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Making section names consistent with style guide
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As recommended by fredg999 (but specifically for 5L 2s), instead of explaining how the scale tree is made in the scale tree section, a link to a separate page (the scale tree page) is given instead
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==Theory ==
==Theory ==


===Introduction to large and small steps===
===Introduction to step sizes===
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 into the form LLsLLLs, with whole-number sizes for the large steps (denoted as "L") and small steps (denoted as "s").
:''Main article: [[Scale tree]] and [[TAMNAMS#Step ratio spectrum]]''
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 (half step), producing [[12edo]]. This can be generalized into the form LLsLLLs, with whole-number sizes for the large steps and small steps, denoted as "L" and "s" respectively.


Different edos are produced by using different ratios of step sizes. A few examples are shown below.
Different edos are produced by using different ratios of 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]].
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]].


The step ratios 1:1 and 1:0 represent the limits for valid step ratios. 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 small step "collapses" to zero, approaches [[5edo]].
All step ratios lie on a spectrum from 1:1 to 1:0, referred to on the wiki as the scale tree. The step ratios 1:1 and 1:0 represent the limits for valid step ratios. 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 small step "collapses" to zero, approaches [[5edo]].


The step ratios shown above form a continuum of step ratios. The section Tuning spectrum shows how this is made, as well as a larger spectrum.
TAMNAMS has names for regions of this spectrum based on whether they are "soft" (between 1:1 and 2:1) or "hard" (between 2:1 and 1:0).


===Temperament interpretations===
===Temperament interpretations===
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*[[Archy7]] – 472edo tuning
*[[Archy7]] – 472edo tuning


==Tuning spectrum==
==Scale tree==
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.
{{Scale tree|5L 2s|depth=6|Comments=7/5:[[Flattone]] is in this region;21/13:[[Golden meantone]] (696.2145¢);5/3:[[Meantone]] is in this region;2/1:(Generators smaller than this are proper);9/4:The generator closest to a just [[3/2]] for EDOs less than 200;16/7:[[Garibaldi]] / [[Cassandra]];21/8:Golden neogothic (704.0956¢);8/3:[[Neogothic]] is in this region;4/1:[[Archy]] is in this region|tuning=5L 2s}}
{{SB tree|Depth=1}}
{{SB tree|Depth=2}}
{{SB tree|Depth=3}}
 
This process can be repeated to produce a finer, larger continuum of step ratios as shown below, with each ratio producing a different edo.{{Scale tree|5L 2s|depth=6|Comments=7/5:[[Flattone]] is in this region;21/13:[[Golden meantone]] (696.2145¢);5/3:[[Meantone]] is in this region;2/1:(Generators smaller than this are proper);9/4:The generator closest to a just [[3/2]] for EDOs less than 200;16/7:[[Garibaldi]] / [[Cassandra]];21/8:Golden neogothic (704.0956¢);8/3:[[Neogothic]] is in this region;4/1:[[Archy]] is in this region|tuning=5L 2s}}
==See also==
==See also==


*[[Diatonic functional harmony]]
*[[Diatonic functional harmony]]
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