User:Ganaram inukshuk/5L 2s: Difference between revisions
Fleshed out tuning ranges, based on info already in main-namespace article and corresponding temperament pages |
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== Step ratios== | == Step ratios== | ||
===Parasoft=== | ===Parasoft=== | ||
:''Main article: [[Flattone]]'' | :''Main article: [[Flattone]]'' | ||
Parasoft tunings (step ratios between 4:3 to 3:2) correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) so it makes the diatonic major 3rd flatter than 5/4 (386¢). Compatible edos include 26edo, 45edo, and 64edo. | Parasoft tunings (step ratios between 4:3 to 3:2) correspond to flattone temperaments, characterized by flattening the perfect 5th (3/2) so it makes the diatonic major 3rd flatter than 5/4 (386¢). Compatible edos include 26edo, 45edo, and 64edo. | ||
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=4/3; 7/5; 10/7}} | {{MOS degrees|Scale Signature=5L 2s|Step Ratio=4/3; 7/5; 10/7}} | ||
===Hyposoft=== | ===Hyposoft=== | ||
:''Main article: [[Meantone]]'' | :''Main article: [[Meantone]]'' | ||
Hyposoft tunings (step ratio between 3:2 to 2:1) correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Compatible edos include 19edo, 31edo, and 50edo. | Hyposoft tunings (step ratio between 3:2 to 2:1) correspond to meantone temperaments, characterized by flattening the perfect 5th (3/2) to achieve a diatonic major 3rd that approximates 5/4 (386¢). Compatible edos include 19edo, 31edo, and 50edo. | ||
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 8/5}} | {{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 8/5}} | ||
===Hypohard === | ===Hypohard === | ||
:''Main articles: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]'' | :''Main articles: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]'' | ||
The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1). | The range of hypohard tunings can be divided into a minihard range (step ratios 2:1 to 5:2) and quasihard range (step ratios 5:2 to 3:1). | ||
==== Minihard ==== | ==== Minihard ==== | ||
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 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo. | 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 81/64 (407.8¢) for its major 3rd. Compatible edos include 41edo, and 53edo. | ||
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4}} | {{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4}} | ||
==== Quasihard ==== | ==== Quasihard ==== | ||
Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. Compatible edos include 29edo and 46edo. | Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is sharper than just, resulting in major 3rds that are sharper than 81/64. Compatible edos include 29edo and 46edo. | ||