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===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.
[[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|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=NONE}}
===Parasoft tunings ===
===Parasoft tunings ===
:''Main article: [[Flattone]]''
:''Main article: [[Flattone]]''
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Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 4/3; 7/5; 10/7|Genchain Extend=0, 5|Notation=NONE}}
===Hyposoft tunings===
===Hyposoft tunings===
:''Main article: [[Meantone]]''
:''Main article: [[Meantone]]''
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Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5|Notation=NONE}}
===Hypohard tunings===
===Hypohard tunings===
:''Main article: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''
:''Main article: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''
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Edos include [[41edo]] and [[53edo]].
Edos include [[41edo]] and [[53edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5|Notation=NONE}}
==== Quasihard tunings====
==== Quasihard tunings====
Quasihard 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 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|Scale Signature=5L 2s|Step Ratio=3/1; 5/2; 8/3|Genchain Extend=0, 5|Notation=NONE}}
===Parahard and ultrahard tunings===
===Parahard and ultrahard tunings===
:''Main article: [[Archy]]''
:''Main article: [[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|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5|Notation=NONE}}
==Modes==
==Modes==
Diatonic modes have standard names from classical music theory:
Diatonic modes have standard names from classical music theory:
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==Scale tree ==
==Scale tree ==
{{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}}
{{MOS tuning spectrum
| Scale Signature = 5L 2s
| Depth = 6
| 7/5 = [[Flattone]] is in this region
| 21/13 = [[Golden meantone]] (696.2145{{c}})
| 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{{c}})
| 8/3 = [[Neogothic]] is in this region
| 4/1 = [[Archy]] is in this region
}}
 
==See also==
==See also==
 
* [[Diatonic functional harmony]]
*[[Diatonic functional harmony]]
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