5L 7s (3/1-equivalent): Difference between revisions

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== Theory ==

=== As a macrochromatic scale ===

It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1|tritave]]. This means it is a [[5L 7s|chromatic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes ~~the~~ unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.

It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1|tritave]]. This means it is a [[5L 7s|chromatic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes them unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.

=== Temperament interpretations ===

It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied [[no-twos ~~subgroup]]s~~ like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied no-twos subgroups like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].

==~~Modes~~==

== Scale properties ==

~~The modes have step patterns which are the same as the modes of the p-chromatic scale.~~

=== ~~Scale degrees~~ ===

=== Intervals ===

=== Generator chain ===

=== Modes ===

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== Scale tree ==

{{~~Scale tree~~|~~Comments=~~2/1: Just [[21/11]] generator (1119.~~463c~~); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar|Minalzidar]]}}

{{MOS tuning spectrum

| 2/1 = Just [[21/11]] generator (1119.463{{c}})

| 12/5 = [[Mintra]]

| 3/1 = [[Mintaka]] is around here

| 10/3 = [[No-twos subgroup temperaments#Nekkar|Nekkar]]

| 4/1 = [[No-twos subgroup temperaments#Minalzidar|Minalzidar]]

}}

@@ Line 4: / Line 4: @@
 == Theory ==
 === As a macrochromatic scale ===
-It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1|tritave]]. This means it is a [[5L 7s|chromatic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes the unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.
+It is a stretched [[p-chromatic]] scale, and an extension of a [[macrodiatonic]] scale ([[5L 2s (3/1-equivalent)]]) with the period of a [[3/1|tritave]]. This means it is a [[5L 7s|chromatic scale]], but has [[2/1|octave]]s stretched out to the size of a [[3/1|tritave]]. Other intervals are also stretched in a way that makes them unrecognizable: the diatonic fifth is now the size of a major seventh. Interestingly, [[27edt]], an approximation of [[17edo]], has a tuning of this scale, meaning it contains both an octave-equivalent and tritave-equivalent p-chromatic.
 === Temperament interpretations ===
-It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied [[no-twos subgroup]]s like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].
+It is possible to construct no-twos [[rank-2 temperament]] interpretations of this scale, but it is difficult to interpret within commonly-studied no-twos subgroups like the 3.5.7 [[subgroup]] used for [[Bohlen-Pierce]]. Hard-of-basic scales can be interpreted in [[Mintaka]] temperament in the 3.7.11 subgroup (or its extensions such as Mintra), which tempers out [[1331/1323]] so that the generator (the stretched counterpart of the fourth) is ~[[11/7]], a stack of 2 generators (equivalent to the minor seventh) is ~[[27/11]], and a stack of three generators (equivalent to the minor third) is ~[[9/7]].
-==Modes==
+== Scale properties ==
-The modes have step patterns which are the same as the modes of the p-chromatic scale.
+{{TAMNAMS use}}
-{{MOS modes}}
-=== Scale degrees ===
+=== Intervals ===
+{{MOS intervals}}
+=== Generator chain ===
+{{MOS genchain}}
+=== Modes ===
 {{MOS mode degrees}}
@@ Line 20: / Line 25: @@
 == Scale tree ==
-{{Scale tree|Comments=2/1: Just [[21/11]] generator (1119.463c); 12/5: [[Mintra]]; 3/1: [[Mintaka]] is around here; 10/3: [[No-twos subgroup temperaments#Nekkar|Nekkar]]; 4/1: [[No-twos subgroup temperaments#Minalzidar|Minalzidar]]}}
+{{MOS tuning spectrum
+| 2/1 = Just [[21/11]] generator (1119.463{{c}})
+| 12/5 = [[Mintra]]
+| 3/1 = [[Mintaka]] is around here
+| 10/3 = [[No-twos subgroup temperaments#Nekkar|Nekkar]]
+| 4/1 = [[No-twos subgroup temperaments#Minalzidar|Minalzidar]]
+}}