User:Ganaram inukshuk/5L 2s: Difference between revisions
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=== Parasoft step ratios === | === Parasoft step ratios === | ||
:''Main article: [[Flattone]]'' | :''Main article: [[Flattone]]'' | ||
Parasoft step ratios (4:3 and 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths (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 step ratios (between 4:3 and 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths (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}} | ||
===Hyposoft step ratios=== | ===Hyposoft step ratios=== | ||
:''Main article: [[Meantone]]'' | :''Main article: [[Meantone]]'' | ||
Hyposoft step ratios (3:2 | 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}} | ||
===Hypohard step ratios === | ===Hypohard step ratios === | ||
:''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 | 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). | ||
==== Minihard step ratios ==== | ==== Minihard step ratios ==== | ||
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 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}} | ||
====Quasihard step ratios==== | |||
==== Quasihard step ratios ==== | |||
Quasihard step ratios correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. | Quasihard step ratios correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. | ||
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===Parahard and ultrahard step ratios=== | ===Parahard and ultrahard step ratios=== | ||
:''Main article: [[Archy]]'' | :''Main article: [[Archy]]'' | ||
The parahard and ultrahard ranges (3:1 | 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}} | ||
==Modes== | |||
== Modes== | |||
Diatonic modes have standard names from classical music theory: | Diatonic modes have standard names from classical music theory: | ||
{{MOS modes|Scale Signature=5L 2s}} | {{MOS modes|Scale Signature=5L 2s}} | ||
Each mode has the following scale degrees, reached by raising or lowering certain naturals by a chroma. | Each mode has the following scale degrees, reached by raising or lowering certain naturals by a chroma. | ||
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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}} | 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]] | ||