While Lance Jonathan Putnam’s dissertation on this topic starts to get heady around page 50, it is more readable than you might expect from the title:
The Harmonic Pattern Function:
A Mathematical Model Integrating Synthesis of Sound and Graphical Patterns
In fact, once you hit page 5 and he discusses how “Leonardo da Vinci noticed that by striking a wooden table covered with a thin layer of dust, various shapes would form displaying the nodal (motionless) regions of the vibration,” you start to realize that what Putnam is writing about has a useful division of the subject matter that Audulus involves.
When he goes on to mention that “in 1872, Sir Howard Warburton Elphinstone published a pattern design book for the lathe with both illustrations and mathematical equations describing the pattern,” and that “one of his unifying principles is the use of the mathematical concept of envelopes—secondary curves or surfaces tangent to a family of curves in close proximity,” it becomes apparent why academic research is invaluable to moving forward with innovation. That is, when you read a well written thesis, not only does it offer a developmental understanding of the material, but the particular contributions of the researcher seem to synthesize otherwise diverse disciplines into a coherent, self-standing field.
One thing that stands out in this respect is Putnam’s inclusion of illustrations.
I thought I would share this paper because it pertains to recent posts about the Chladni Sequencer and Logograms.
If you make it past page 50 where he moves on the the Fourier Series, please share some thoughts here.