Ringer scale: Difference between revisions

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A '''[[#Origin of ~~the term~~ Ringer|Ringer]] ''n'' scale''' is a minimal complexity* [[constant structure]] (CS) [[neji]] [[periodic scale]] with a [[period]] of an [[octave]] which has ''n'' notes (AKA scale degrees) per octave. (*What "minimal complexity" means is discussed [[#Minimal complexity|later in this article]].) The fact that it has a constant structure implies there is at least one [[val]] - corresponding to ''n'' [[edo]] - that will [[map]] every [[interval]] present to the same number of abstract "scale steps". (This means [[2/1]] ''must'' be mapped to ''n'' (scale) steps.) Note that the val is not required to be [[patent val|patent]] and that the most [[consistent]] val is not always the [[patent val]] and usually depends on the tendency towards sharpness or flatness of the corresponding [[edo]]. The name, "Ringer", comes from the tendency of these JI scales to "ring" a lot because of them generally being as low complexity as possible in the sense of [[odd-limit]].

A '''[[#Origin of Ringer scales|Ringer]] ''n'' scale''' is a minimal complexity* [[constant structure]] (CS) [[neji]] [[periodic scale]] with a [[period]] of an [[octave]] which has ''n'' notes (AKA scale degrees) per octave. (*What "minimal complexity" means is discussed [[#Minimal complexity|later in this article]].) The fact that it has a constant structure implies there is at least one [[val]] - corresponding to ''n'' [[edo]] - that will [[map]] every [[interval]] present to the same number of abstract "scale steps". (This means [[2/1]] ''must'' be mapped to ''n'' (scale) steps.) Note that the val is not required to be [[patent val|patent]] and that the most [[consistent]] val is not always the [[patent val]] and usually depends on the tendency towards sharpness or flatness of the corresponding [[edo]]. The name, "Ringer", comes from the tendency of these JI scales to "ring" a lot because of them generally being as low complexity as possible in the sense of [[odd-limit]].

An important consideration when building a Ringer ''n'' scale is what odd harmonics to add once you have reached the maximum [[odd-limit]]. To figure out where to place odd harmonics imbetween simpler odd harmonics already present, you need to use a choice of [[val]] to see what adjacent harmonics in the scale are mapped to more than 1 abstract scale step. The goal then is to make it so that every adjacent pair of harmonics in the Ringer ''n'' scale is mapped by the [[val]] to 1 scale degree.

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Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].

== Origin of ~~the term~~ Ringer ==

== Origin of Ringer scales ==

The name "Ringer" was chosen by tuning theorist Scott Dakota to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of Ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].

The name "Ringer" was chosen by tuning theorist Scott Dakota (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of Ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].

== Example: Ringer 15 ==

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-A '''[[#Origin of the term Ringer|Ringer]] ''n'' scale''' is a minimal complexity* [[constant structure]] (CS) [[neji]] [[periodic scale]] with a [[period]] of an [[octave]] which has ''n'' notes (AKA scale degrees) per octave. (*What "minimal complexity" means is discussed [[#Minimal complexity|later in this article]].) The fact that it has a constant structure implies there is at least one [[val]] - corresponding to ''n'' [[edo]] - that will [[map]] every [[interval]] present to the same number of abstract "scale steps". (This means [[2/1]] ''must'' be mapped to ''n'' (scale) steps.) Note that the val is not required to be [[patent val|patent]] and that the most [[consistent]] val is not always the [[patent val]] and usually depends on the tendency towards sharpness or flatness of the corresponding [[edo]]. The name, "Ringer", comes from the tendency of these JI scales to "ring" a lot because of them generally being as low complexity as possible in the sense of [[odd-limit]].
+A '''[[#Origin of Ringer scales|Ringer]] ''n'' scale''' is a minimal complexity* [[constant structure]] (CS) [[neji]] [[periodic scale]] with a [[period]] of an [[octave]] which has ''n'' notes (AKA scale degrees) per octave. (*What "minimal complexity" means is discussed [[#Minimal complexity|later in this article]].) The fact that it has a constant structure implies there is at least one [[val]] - corresponding to ''n'' [[edo]] - that will [[map]] every [[interval]] present to the same number of abstract "scale steps". (This means [[2/1]] ''must'' be mapped to ''n'' (scale) steps.) Note that the val is not required to be [[patent val|patent]] and that the most [[consistent]] val is not always the [[patent val]] and usually depends on the tendency towards sharpness or flatness of the corresponding [[edo]]. The name, "Ringer", comes from the tendency of these JI scales to "ring" a lot because of them generally being as low complexity as possible in the sense of [[odd-limit]].
 An important consideration when building a Ringer ''n'' scale is what odd harmonics to add once you have reached the maximum [[odd-limit]]. To figure out where to place odd harmonics imbetween simpler odd harmonics already present, you need to use a choice of [[val]] to see what adjacent harmonics in the scale are mapped to more than 1 abstract scale step. The goal then is to make it so that every adjacent pair of harmonics in the Ringer ''n'' scale is mapped by the [[val]] to 1 scale degree.
@@ Line 21: / Line 21: @@
 Notice how all of these do not skip any harmonics while representing the harmonic series ''completely'' up to some [[odd-limit]].
-== Origin of the term Ringer ==
+== Origin of Ringer scales ==
-The name "Ringer" was chosen by tuning theorist Scott Dakota to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of Ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].
+The name "Ringer" was chosen by tuning theorist Scott Dakota (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of Ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].
 == Example: Ringer 15 ==