Idea: A Violin Resonant Fiter Array with the Vox H Boards

Bowed string instruments are characterized by dozens of very sharp resonances. This means that even moderate vibrato can result in significant variation of harmonics: indeed, violins have such a large variation it is difficult to talk of a “typical” spectrum of individual harmonics.

Conventional analog approaches for synthesizing these have noticeable limits: using e.g. 31 channel EQs does not give a fine enough resonant band for the vibrato effect, but using parametric EQs requires too many units to be feasible. The approach of using flanging or constant-breadth pulses results in too simplisitic dropouts and emphasis, but the approach using more complex static waveshapes results in too consistent a tone. The approach of an array of evenly spaced highly resonant bandpass filters gives lots of variation, but not of a kind consistent with strings.

This is a thought experiment on how to use Vox H boards to make a Violin resonant filter array. The same approach could be used for viola and cello.

The first intution is that the resonant peaks of a good violin are not random or even, but specifically chosen and tuned:

• The major lower resonant points are chosen to emphasize an (C) arpeggio, but also so that if one note has a resonant peak for one harmonic, it won’t have it for the previous harmonic, for balance.
  https://pages.mtu.edu/~suits/notefreq432.html
• Emphasize second harmonic of lower tones
  http://hansjohannsson.com/rapidweaver%20export/rapidweaver%20export/ac.html
• The major higher resonant points are chosen to equate to formants of human vocal vowels (more female for violins, more male for cellos)

Requirements

The first practical step is to look at the major sets of resonances of a violin (Bold numbers are filter parameters for Sallen Key LPF i.e. Vox H boards):

• A. Air resonances. =/-12db
  • A0 is the resonance through the f holes. (Set same as B0 length) Typically 266 old, 285 Hz modern. [C4-D4]
    • Range: 260 – 290 (lower can get softer, for historical reasons)
    • Q: 14 – 20
    • 22k+10k, 15k, 1u, 1n 277/15 – 230/15 (20% = 266) [C#4 = A#3-]
      • Viola is ~224 and softer top plate.
  • A1 is an sharp anti-resonance (notch), halfway between B1- and B1+. 456 old, 480 modern. 1.7x A0 for vioin but 2x A0 for cello.
  • • Range: 456 – 500 (close to B1+ eg 20Hz apart = solo, far=orchestral 60-90Hz apart) [A4+ – C5]
    • Q:
    • Fix at 456? A+
  • Notch at 700: 710 [F5+]
  • Anti A1:
    • Range: 910 – 1k [Bb5 – C6]
    • Q: 23 – 79
    • 22k 7.5k 1Uf 150pF 1011/36 – 839/32 [B5+ Ab5+ ] 50% = 913
• B. Top plate resonances = + 12db
  • B1– eg 420Hz [Ab4+-A4+]
    • Range: 420 -450
    • Q: 30 – 47
    • 33k+10 18k 1uF 220pF 440Hz/32 – 385/30 [Ab4 – A4]
  • B1+ aka T1 e.g 530 old, 580 modern , [C5+ -D#]
    • Range: 500 – 600 (490 – 580)
    • Q: 28 – 86
    • 36k 9.1k 1uF 200pF 590Hz Q=27
    • 39k+10 9.1k 1uF 200pf 597/28 – 532/26 [C5 – D5]
  • ??: 755
    • Range: 775 – 878 [G5-A5]
    • Q: 28 – 37
    • 22k 6.8l 1uF 220pF 877Hz Q=28
    • 22k+10 6.8k 1uF 220pf 877/29 – 727/25 [G5-A5]
• B. Back plate resonances = +12 db: these are slighty offset from the front plate
  • C2 aka CBR e.g 411 [Ab4]
    • Range: 386 – 411
    • Q: 29 – 77
    • 36k 15k 1U 270pF 416Hz Q=28
    • 33k+10 15k 1u 270pF 435/28 – 381/27 [G4 – A4]
  • C1 aka B1- eg 450 [A4+]
    • Range: 405 – 490
    • Q: 36-45
    • 36k 16k 1uF 180pf 494Hz Q=34
    • 42k+10 20k 1u 150p 448/38 – 401/36 [G4+ – A4] ?? surely too low
  • C4 = B1++ eg 620 [Eb5]
    • Range: 540 – 620
    • Q: 29 – 50
    • 22k 11k 1uF 270pF 622Hz Q=29
    • 20k+10 12k 1u 270p 625/29 – 510/27 [C6 – Eb6]
• Bridge resonances = +12db
  • 1.7
    • Range: 1k3 – 2k4
    • Limit Range: 1500 – 1570 [F#6+ – G6+]
    • 39k 20k .1u 56pf 2408 Q=20
    • 47k 39k .1u 56pF 1570 Q=21
    • 5.6k 2.7k 1uF 560pF 1310Hz Q=21
    • 43k + 10 39k .1u 56p 1480/21 – 1642/21 [F#6 -G#6]
  • 2.4
    • Range: 2k2 – 3k
    • Limit range: 2490 – 2640 [E#7 – E7]
    • 33k 18k .1uF 47pF 3012Hz Q=22
    • 36k 18k .1u 56pF 2642Hz Q= 20
    • 39k 20k .1uF 56pF 2410Hz Q=20
    • 43k 22k .1u 56pF 2186Hz Q=20
    • 33k+10 20k .156p 2293/20 – 2618/20 [C#7+ – E7]
  • 3.7k
    • Limit Range: 3k5 – 3k7 to 4k
    • 24k 12k .1uF 56pF 3963HzQ=20
    • 18k 15k .1uF .68pF 3714Hz Q=19
    • 20k 13k .1uF 82pF 3446Hz Q=17
    • 22k+10 12k .1u 56p 3432/19 – 4140/20 [A7 – A#7]

These vary enormously in their relative levels: some ability to tweak balance might be good, especially for A0.

The notes roughly form arpeggios (B1+, Bridge 1, Bridge 2, Bridge 3):

• the Bortoli in modern pitch names B4 (493), F#+6 (1500), D#7 (2490), A7 (3500) but at A=415 these would correspond to C5, G+6, E7, Bb7 ie C7.
• the 1727 A. Strad has resonances at modern c#5 (554) f#+6 (1500), E7 (2640) A7 (3500)(at A=415 D5 G+6 F7 Bb7 ie Gm7).
• the 1744 O. Strad is slightly sharper than modern D5 (587) G6(1570), E7 (2640) Bb7 (3730) (Gm6)

Boards

So we can imagine an archiecture of 4 Vox H boards:

• Signal comes in to 1 board for the air resonances
  • Configured for A0 LPF and A1 notch
  • Top pot connects to frequency
  • LPF with non-sharp resonance around 4k – bright
  • Might be good to have some positive-side diode clipper at 2V to prevent over-signals (and simulate violin saw shape better?)
• Then combines these into another board for the bridge resonancesUses 3 LPF in parallel as standard
  • Input and output have +/-5V soft clipping?
  • 3.7k can be fixed. 2k5 – 3k span (Pot mixes in extra as balance control)
• Then splits to two parallel boards for the Wood resonances
  • Uses 3 LPF in parallel as standard
  • Top pot connects to frequency
  • Because in parallel, probably want to have 24db resonant height, if available.
  • May as well keep the inputs.

[OLD] Front plate (Q=30):

For	R4	R5 pot	R19	R20	C1	C2
B1–	x	20k	120k	43k	330nF	73pF
For	R13	R14	R22	R23	C5	C5
B+	x	40k	91k	33k	330nF	73pF
For	R15	R16	R24	R25	C6	C7
??	x	x	62k	22k	330nF	73pF

Back plate:

For	R4	R5 pot	R19	R20	C1	C2
CBR/C2 (Q=33)	x	20k	110k	56k	330nF	73pF
For	R13	R14	R22	R23	C5	C5
B1-/C1 (Q=37)	x	50k	82k	68k	330nF	56pF
For	R15	R16	R24	R25	C6	C7
B1++/C4	x	10k	82k	33k	330nF	73pF

Bridge:

For	R4	R5 pot	R19	R20	C1	C2
(Q=25)	x	22k	33k	5.6k	330nF	73pF
For	R13	R14	R22	R23	C5	C5
	x	5k	20k	7.5	330nF	73pF
For	R15	R16	R24	R25	C6	C7
(Q=25)	x	5k	18k (19k)	3.6k	330nF	73pF

Viola: A0= 199-242 B1-=331-359 B1+=399-431

Cello A0 = 98Hz, T1 185 Double bass A0 = 62Hz, T1 99

So 4 inputs with HPF cutoffs at 62, 98, 305, 411. [bass Vel Va Vin]. Feed into chain with same peaks. So