Hello
On real drums the sound of the drum change with where you hit the drum skin.
But on public information there is nothing , as far i know, that says how each modes of the drum evolves with the hit position.
And after some research based on some pictures of the modes, and a map of real amplitudes of a drum skin , i have a personal answer, a mix of mathematics knowledge, understanding of the problem and personal guess , i have a practical answer.
It plays with 8 drum modes modes . Each mode has it own formula , that use either a sine or cosine function, the position is transformed in the desired phase range for the sine and cosine , on some mode there are transformations on the phase like a square transformation,, or at the output.
The easiest formulas are the ones that just replicate the theoric mode behavior , while some behave following a real scientific graphic based on the imperfections of the skin material of real drum, and then it is more based on personal guess. For the mode 1,3 , i had no reference else the theoric mode map, i had to adjust the level along the position for a more realist sound, else it was out of place around the center.
For my amateur ears it sounds good, i think i am good for some of the mode, and that there is some adjustments to do with some, for a more scientific result.
There is an ouput for each mode, with the name of the mode (n,m formula ), you just have to multiply the output with the good mode with the good ratio from the tone frequency.
I have made a block called "stick pos" , because it is in a snare drum, and it is played with a stick.
The position is controlled by a knob.
Position = 0.0 is the virtual center of the drum skin. With the typical sound at the center of the drum where it is almost only the tone mode. This is what emulate many kick drum synths .
Position = 1.0 is the virtual border . It has almost only high ratio modes, and sounds very metallic, like a cowbell percussion.
All along the position it sounds like a drum for me, with different color along the position. In a full drum mode, with a frequency of 300 hz, it sounds like some small tam tam, drums .
The raw formula send all modes levels at the same maximum level, then the high frequencies can be at the same level than the lower, or at greater level, it sounds metallic. You need to adjust by a 1P LP filter the overtones for a softer drum like drums with wooden ring.
Feel free to command the position with some other commands like MIDI mod wheel, or other elements of your synth.
Good creation and music
