Does anyone know where to find inharmonic ratio charts?

Michael O'Hagan

I'm looking for charts of inharmonic ratios of plucked/struck instruments to build a module for an additive synth.

Like a Free bar strike harmonic ratios for 32 harmonics are these…

(Thanks to Chet Singer for helping me with this)

1
2.76
5.402
8.93
13.34
18.632
24.806
31.862
39.8
48.62
58.32
68.906
80.372
92.72
105.95
120.062
135.056
150.932
167.69
185.33
203.852
223.256
243.542
264.71
286.76
309.692
333.506
358.202
383.78
410.24
437.582
465.806

I'd like to find similar information for various different bells and mallets type of instruments, basically as many inharmonic strike played instruments as I can find.

I've done all your basic google searches but I haven't found a listing that has the necessary information, does anyone know any resources for this type of info?

Thanks

colB

I wonder if the reason for the lack of data is that an instrument made of multiple bars of the same material mounted/suspended in the same way, will have slightly different harmonic ratios for each note dependent on the physical proportions of each individual bar?

(Similar to a piano where the amount of inharmonicity in the higher harmonics depends on the length and stiffness of the strings which differs for each note)

In that case, there would be no single 'correct' set of harmonics for any particular class of inharmonic instrument. It's something that would need to be multi-sampled and analysed, and that's a costly process, so maybe less likely to be freely available?

It would be interesting to try and build a parameterised model. Looking at the example you posted, it seems that after the initial large jump from 1 to 2.76, the ratio between each successive harmonic drops of logarithmically (or exponentially?).

2.76
1.957
1.653
1.493
1.396
1.331
...
...
1.064 (last one)

…

So having a parameter of the initial ratio, one for the drop off rate, and one for the curve might immediately give you a whole class of inharmonic sounds. Then factor in amplitude drop off rate as another parameter…

Amplitude might be sticky though. Do the charateristics of different materials depend on some harmonics standing out louder than others? Are there times when there needs to be frequency modulation?

It's fascinating :)

Michael O'Hagan

I'm still working on this, I'll let you know if I find anything useful.