Structural beating
Structural beating [idiosyncratic term ] is a hypothesised property of equal-step tunings proposed by Budjarn Lambeth in 2025.
Structural beating is where the period of an equal-step scale is different to its interval of psychoacoustic equivalence, causing the two to fall gradually further out of sync as the scale ascends or descends away from 1/1, creating the illusion that the scale isn't repeating, even though it is.
Explanation of concept
One may consider 2/1, and possibly 3/1, 4/1, 5/1 or other similar ratios, to exhibit a property called psychoacoustic equivalence, where they divide up pitch space into a repeating tower with identical floors. In a 2/1-equivalent scale for example, a note plus 2/1 equals the same note but higher. Endless repetitions up and down.
If this is the case, then what happens when one constructs an equal-step tuning, but the period of that tuning does not exhibit equivalence?
Perhaps, something like beating occurs, except instead of the micro scale of individual notes, the beating occurs on the macro scale on the entire scale structure? One could call this structural beating.
Structural beating may actually be a desirable property. It could make a periodic scale feel less repetitive, because as the periods of the scale fall in and out of sync with the psychoacoustic interval of equivalence - as they start to 'beat' - the scale starts to feel like it's different every period, with new colors and shapes - even though it's not. The composer gets something from nothing.
By interval region
If structural beating does exist, then the greatest determining factor of a scale's structural beating will be the interval region of the scale's period.
If the equivalence is considered to be the octave, 2/1, the perfect eighth, then one would expect equal divisions of sevenths or ninths to have the most vivid structural beating. That would include tunings like ed7/4s, ed16/9s, ed9/5s, ed15/8s, edφφs, ed11/5s & ed9/4s.
If the equivalence is considered to be the tritave, 3/1, the perfect twelfth, then one would expect equal divisions of elevenths or thirteenths to have the most vivid structural beating. That would include tunings like ed8/3s, EDNs, ed11/4s, ed(pi)s, ed13/4s & ed10/3s.
If the equivalence is considered to be the double octave, 4/1, the perfect fifteenth, then one would expect equal divisions of fourteenths or sixteenths to have the most vivid structural beating. That would include tunings like ed7/2s, ed11/3s, ed15/4s & ed9/2s.
If the equivalence is considered to be the pentave, 5/1, the classic major seventeenth, then one would expect equal divisions of sixteenths, seventeenths or eighteenths to have the most vivid structural beating. That would include tunings like ed9/2s & ed11/2s.