User:BudjarnLambeth/Structural beating: Difference between revisions

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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.

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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.

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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]]

@@ 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?
-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.
@@ 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 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.
@@ 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 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]]