173zpi: Difference between revisions

The creation of the page for 173zpi! It's sparse at the moment due to personal time constraints, but more will be added soon.
 
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== Theory ==
== Theory ==
173zpi is the strongest [[Zeta peak index|zeta peak]] within ±0.5 [[EDO|divisions]] of [[39edo]], and serves as a [[Stretched and compressed tuning|compressed-octave]] version thereof ([[2/1]] ≈ 1196.204¢), narrowing the octave by ~3.796¢. 39edo, being a [[zeta valley edo|zeta ''valley'' EDO]], poorly approximates [[Just intonation]] relative to its step size. Its harmonics routinely exceed 30% [[relative error]], so using 173zpi instead—the strongest zeta ''peak'' within 39edo's vicinity—is a logical way of correcting for this, if desired.
173zpi is the strongest [[Zeta peak index|zeta peak]] within ±0.5 [[EDO|divisions]] of [[39edo]], and serves as a [[Stretched and compressed tuning|compressed-octave]] version thereof ([[2/1]] ≈ 1196.204¢), narrowing the octave by ~3.796¢. 39edo, being a [[zeta valley edo|zeta ''valley'' EDO]], poorly approximates [[Just intonation]] relative to its size. Its harmonics routinely exceed 30% [[relative error]], so using 173zpi instead—the strongest zeta ''peak'' within 39edo's vicinity—is a logical way of correcting for this, if desired.