Xenharmonic Wiki

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

← Older edit
VisualWikitext
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Mockup of changes for notationally agnostic mos page
ArrowHead294 (talk | contribs)
15,220 edits
mNo edit summary
 
(4 intermediate revisions by one other user not shown)
Line 1: Line 1:
{{Infobox MOS|Tuning=5L 2s}}
{{Infobox MOS|Tuning=5L 2s|debug=1}}
:''This is a test page. For the main page, see [[5L 2s]].''
:''This is a test page. For the main page, see [[5L 2s]].''
{{MOS intro|Scale Signature=5L 2s}}
{{MOS intro|Scale Signature=5L 2s}}
Line 9: Line 9:


==Intervals==
==Intervals==
:''This article assumes [[TAMNAMS]] for naming mossteps.''
:''This article assumes [[TAMNAMS]] for naming step ratios, mossteps, and mosdegrees.''
Intervals are identical to that of standard notation. As such, the usual [[Interval quality|interval qualities]] of major/minor and augmented/perfect/diminished apply here.
Names for this scale's intervals (mossteps) and scale degrees (mosdegrees) are based on the number of large and small steps from the root, starting at 0 (the 0-mosstep and 0-mosdegree) for the unison.


{{MOS intervals|Scale Signature=5L 2s}}
Except for the unison and octave, all [[Interval class|interval classes]] have two [[Interval variety|varieties]] or sizes, denoted using the terms ''major'' and ''minor'' for the large and small sizes, respectively. The exception to this rule are the generators, which use the terms ''augmented'', ''perfect'', and ''diminished'' instead.
{| class="wikitable"
|+5L 2s interval varieties
!Interval class
!Specific intervals
!Size (in ascending order)
|-
|'''0-diastep'''
|'''Perfect 0-diastep (unison)'''
|0
|-
| rowspan="2" |1-diastep
|Minor 1-diastep
|s
|-
|Major 1-diastep
|L
|-
| rowspan="2" |2-diastep
|Minor 2-diastep
|L + s
|-
|Major 2-diastep
|2L
|-
| rowspan="2" |'''3-diastep'''
|'''Perfect 3-diastep'''
|2L + s
|-
|Augmented 3-diastep
|3L
|-
| rowspan="2" |'''4-diastep'''
|Diminished 4-diastep
|2L + 2s
|-
|'''Perfect 4-diastep'''
|3L + s
|-
| rowspan="2" |5-diastep
|Minor 5-diastep
|3L + 2s
|-
|Major 5-diastep
|4L + s
|-
| rowspan="2" |6-diastep
|Minor 6-diastep
|4L + 2s
|-
|Major 6-diastep
|5L + s
|-
|'''7-diastep (octave)'''
|'''Perfect 7-diastep (octave)'''
|5L + 2s
|}
A 7-note scale using these intervals will typically use scale degrees that represents one size from each interval class, with the true MOS upholding the step pattern of LLLsLLs, or some rotation thereof. MODMOS scales may be formed this way without upholding the step pattern, thereby creating a non-MOS pattern such as LLLLsLs, or may include alterations that exceed the two varieties typical of a MOS scale.


==Notation==
==Notation==
Line 99: Line 156:
===Simple tunings===
===Simple tunings===
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
[[17edo]] and [[19edo]] are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=2/1; 3/1; 3/2|Genchain Extend=7|Notation=NONE}}
===Parasoft tunings ===
===Parasoft tunings ===
:''Main article: [[Flattone]]''
:''Main article: [[Flattone]]''
Line 106: Line 161:


Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
Edos include [[19edo]], [[26edo]], [[45edo]], and [[64edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 4/3; 7/5; 10/7|Genchain Extend=0, 5|Notation=NONE}}
===Hyposoft tunings===
===Hyposoft tunings===
:''Main article: [[Meantone]]''
:''Main article: [[Meantone]]''
Line 113: Line 166:


Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
Edos include [[19edo]], [[31edo]], [[43edo]], and [[50edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/2; 5/3; 7/4; 8/5|Genchain Extend=0, 5|Notation=NONE}}
===Hypohard tunings===
===Hypohard tunings===
:''Main article: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''
:''Main article: [[Pythagorean tuning]] and [[Schismatic family#Schismatic aka Helmholtz|schismatic temperament]]''
Line 122: Line 173:


Edos include [[41edo]] and [[53edo]].
Edos include [[41edo]] and [[53edo]].
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=7/3; 9/4|Genchain Extend=0, 5|Notation=NONE}}
==== Quasihard tunings====
==== Quasihard tunings====
Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294¢).
Quasihard tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of [[32/27]] (294¢).


Edos include [[17edo]], [[29edo]], and [[46edo]]. 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.
Edos include [[17edo]], [[29edo]], and [[46edo]]. 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|Notation=NONE}}
===Parahard and ultrahard tunings===
===Parahard and ultrahard tunings===
:''Main article: [[Archy]]''
:''Main article: [[Archy]]''
Line 135: Line 182:


Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
Edos include [[17edo]], [[22edo]], [[27edo]], and [[32edo]], among others.
{{MOS degrees|Scale Signature=5L 2s|Step Ratio=3/1; 4/1; 5/1; 6/1|Genchain Extend=0, 5|Notation=NONE}}
==Modes==
==Modes==
Diatonic modes have standard names from classical music theory:
Diatonic modes have standard names from classical music theory:
Line 234: Line 279:
|Perfect (C)
|Perfect (C)
|}
|}
== Generator chain ==
''Explain how the scale can also be generated by stacking 6 generating intervals in any combination of up or down from the root. Also explain how this can be extended further to 11 generators to produce chromatic scales.''


==Scales==
==Scales==
Line 259: Line 307:


==Scale tree ==
==Scale tree ==
{{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}}
{{MOS tuning spectrum
| Scale Signature = 5L 2s
| Depth = 6
| 7/5 = [[Flattone]] is in this region
| 21/13 = [[Golden meantone]] (696.2145{{c}})
| 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{{c}})
| 8/3 = [[Neogothic]] is in this region
| 4/1 = [[Archy]] is in this region
}}
 
==See also==
==See also==
 
* [[Diatonic functional harmony]]
*[[Diatonic functional harmony]]
Retrieved from "https://en.xen.wiki/w/User:Ganaram_inukshuk/5L_2s"