Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
mNo edit summary
Ganaram inukshuk (talk | contribs)
autopatrolled
4,810 edits
"Tuning ranges" was more common than "step ratio ranges"
Line 154: Line 154:
**Ultrapyth, with generators around 713.7¢.
**Ultrapyth, with generators around 713.7¢.


==Step ratio ranges==
==Tuning ranges==
===Simple step ratios===
===Simple tunings===
17edo and 19edo, produced using step ratios of 3:1 and 3:2 respectively, 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}}
17edo and 19edo, produced using step ratios of 3:1 and 3:2 respectively, 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}}
===Parasoft step ratios===
===Parasoft tunings===
:''Main article: [[Flattone]]''
:''Main article: [[Flattone]]''
Parasoft step ratios (between 4:3 and 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths ([[3/2]], flat of 702¢) to produce major 3rds that are flatter than [[5/4]] (386¢).{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 4/3; 7/5; 10/7|Genchain Extend=0, 5}}
Parasoft tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths ([[3/2]], flat of 702¢) to produce major 3rds that are flatter than [[5/4]] (386¢).
=== Hyposoft step ratios===
 
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}}
=== Hyposoft tunings===
:''Main article: [[Meantone]]''
:''Main article: [[Meantone]]''
Hyposoft step ratios (between 3:2 and 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5}}
Hyposoft tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).
===Hypohard step ratios===
 
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}}
===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]]''
The range of hypohard step ratios can be divided into a minihard range (between 2:1 and 5:2) and quasihard range (between 5:2 and 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).
====Minihard step ratios ====
====Minihard tunings ====
Minihard step ratios correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in a major 3rd of [[81/64]] (407¢).{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}
Minihard tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in a major 3rd of [[81/64]] (407¢).
====Quasihard step ratios====
 
Quasihard step ratios 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 [[41edo]] and [[53edo]].{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}
====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¢).


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}}
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}}
===Parahard and ultrahard step ratios===
===Parahard and ultrahard tunings===
:''Main article: [[Archy]]''
:''Main article: [[Archy]]''
The parahard and ultrahard ranges (between 3:1 and 1:1) correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}
Parahard (3:1 to 4:1) and ultrahard tunings (4:1 to 1:0) correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.
 
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}}
== Modes ==
== Modes ==
Diatonic modes have standard names from classical music theory:
Diatonic modes have standard names from classical music theory:
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/5L_2s"