User:Ganaram inukshuk/5L 2s: Difference between revisions

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: ''This is a test page. For the main page, see [[5L 2s]].''

~~{{Infobox MOS~~

:''This is a test page. For the main page, see [[5L 2s]].''

~~|Tuning=5L 2s}}~~{{MOS intro|Scale Signature=5L 2s}}

==Name==

TAMNAMS suggests the name '''diatonic''' for this scale, referring to the use of this term to refer to a scale with 5 whole steps and 2 small steps.

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===5L 2s as a moment-of-symmetry scale===

The familiar interpretation of whole and half steps has step sizes of 2 and 1 ~~steps~~, producing [[12edo]]. Viewing 5L 2s as a moment-of-symmetry scale involves generalizing the step pattern of 5 whole steps and 2 whole steps~~, commonly written as WWHWWWH for the major scale,~~ as being different step sizes. As such, the generalized form LLsLLLs is used, as most step ratios have step sizes that cannot be interpreted as being "whole" or "half" steps.

The familiar interpretation of whole and half steps, commonly written as WWHWWWH for the major scale, has step sizes of 2 (whole step) and 1 (small step), producing [[12edo]]. Viewing 5L 2s as a moment-of-symmetry scale involves generalizing the step pattern of 5 whole steps and 2 whole steps as being different step sizes. As such, the generalized form LLsLLLs is used, as most step ratios have step sizes that cannot be interpreted as being "whole" or "half" steps.

====Substituting step sizes====

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====Expanding the tuning spectrum====

The tuning spectrum shown in the previous section ~~starts~~ with the step ratios 1:1 and 1:0 and repeatedly finding the [[Mediant|mediants]] between adjacent ratios. The first ~~few~~ iterations are shown below.

The tuning spectrum shown in the previous section is produced by starting with the step ratios 1:1 and 1:0 and repeatedly finding the [[Mediant|mediants]] between adjacent ratios. The first three iterations are shown below.

~~Thus, reaching larger~~ edos, such as [[53edo]] or [[311edo]], ~~is a matter of~~ expanding the tuning spectrum ~~until the desired step ratio is found~~. The section tuning spectrum contains a much larger tuning spectrum.

Larger edos, such as [[53edo]] or [[311edo]], can be reached by repeatedly expanding the tuning spectrum. The section tuning spectrum contains a much larger tuning spectrum.

The step ratios 1:1 and 1:0 represent the extremes of the tuning spectrum. A step ratio where the large and small step ~~approach being~~ equal to ~~each other~~ approaches [[7edo]], and a step ratio where the size of the small step approaches 0 approaches [[5edo]].

The step ratios 1:1 and 1:0 represent the extremes of the tuning spectrum. A step ratio that approaches 1:1, where the large and small step are equal to one another, approaches [[7edo]], and a step ratio that approaches 1:0, where the size of the small step approaches 0 relative to the size of the large step, approaches [[5edo]].

===Temperament interpretations===

@@ Line 1: / Line 1: @@
-: ''This is a test page. For the main page, see [[5L 2s]].''
+{{Infobox MOS|Tuning=5L 2s}}
-{{Infobox MOS
+:''This is a test page. For the main page, see [[5L 2s]].''
-|Tuning=5L 2s}}{{MOS intro|Scale Signature=5L 2s}}
+{{MOS intro|Scale Signature=5L 2s}}
 ==Name==
 TAMNAMS suggests the name '''diatonic''' for this scale, referring to the use of this term to refer to a scale with 5 whole steps and 2 small steps.
@@ Line 78: / Line 78: @@
 ===5L 2s as a moment-of-symmetry scale===
-The familiar interpretation of whole and half steps has step sizes of 2 and 1 steps, producing [[12edo]]. Viewing 5L 2s as a moment-of-symmetry scale involves generalizing the step pattern of 5 whole steps and 2 whole steps, commonly written as WWHWWWH for the major scale, as being different step sizes. As such, the generalized form LLsLLLs is used, as most step ratios have step sizes that cannot be interpreted as being "whole" or "half" steps.
+The familiar interpretation of whole and half steps, commonly written as WWHWWWH for the major scale, has step sizes of 2 (whole step) and 1 (small step), producing [[12edo]]. Viewing 5L 2s as a moment-of-symmetry scale involves generalizing the step pattern of 5 whole steps and 2 whole steps as being different step sizes. As such, the generalized form LLsLLLs is used, as most step ratios have step sizes that cannot be interpreted as being "whole" or "half" steps.
 ====Substituting step sizes====
@@ Line 119: / Line 119: @@
 ====Expanding the tuning spectrum====
-The tuning spectrum shown in the previous section starts with the step ratios 1:1 and 1:0 and repeatedly finding the [[Mediant|mediants]] between adjacent ratios. The first few iterations are shown below.
+The tuning spectrum shown in the previous section is produced by starting with the step ratios 1:1 and 1:0 and repeatedly finding the [[Mediant|mediants]] between adjacent ratios. The first three iterations are shown below.
 {{SB tree|Depth=1}}
 {{SB tree|Depth=2}}
 {{SB tree|Depth=3}}
-Thus, reaching larger edos, such as [[53edo]] or [[311edo]], is a matter of expanding the tuning spectrum until the desired step ratio is found. The section tuning spectrum contains a much larger tuning spectrum.
+Larger edos, such as [[53edo]] or [[311edo]], can be reached by repeatedly expanding the tuning spectrum. The section tuning spectrum contains a much larger tuning spectrum.
-The step ratios 1:1 and 1:0 represent the extremes of the tuning spectrum. A step ratio where the large and small step approach being equal to each other approaches [[7edo]], and a step ratio where the size of the small step approaches 0 approaches [[5edo]].
+The step ratios 1:1 and 1:0 represent the extremes of the tuning spectrum. A step ratio that approaches 1:1, where the large and small step are equal to one another, approaches [[7edo]], and a step ratio that approaches 1:0, where the size of the small step approaches 0 relative to the size of the large step, approaches [[5edo]].
 ===Temperament interpretations===