

1. Parts and components

Eb alto saxhorn  
p.m.
Steel 2.5 €/kg
Solenoids 3 Banggood 12V, 1.5 Ohm
99.00
Membrane Compressor 1 Atlas driver, 3/8" 18TPI mounting thread
180.00
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 3
75.00
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-2A power supply module, Weidmueller connectors
355.00
PCB Generator board 2 16 bit PIC 24EP128MC202, 4 low noise op amps, 2 Burr-Brown multipliers, Weidmueller connectors, 1% precision resistors, 5 inductors
435.00
IEC Mains power entry Schaffner FN-372 6 (230V - 6A) with switch and fuse
13.50
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, 1 3-contacts
3.00
Wiring 30 m of mounting wire in coded colors
18.00
Heatshrink tube Polyolefine 1 m
6.00
Felt 10mm thick for mounting and dampening
2.00
6 mm shock absorbers 2
8.00
3 mm shock absorbers 4
12.00
M 10 stainless steel bolts and nuts 2
6.00
Polycarbonate 8mm thick  
2.50
Mounting feet, M10 threads 4, with two nuts each
14.00
Zinc sulphate spray can 1
15.00
Zinc sulphate primer paint 250ml
12.00
     
Subtotal parts:  
1653.10

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/Thorium electrodes
10.00
Cutting disks 2 (A60 T-BF41 125 x 1.0 x 22.2
8.00
Flap disc, 160mm 1
12.00
Sanding disks and paper 1
4.00
TIG welding nozzle, nr.5 1
12.00
Cutting oil (spray can) 1
1.00
Solder Pb/Sn 40/60 & leadfree 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
35 mm hole saw 1
27.00
Saw blade, ridgid 1
4.70
     
     
     
Subtotal:  
114.00

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)

28.06.2021 4 h
180.00
01.07.2021 2 h
90.00
02.07.2021 8 h
360.00
03.07.2021 5 h
225.00
04.07.2021 8 h
360.00
05.07.2021 1 h
45.00
06.07.2021 6 h
270.00
07.07.2021 8 h
360.00
09.09.2021 6 h
270.00
10.09.2021 5 h
225.00
11.09.2021 6h
270.00
12.09.2021 4h
180.00
13.09.2021 8h
360.00
14.09.2021 1h
45.00
18.09.2021 1h
45.00
20.09.2021 3h
135.00
   
   
Subtotal:  

[EOF]