User:Contribution/Collection of tunings: Difference between revisions

Line 8:

* '''Prominent peaks after removing the prime 3'''

* '''Prominent peaks after simultaneously removing the primes 2 and 3'''

* '''The α–β–γ family, with an equave sliding from 2/1 down to 4/3'''

* '''The α–β–γ family, with an equave sliding from 3/1 down to 4/3'''

These tunings earn the label “optimized” only relative to the limited set of zeta-derived functions explored here. In practice, you can make convincing music with ''any'' equal-step interval, every real-number step size repeated ad infinitum forms its own viable lattice. When you layer many differently pruned zeta functions in a tool such as Wolfram Mathematica, striking peaks emerge almost everywhere; the peaks simply shift as each combination of omitted primes reshapes the landscape. That ubiquity means there is no absolute “good” or “bad” equal-step tuning, only different alignments of primes that reveal different musical affordances.

@@ Line 8: / Line 8: @@
 * '''Prominent peaks after removing the prime 3'''
 * '''Prominent peaks after simultaneously removing the primes 2 and 3'''
-* '''The α–β–γ family, with an equave sliding from 2/1 down to 4/3'''
+* '''The α–β–γ family, with an equave sliding from 3/1 down to 4/3'''
 These tunings earn the label “optimized” only relative to the limited set of zeta-derived functions explored here. In practice, you can make convincing music with ''any'' equal-step interval, every real-number step size repeated ad infinitum forms its own viable lattice. When you layer many differently pruned zeta functions in a tool such as Wolfram Mathematica, striking peaks emerge almost everywhere; the peaks simply shift as each combination of omitted primes reshapes the landscape. That ubiquity means there is no absolute “good” or “bad” equal-step tuning, only different alignments of primes that reveal different musical affordances.