Xenharmonic Wiki

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

← Older editNewer edit →
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
No edit summary
Line 144: Line 144:
5L 2s has several rank-2 temperament interpretations, such as:
5L 2s has several rank-2 temperament interpretations, such as:


* Meantone, with generators around 696.2¢.
* Meantone, with generators around 696.2¢. These temperaments flatten the perfect 5th (702¢) to produce 5/4 (386¢) for a major 3rd.
** Flattone, with generators around 693.7¢.
** Flattone, with generators around 693.7¢. These temperaments have major 3rds that are flatter than 5/4.
*Schismic, with generators around 702¢, a just perfect 5th (3/2).
*Schismic, with generators around 702¢. These temperaments have perfect 5ths that are close to just, producing 81/64 (407¢) for a major 3rd.
*Parapyth, with generators around 704.7¢.
*Parapyth, with generators around 704.7¢. These temperaments have major 3rds that are sharper than 81/64.
*Archy, with generators around 709.3¢.
*Archy, with generators around 709.3¢. These temperaments have perfect 5ths that are significantly sharp.
**Supra, with generators around 707.2¢
**Supra, with generators around 707.2¢
**Superpyth, with generators around 710.3¢
**Superpyth, with generators around 710.3¢
Line 160: Line 160:
:''Main article: [[Meantone]] and [[Flattone]]''
:''Main article: [[Meantone]] and [[Flattone]]''
Most of the soft step ratio range (1:1 to 2:1) correspond to meantone temperaments. More specifically, the hyposoft range (3:2 to 2:1) corresponds to meantone and the parasoft range (4:3 and 3:2) corresponds to flattone.
Most of the soft step ratio range (1:1 to 2:1) correspond to meantone temperaments. More specifically, the hyposoft range (3:2 to 2:1) corresponds to meantone and the parasoft range (4:3 and 3:2) corresponds to flattone.
Both meantone and flattone are characterized with flattening the perfect 5th (3/2) to achieve major 3rds that are close to 5/4 (386¢), where the latter has major 3rds that are flatter than 5/4.


==== Parasoft step ratios ====
==== Parasoft step ratios ====
Line 169: Line 167:
===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 to 5:2) and quasihard range (between  5:2 to 3:1).
The range of hypohard step ratios can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1). Specifically, the minihard range corresponds to Pythagorean tuning and schismatic temperament, and quasihard to "neogothic" or "parapyth" systems.
==== 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 81/64 (407.8¢) for its major 3rd.
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5}}
{{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.
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}}
{{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 step ratios===
Parahard and ultrahard step ratios (3:1 or sharper) correspond to "archy" systems, whose perfect 5th is significantly sharper than just.
:''Main article: [[Superpyth]]''
Parahard and ultrahard step ratios (3:1 or harder) correspond to "archy" systems, such as superpyth.
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5}}


Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/5L_2s"