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== Tuning ranges ==
== Tuning ranges ==
{{Todo|Populate|inline=1|text=Populate tables}}
=== Simple tunings ===
=== Simple tunings ===
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7}}
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
 
{{MOS tunings}}


=== Ultrasoft tunings ===
=== Ultrasoft tunings ===
{{MOS degrees|Step Ratio=4/3; 1/1; 5/4; 6/5|Genchain Extend=0, 5|MOS Prefix=dia}}
{{MOS tunings|Step Ratios=5/4; 4/3}}


=== Parasoft tunings ===
=== Parasoft tunings ===
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Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
{{MOS degrees|Step Ratio=3/2; 4/3; 7/5; 10/7|Genchain Extend=0, 5|MOS Prefix=dia}}
 
{{MOS tunings|Step Ratios=4/3; 7/5; 10/7; 3/2}}


=== Hyposoft tunings ===
=== Hyposoft tunings ===
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Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
{{MOS degrees|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5}}
 
{{MOS tunings|Step Ratios=Hyposoft}}


=== Hypohard tunings ===
=== Hypohard tunings ===
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The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).
The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).
{{MOS tunings|Step Ratios=2/1; 5/2; 3/1; 9/4}}


==== Minihard tunings ====
==== Minihard tunings ====
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Edos include [[41edo]] and [[53edo]].
Edos include [[41edo]] and [[53edo]].
{{MOS degrees|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}
==== Quasihard tunings ====
==== Quasihard tunings ====
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294¢).
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294¢).


Edos include [[17edo]], [[29edo]], and [[46edo]]. 17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
Edos include [[17edo]], [[29edo]], and [[46edo]]. 17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
{{MOS degrees|Step Ratio=3/1; 5/2; 8/3|Genchain Extend=0, 5}}
=== Parahard and ultrahard tunings ===
=== Parahard and ultrahard tunings ===
{{See also| Archy }}
{{See also| Archy }}
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Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
{{MOS degrees|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}
 
{{MOS tunings|Step Ratios=3/1; 4/1; 5/1; 6/1}}


== Modes ==
== Modes ==
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