Soul from Scratch: Designing a More Portable Organ

Your Hammond B-3 sounds like nothing on Earth, but at 450 lbs your friends are sick of helping you carry it. They demand that you make it lighter, or they'll stop showing up to your gigs.

I will present the technical design of the Hammond B-3 and its frequent collaborator the Leslie rotating speaker cabinet, then model their audio components digitally. I'll show how to implement each of these components on a microcontroller. With a 20,000x savings in weight, you won't need friends!

This organ synthesizer includes full MIDI control of notes, drawbar settings, and effects. Recreate it inexpensively at home or apply its principles in other contexts.

The journey follows successes and failures of my initial design and optimizations that allow the simulation to run on a very low powered device. There's something for creative programmers, music fans, makers, and optimizers. My intent is to give enough groundwork that you can walk away and write your own synthesizer.

Transcript

1. Soul from Scratch
2. Hello
3. @pteichman
9. ❤
10. Super Heavy Organ PRELUDE
11. Telharmonium: 1906
16. Telharmonium: 200 Tons
18. Hammond B-3: 420 lbs
19. Hammond B-3: 420 lbs
 Leslie 122: 140 lbs
20. Roto
23. “If you wish to make ‘Green Onions’ from scratch, you must first invent the universe” CARL SAGAN
31. https://www.flickr.com/photos/vitroids/6239481883
32. Drawbars Tonewheel Oscillators
35. fully polyphonic
36. fully cacophonic
37. 16 MHz 8 bit USB Serial 72 MHz 32 bit USB+++
40. Project Scope ROTO
41. Hammond B-3 Leslie 122
42. By Hustvedt - Own work, CC BY-SA 3.0, https:// commons.wikimedia.org/w/index.php?curid=3472626
43. http://www.theatreorgans.com/hammond/faq/mystery/mystery.html
46. MIDI Messages Note on 1001 CCCC 0NNNNNNN 0VVVVVVV Note off 1000 CCCC 0NNNNNNN 0VVVVVVV Control change 1011 CCCC 0NNNNNNN 0VVVVVVV byte 1 byte 2 byte 3 4 bit channel 7 bit note 7 bit velocity
47. Standard MIDI ports DIN USB 3.5mm
48. Teensy 3.6 44.1 kHz / 16 bit
49. 181,000 kg 250 kg 0.003 kg
50. TODO DISTORTION TREMOLO / VIBRATO 2 ROTATING SPEAKERS STEREO OUTPUT SINE OSCILLATOR VIBRATO / CHORUS PERCUSSION SWELL
51. Hammond B-3
52. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches
53. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches 53
54. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches 54
56. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches 56
57. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches 57
58. 91 tonewheel oscillators upper manual lower manual upper drawbars lower drawbars vibrato / chorus swell pedal percussion switches 58
60. 91 Tonewheels HAMMOND 1/7
61. Tonewheels
62. Tonewheels
63. Tonewheels 44.1kHz means 
 22µs per sample
64. Tonewheels
65. Tonewheels
66. Tonewheels void transmit( audio_block_t *block, unsigned char index = 0); typedef struct audio_block_struct { int16_t data[128]; /* other stuff deleted */ } audio_block_t;
67. Direct Digital Synthesis HAMMOND 2/7
68. Direct Digital Synthesis uint32_t counter = 0; while (1) { counter += 1; } while (1) { counter += 2; }
69. sine lookup table: 16 bit signed values, 256 elements int16_t sine[256] uint32_t counter 32 24 16 8 oscillator { uint32_t counter; uint32_t increment; } int16_t next() { counter += increment; index = counter >> 24; return sine[index]; } Direct Digital Synthesis
70. sine lookup table: 16 bit signed values, 256 elements int16_t sine[256] uint32_t counter 32 24 16 8 oscillator { uint32_t counter; uint32_t increment; } int16_t next() { counter += increment; index = counter >> 24; return sine[index]; } Direct Digital Synthesis
71. sine lookup table: 16 bit signed values, 256 elements int16_t sine[256] uint32_t counter 32 24 16 8 oscillator { uint32_t counter; uint32_t increment; } int16_t next() { counter += increment; index = counter >> 24; return sine[index]; } incr = 00000001 00000000 00000000 00000000 Direct Digital Synthesis
72. sine lookup table: 16 bit signed values, 256 elements int16_t sine[256] uint32_t counter 32 24 16 8 oscillator { uint32_t counter; uint32_t increment; } int16_t next() { counter += increment; index = counter >> 24; return sine[index]; } Direct Digital Synthesis sine lookup table: 16 bit signed values, 256 elements int16_t sine[256] uint32_t counter 32 24 16 8 oscillator { uint32_t counter; uint32_t increment; } int16_t next() { counter += increment; index = counter >> 24; return sine[index]; }
73. Direct Digital Synthesis oscillator { uint32_t accumulator; uint32_t increment; } oscillator position frequency
74. Setting Frequency HAMMOND 3/7
75. increment < 2^24? increment > 2^24? incr = 00000001 00000000 00000000 00000000 frequency < 172Hz frequency > 172Hz uint32_t counter = 0; while (1) { counter += 1; } while (1) { counter += 2; } Setting Frequency
76. Setting Frequency incr = 232 44100 * freq increment < 2^24? increment > 2^24? incr = 00000001 00000000 00000000 00000000 frequency < 172Hz frequency > 172Hz
77. Setting Frequency uint32_t counter 32 24 16 8 32 24 16 8 table index interpolation scale value = interpolate(v1, v2, scale); v1 v2
78. Setting Volume HAMMOND 4/7
79. Setting Volume oscillator { uint32_t accumulator; uint32_t increment; uint16_t volume; } int16_t next() { accumulator += increment; index = accumulator >> 24; scale = (accumulator >> 8) & 0xFFFF; sample = interpolate(sine[index], sine[index+1], scale); return (sample * volume) >> 16; } top 8 bits next 16 bits apply volume
80. Setting Volume int16 sample; int16 volume; int16 result = (sample * volume) >> 16; (N bits) * (M bits) = N+M bits (N bits) + (M bits) = (max(N, M) + 1) bits
81. Setting Volume oscillator { uint32_t accumulator[91]; uint32_t increment[91]; uint16_t volume[91]; }
82. fully cacophonic
83. Vibrato / Chorus HAMMOND 5/7
84. Vibrato / Chorus
88. writer reader read offset from writer t Vibrato / Chorus
89. writer reader read offset from writer t writer reader read offset from writer t Vibrato / Chorus
90. Vibrato / Chorus int16_t triangle[256]; oscillator { uint32_t accumulator; uint32_t increment; uint16_t depth; } oscillator position frequency (7Hz) vibrato depth
91. Percussion HAMMOND 6/7
92. Volume held notes percussion chirp key down key up Percussion
93. Percussion 91 original oscillators upper manual lower manual upper drawbars lower drawbars percussion switches 91 percussion oscillators percussion envelope to vibrato / chorus
95. Swell HAMMOND 7/7
96. B-3 Reprise SINE OSCILLATOR VIBRATO / CHORUS PERCUSSION SWELL
97. Bridge
99. Laurens Hammond “I never intended for my organ to sound that way.”
100. Laurens Hammond “I never intended for my organ to sound that way.”
101. Don Leslie "I was amazed at all the publicity Hammond created for me by their continuous bad-mouthing of my product. This word-of-mouth advertising was so good that from the start until the company was sold to CBS in 1965, no advertising was ever needed and my problem has always been keeping up production to match sales."
102. Leslie 122
103. Leslie 122 tube amplifier 800Hz crossover treble rotor bass rotor
104. Bass LESLIE 1/4
105. Bass rotor bass speaker drum rotor
106. Treble LESLIE 2/4
107. Treble horn
108. Treble horn real pitch perceived increase perceived decrease
109. Treble horn amfm { int16 ringbuf[] uint32 accumulator uint32 increment uint16 read_shift[256] uint16 volume[256] } sawtooth oscillator frequency control vibrato tremelo
110. audio from organ amplifier (growl) crossover filter treble horn (vibrato + tremolo) bass speaker (tremolo) audio to output high freqs low freqs Leslie Block Diagram Leslie 122 block diagram
111. Growl LESLIE 3/4
113. Growl zero 16-bit signed lookup table Growl Soft clipping
114. Stereo LESLIE 4/4
115. Stereo
116. Stereo
117. audio from organ amplifier (growl) crossover filter treble horn (vibrato + tremolo) bass speaker (tremolo) audio to L output high freqs low freqs Leslie Stereo Block Diagram crossover filter treble horn (vibrato + tremolo) bass speaker (tremolo) audio to R output high freqs low freqs phase shifted 90° Leslie stereo block diagram Stereo
118. Leslie Reprise DISTORTION TREMOLO / VIBRATO 2 ROTATING SPEAKERS STEREO OUTPUT
119. Coda
120. github.com/ pteichman/roto
121. github.com/ pteichman/roto