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===5L 2s as a moment-of-symmetry scale===
===5L 2s as a moment-of-symmetry scale===
The familiar interpretation of 5 whole and 2 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 this step pattern to 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 pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, has step sizes of 2 (whole step) and 1 (small step), producing [[12edo]]. This can be generalized to form the pattern LLsLLLs with whole-number step sizes for L and s, where L is greater than s. The terms "large step" and "small step" are preferred as most step size pairings cannot be interpreted as "whole" and "half" steps.


====Substituting step sizes====
Different edos are produced by using different ratios of step sizes. A few examples are shown below.
Different edos are produced by substituting different step sizes. A few examples are shown below.
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Edos that are multiples of the examples above can be reached by entering non-simplified step ratios. For example, edos that are multiples of 12 are reached by using larger values whose ratio simplifies to 2:1, such as 4:2 for [[24edo]] and 12:6 for [[72edo]]. The step sizes may be called whole and half in this case.
Edos that are multiples of the examples above can be reached by entering non-simplified step ratios. For example, edos that are multiples of 12 are reached by using larger values whose ratio simplifies to 2:1, such as 4:2 for [[24edo]] and 12:6 for [[72edo]]. The step sizes may be called whole and half in this case.


====Expanding the tuning spectrum====
A spectrum of step ratios can be produced by starting with the ratios 1:1 and 1:0 and repeatedly finding the [[Mediant|mediants]] between adjacent ratios. The first three iterations are shown below, yielding the step ratios previously mentioned.{{SB tree|Depth=1}}
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=2}}
{{SB tree|Depth=3}}
{{SB tree|Depth=3}}
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.
Larger edos, such as [[53edo]] (step ratio 9:4), can be reached by repeatedly expanding the tuning spectrum. A larger tuning spectrum can be found in the section tuning spectrum.


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]].
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===
===Temperament interpretations===
==Tuning ranges==
 
: ''Main article: [[5L 2s/Temperaments]]''
 
5L 2s has several temperament interpretations, such as:
 
* Flattone, with a generator size around 694¢, corresponding to a step ratio of around 4:3.
* Meantone, with a generator size around 696¢, corresponding to a step ratio of around 5:3.
* Schismic, with a generator size around 702¢ (just perfect 5th, or 3/2), corresponding to a step ratio between 2:1 and 5:2.
** Pythagorean tuning also has a generator of 702¢.
* Parapyth, with a generator size ranging between 702¢ and 705¢, corresponding to a step ratio between 5:2 and 3:1.
* Archy, with a generator size greater than 705¢, corresponding to a step ratio between 3:1 and 5:1.
 
==Modes==
==Modes==
Diatonic modes have standard names from classical music theory:
Diatonic modes have standard names from classical music theory:
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