Xenharmonic Wiki

7L 3s (4/1-equivalent): Difference between revisions

← Older edit

FloraC (talk | contribs)

4 user groups
27,346 edits
VisualWikitext
CompactStar (talk | contribs)
autopatrolled
5,879 edits
No edit summary
- duplicate data
 
(35 intermediate revisions by 4 users not shown)
Line 1: Line 1:
{{Infobox MOS}}
{{Infobox MOS}}
'''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.
{{MOS intro}}


== Modes ==
These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685{{c}} flat fifth and [[5edo]]/10ed4's 720{{c}} sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720{{c}} fifth and collapsed is 685{{c}} fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.
* LLLsLLsLLs 9|0
 
* LLsLLLsLLs 8|1
== Scale properties ==
* LLsLLsLLLs 7|2
{{TAMNAMS use}}
* LLsLLsLLsL 6|3
 
* LsLLLsLLsL 5|4
=== Intervals ===
* LsLLsLLLsL 4|5
{{MOS intervals}}
* LsLLsLLsLL 3|6
 
* sLLLsLLsLL 2|7
=== Generator chain ===
* sLLsLLLsLL 1|8
{{MOS genchain}}
* sLLsLLsLLL 0|9
 
=== Modes ===
{{MOS mode degrees}}
 
== Scale tree ==
{{MOS tuning spectrum
| 5/3 = [[Quarchy]] is around here
| 3/1 = [[Tetrominant]] is around here
| 4/1 = [[Meanquad]] is around here
}}


== Temperaments ==
== Temperaments ==
There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]].
There are two major rank-2 temperament interpretations of diaquadic, [[meanquad]] and [[quarchy]], corresponding to double-octave clones of [[meantone]] and [[archy]].
=== Meanquad ===
''Main article: [[Meanquad]]''
* [[Subgroup]]: 4.5.6
* [[Comma list]]: 81/80
* [[Val]]s: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
* [[CTE tuning]]: ~[[3/2]] = 697.214
Retrieved from "https://en.xen.wiki/w/7L_3s_(4/1-equivalent)"