3L 5s: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) |
||
(8 intermediate revisions by 3 users not shown) | |||
Line 8: | Line 8: | ||
| Pattern = LsLssLss | | Pattern = LsLssLss | ||
}} | }} | ||
{{MOS intro|Other Names=anti-oneirotonic}} | |||
== Name == | == Name == | ||
[[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale. | [[TAMNAMS]] suggests the temperament-agnostic name '''checkertonic''' for this scale. | ||
== | == Scale properties == | ||
{{TAMNAMS use}} | {{TAMNAMS use}} | ||
=== Intervals === | |||
{{MOS intervals}} | {{MOS intervals}} | ||
== | === Generator chain === | ||
{{MOS genchain}} | |||
== | === Modes === | ||
{{MOS mode degrees}} | {{MOS mode degrees}} | ||
=== Proposed names === | ==== Proposed mode names ==== | ||
The modes of checkertonic can be named after its sister | The modes of checkertonic can be named after its sister mos [[5L 3s]] (oneirotonic). {{u|R-4981}} has also proposed names based on {{w|grand chess}} pieces. | ||
{{MOS modes | |||
{{MOS modes|Table Headers=Anti-modes of 5L 3s | | Table Headers= | ||
King | Anti-modes of 5L 3s $ | ||
Anti-Hlanithian (lə-NITH-iən) | Grand chess names<sup>[proposed]</sup> | ||
Queen | | Table Entries= | ||
Anti-Kadathian (kə-DA(H)TH-iən) | Anti-Sarnathian (sar-NA(H)TH-iən) $ | ||
Marshall | King $ | ||
Anti-Mnarian (mə-NA(I)R-iən) | Anti-Hlanithian (lə-NITH-iən) $ | ||
Cardinal | Queen $ | ||
Anti-Ultharian (ul-THA(I)R-iən) | Anti-Kadathian (kə-DA(H)TH-iən) $ | ||
Rook | Marshall $ | ||
Anti-Celephaïsian (kel-ə-FAY-zhən) | Anti-Mnarian (mə-NA(I)R-iən) $ | ||
Bishop | Cardinal $ | ||
Anti-Illarnekian (ill-ar-NEK-iən) | Anti-Ultharian (ul-THA(I)R-iən) $ | ||
Knight | Rook $ | ||
Anti-Dylathian (də-LA(H)TH-iən) | Anti-Celephaïsian (kel-ə-FAY-zhən) $ | ||
Pawn | Bishop $ | ||
Anti-Illarnekian (ill-ar-NEK-iən) $ | |||
Knight $ | |||
Anti-Dylathian (də-LA(H)TH-iən) $ | |||
Pawn $ | |||
}} | |||
The order of modes on the white keys JKLMNOPQ are: | The order of modes on the white keys JKLMNOPQ are: | ||
Line 202: | Line 189: | ||
| (J) | | (J) | ||
|} | |} | ||
== Notation == | |||
The [[TAMNAMS]] system is used in this article to refer to {{PAGENAME}} step size ratios and step ratio ranges. | |||
The notation used in this article is JKLMNOPQJ = sLssLsLs (Anti-Ultharian), &/@ = up/down by chroma. | |||
== Theory == | |||
In contrast to oneirotonic ([[5L 3s]]), which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth ([[3/2]], usually as a dim. chk6th or maj. chk5th), and thus can be used for traditional root-3rd-P5 harmony. | |||
=== Low harmonic entropy scales === | |||
There are two significant harmonic entropy minima with this MOS pattern: | |||
* [[Sensipent family|Sensi]], in which the generator is a 9/7, two of them make a 5/3, and seven of them make a 3/2, which is proper. | |||
* [[Meantone family #Squares|Squares]], in which the generator is also a 9/7, but two of them make an 18/11 and four of them make a 4/3, which is improper. | |||
== Tuning ranges == | |||
=== Simple tunings === | |||
{{MOS tunings}} | |||
=== Parasoft tunings === | |||
Parasoft tunings (step ratios 4:3 to 3:2) are associated with [[sensi]] tempermament. | |||
{{MOS tunings|Step Ratios=Parasoft|JI Ratios=Subgroup: 2.3.5.7.13; Int Limit: 50; Tenney Height: 8; Complements Only: 1|Tolerance=10}} | |||
== Temperaments == | == Temperaments == | ||
Line 209: | Line 218: | ||
== Music == | == Music == | ||
; [[Uncreative Name]] | |||
* [https://www.youtube.com/watch?v=XZ3zB3EDKOM ''The Nachtlandian Somersault''] (19edo) | |||
== Scale tree == | == Scale tree == | ||
Generator ranges: | Generator ranges: | ||
* Chroma-positive generator: 750 | * Chroma-positive generator: 750{{c}} (5\8) to 800{{c}} (2\3) | ||
* Chroma-negative generator: 400 | * Chroma-negative generator: 400{{c}} (1\3) to 450{{c}} (3\8) | ||
{{MOS tuning spectrum | |||
{{ | | 7/5 = [[Sensi]] (optimal around here) | ||
7/5 | | 11/7 = [[Clyde]] | ||
11/7 | | 13/8 = Golden [[sentry]] (759.4078{{c}}) | ||
13/8 | | 13/5 = Unnamed golden tuning (768.8815{{c}}) | ||
13/5 | | 11/4 = [[Hamity]] | ||
11/4 | | 7/2 = [[Squares]] (optimal around here) | ||
7/2 | | 6/1 = [[Roman]]↓, [[hocus]]↓ | ||
6/1 | |||
}} | }} | ||