User:FloraC/Hard problems of harmony and psychoacoustically supported optimization
This page is a work in progress.
In the study of tuning optimization, we find two blocker issues that deserve the title "hard problems of harmony". Versed in a catchy way, they are:
- Is compositeness heard?
- Are divisive ratios more important than multiplicative ratios?[1]
In fact, they can be modeled in terms of parameters of the norm used in optimization. The first problem is about the weight, and the second about the skew. The order of the norm is the third parameter. Although not versed into a "hard problem" rhetoric since it is a little bit abstract, we must still consider it along with the first two. Collectively, they are parameters of the norm. Being independent of specific temperaments, they are genuine metaproblems of tuning optimization, and well worth a dive.
But let us remember a metaproblem of tuning optimization is a problem of harmony – of temporal interactions of sound. Solution attempt without touching on the psychoacoustic side of harmony would be baseless. So that is where we start with.
Chapter I. Harmonic Rootedness
Chapter II. Divisive and Multiplicative Ratios
Chapter III. Power in Proportion
Chapter IV. Art of Compromise
Chapter V. Towards an Optimization Strategy
Notes
- ↑ Prior to this material, the two problems are often said in the other order, but this essay inverts them since weight is usually considered before the skew in tuning optimization.