User:BudjarnLambeth/Structural beating - Revision history

BudjarnLambeth: BudjarnLambeth moved page Structural beating to User:BudjarnLambeth/Structural beating

2025-05-07T02:54:15Z

BudjarnLambeth moved page Structural beating to User:BudjarnLambeth/Structural beating

← Older revision	Revision as of 02:54, 7 May 2025
(No difference)

BudjarnLambeth: /* By interval region */

2025-01-12T23:43:57Z

By interval region

← Older revision		Revision as of 23:43, 12 January 2025
Line 17:		Line 17:
	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 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 [[ed7/4]]s, [[ed16/9]]s, [[ed15/8]]s, [[phi to the phi\|edφ<sup>φ</sup>s]], [[ed11/5]]s & [[ed9/4]]s.		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 [[ed7/4]]s, [[ed16/9]]s, [[ed9/5]]s, [[ed15/8]]s, [[phi to the phi\|edφ<sup>φ</sup>s]], [[ed11/5]]s & [[ed9/4]]s.

	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 [[ed8/3]]s, [[EDN]]s, [[ed11/4]]s, [[acoustic pi\|ed(pi)s]], [[ed13/4]]s & [[ed10/3]]s.		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 [[ed8/3]]s, [[EDN]]s, [[ed11/4]]s, [[acoustic pi\|ed(pi)s]], [[ed13/4]]s & [[ed10/3]]s.

BudjarnLambeth: /* By interval region */

2025-01-12T13:17:25Z

By interval region

← Older revision		Revision as of 13:17, 12 January 2025
Line 23:		Line 23:
	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 [[ed7/2]]s, [[ed11/3]]s, [[ed15/4]]s & [[ed9/2]]s.		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 [[ed7/2]]s, [[ed11/3]]s, [[ed15/4]]s & [[ed9/2]]s.

	If the equivalence is considered to be the pentave, 5/1, the classic major seventeenth, then one would expect equal divisions of sixteenths or eighteenths to have the most vivid structural beating. That would include tunings like [[ed9/2]]s & [[ed11/2]]s.		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 [[ed9/2]]s & [[ed11/2]]s.

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]

BudjarnLambeth: /* By interval region */

2025-01-12T11:57:47Z

By interval region

← Older revision		Revision as of 11:57, 12 January 2025
Line 17:		Line 17:
	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 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 [[ed7/4]s, [[ed16/9]]s, [[ed15/8]]s, [[phi to the phi\|edφ<sup>φ</sup>s]], [[ed11/5]]s & [[ed9/4]]s.		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 [[ed7/4]]s, [[ed16/9]]s, [[ed15/8]]s, [[phi to the phi\|edφ<sup>φ</sup>s]], [[ed11/5]]s & [[ed9/4]]s.

	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 [[ed8/3]]s, [[EDN]]s, [[ed11/4]]s, [[acoustic pi\|ed(pi)s]], [[ed13/4]]s & [[ed10/3]]s.		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 [[ed8/3]]s, [[EDN]]s, [[ed11/4]]s, [[acoustic pi\|ed(pi)s]], [[ed13/4]]s & [[ed10/3]]s.

BudjarnLambeth: /* Explanation of concept */

2025-01-12T11:56:23Z

Explanation of concept

← Older revision		Revision as of 11:56, 12 January 2025
Line 9:		Line 9:
	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?		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''.		Perhaps, something like {{w\|beat (acoustics)\|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.		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.

BudjarnLambeth: Created page with "'''Structural beating'''{{idiosyncratic}} is a hypothesised property of equal-step tunings proposed by Budjarn Lambeth in 2025. Structural beating is where the per..."

2025-01-12T11:55:15Z

Created page with "'''Structural beating'''{{idiosyncratic}} is a hypothesised property of equal-step tunings proposed by Budjarn Lambeth in 2025. Structural beating is where the per..."

New page

'''Structural beating'''{{idiosyncratic}} is a hypothesised property of [[equal-step tuning]]s 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 [[ed7/4]s, [[ed16/9]]s, [[ed15/8]]s, [[phi to the phi|edφ<sup>φ</sup>s]], [[ed11/5]]s & [[ed9/4]]s.

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 [[ed8/3]]s, [[EDN]]s, [[ed11/4]]s, [[acoustic pi|ed(pi)s]], [[ed13/4]]s & [[ed10/3]]s.

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 [[ed7/2]]s, [[ed11/3]]s, [[ed15/4]]s & [[ed9/2]]s.

If the equivalence is considered to be the pentave, 5/1, the classic major seventeenth, then one would expect equal divisions of sixteenths or eighteenths to have the most vivid structural beating. That would include tunings like [[ed9/2]]s & [[ed11/2]]s.

[[Category:Equal-step tuning]]