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{{Infobox MOS|Tuning=4L 3s|debug=1}}
{{User:Ganaram inukshuk/Template:Rewrite draft
 
|4L 3s|compare=https://en.xen.wiki/w/Special:ComparePages?page1=4L+3s&rev1=&page2=User%3AGanaram+inukshuk%2F4L+3s&rev2=&action=&diffonly=&unhide=
:''This is a test page. For the main page, see [[4L 3s]].''
|changes=see what the page looks like with proposed changes (scale characteristics section) and quickstart guide}}
 
{{Has quickstart}}
{{Infobox MOS|debug=1|Tuning=4L 3s}}
{{MOS intro|Scale Signature=4L 3s}}
{{MOS intro|Scale Signature=4L 3s}}
4L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.
4L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], where one large step of diatonic ([[5L 2s]]) is replaced with a small step.
 
==Name ==
== Name ==
[[TAMNAMS]] suggests the temperament-agnostic name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of [[6/5]] (just minor 3rd, 315.6¢).
[[TAMNAMS]] suggests the temperament-agnostic name '''smitonic''' ''smy-TON-ik'' /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of [[6/5]] (just minor 3rd, 315.6¢).
 
== Notation==
== Intervals ==
:''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees, and [[Diamond-mos notation|diamond-MOS notation]] for note names.''
 
===Intervals and degrees===
: ''This article assumes [[TAMNAMS]] for naming step ratios, intervals, and scale degrees.''
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 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.
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 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.


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.
Being a moment-of-symmetry scale, every [[interval class]] of 4L 3s, except for the unison and octave, has two [[Interval variety|varieties]] – large and small – whose [[Interval quality|relative qualities]] are denoted as major or minor, or augmented, perfect, and diminished for the generators.
{| class="wikitable"
{{MOS intervals|Scale Signature=4L 3s}}
|+Intervals of 4L 3s
===Note names===
!Interval class
For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following:
!Specific intervals
!Size (in ascending order)
|-
|'''0-smistep'''
|'''Perfect 0-smistep (unison)'''
|0
|-
| rowspan="2" |1-smistep
|Minor 1-smistep
|s
|-
|Major 1-smistep
|L
|-
| rowspan="2" |'''2-smistep'''
|'''Perfect 2-smistep'''
|L + s
|-
|Augmented 2-smistep
|2L
|-
| rowspan="2" |3-smistep
|Minor 3-smistep
|L + 2s
|-
|Major 3-smistep
|2L + s
|-
| rowspan="2" |4-smistep
|Minor 4-smistep
|2L + 2s
|-
| Major 4-smistep
|3L + s
|-
| rowspan="2" |'''5-smistep'''
|Diminished 5-smistep
| 2L + 3s
|-
|'''Perfect 5-smistep'''
|3L + 2s
|-
| rowspan="2" |6-smistep
|Minor 6-smistep
|3L + 3s
|-
|Major 6-smistep
|4L + 2s
|-
|'''7-smistep (octave)'''
|'''Perfect 7-smistep (octave)'''
|4L + 3s
|}
Different forms of this MOS are generally built using one specific interval for each interval class, while the step pattern LLsLsLs, or some rotation thereof, is formed between consecutive scale degrees. Alternatively, MODMOS scales can be formed by deviating from the step pattern, such as with LLLssLs, or by including alterations outside the specific sizes described.
 
== Notation ==
Names for notes in this scale can be denoted using the following notation schemes.
 
=== Ups and downs notation ===
:''Main article: [[Ups and downs notation]]''
(Insert [[Ups and downs notation|ups-and-downs]] example here)
 
=== Diamond-mos notation ===
:''Main article: [[Diamond-mos notation]]''
[[Diamond-mos notation|Diamond-mos]] can be used by assigning the note names JKLMNOP to one of the modes and using the symbols "&" and "@" to denote generalized sharps and flats, respectively. Using the symmetric mode (LsLsLsL), the basic 10edo gamut is as follows:


{{MOS gamut|Scale Signature=4L 3s}}
{{MOS gamut|Scale Signature=4L 3s}}
==Theory==
==Theory==
===Low harmonic entropy scales===
===Low harmonic entropy scales===
There are two notable harmonic entropy minima:
There are two notable harmonic entropy minima:
*[[Kleismic family|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.
*[[Kleismic family|Kleismic temperament]], in which the generator is 6/5 and 6 of them make a 3/1.
*[[myna|Myna temperament]], in which the generator is also 6/5 but 10 of them make a 6/1, resulting in the intervals 4/3 and 3/2 being absent.
*[[myna|Myna temperament]], in which the generator is also 6/5 but 10 of them make a 6/1, resulting in the intervals 4/3 and 3/2 being absent.
===Temperament interpretations===
===Temperament interpretations===
:''Main article: [[4L 3s/Temperaments]]''
:''Main article: [[4L 3s/Temperaments]]''
4L 3s has the following temperament interpretations:
4L 3s has the following temperament interpretations:
*[[Sixix]], with generators around 338.6¢.
*[[Sixix]], with generators around 338.6¢.
*[[Orgone]], with generators around 323.4¢.
*[[Orgone]], with generators around 323.4¢.
*[[Kleismic]], with generators around 317¢.
*[[Kleismic]], with generators around 317¢.
Other temperaments, such as [[amity]] and [[myna]], require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches.
Other temperaments, such as [[amity]] and [[myna]], require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a [[MODMOS]] or a larger MOS gamut is necessary to access these pitches.
 
== Tuning ranges ==
==Tuning ranges==
===Simple tunings===
===Simple tunings===
The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Other small edos include 15edo and 18edo.{{MOS degrees|Scale Signature=4L 3s|Step Ratio=2/1; 3/1; 3/2|Notation=NONE}}
The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Other small edos include [[15edo]] and [[18edo]].{{MOS degrees|Step Ratio=2/1; 3/1; 3/2|JI Ratios=M1md: [[8/7]];
P2md: [[6/5]], [[77/64]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]]
|Scale Signature=4L 3s}}
===Parasoft tunings===
===Parasoft tunings===
Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:
Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings:


*The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
*The major 1-mosstep, or large step, is around [[10/9]] to [[9/8]], thus making it a "meantone".
*The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.
* The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.


These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702¢), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range.
These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702¢), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range.
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**18edo has a major 1-mosstep that is close to 9/8 (203¢).
**18edo has a major 1-mosstep that is close to 9/8 (203¢).
**18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700¢) by 33.3¢.
**18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700¢) by 33.3¢.
**18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
** 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
*The augmented 2-mosstep of 25edo is very close to 5/4 (386¢).
* The augmented 2-mosstep of 25edo is very close to 5/4 (386¢).
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 4/3; 7/5|Genchain Extend=9|Notation=NONE}}
*The various interval flavors separated by a chroma shows that parasoft smitonic is a useful [[cluster MOS]]. However, many of these intervals lack simple JI interpretations.
{{MOS degrees|Step Ratio=3/2; 4/3; 7/5|Number of Alterations=1|JI Ratios=m1md: [[13/12]];
M1md: [[9/8]], [[10/9]];
P2md: [[17/14]], [[40/33]];
A2md: [[5/4]];
m3md: [[21/16]];
M3md: [[19/14]], [[34/25]];
A3md: [[7/5]];
d4md: [[10/7]];
m4md: [[28/19]], [[25/17]];
M4md: [[32/21]];
d5md: [[8/5]];
P5md: [[28/17]], [[33/20]];
m6md: [[16/9]], [[9/5]];
M6md: [[24/13]]
|Scale Signature=4L 3s}}
===Hyposoft tunings===
===Hyposoft tunings===
Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327¢ and 333¢. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "[[Gentle region|neogothic]] smitonic" or "[[archy]] smitonic".
Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327¢ and 333¢. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "[[Gentle region|neogothic]] smitonic" or "[[archy]] smitonic".


Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
Edos include [[11edo]] (not shown), [[18edo]], and [[29edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/2; 5/3|Genchain Extend=3|Notation=NONE}}
{{MOS degrees|Step Ratio=3/2; 5/3|JI Ratios=m1md: [[14/13]];
M1md: [[9/8]];
P2md: [[23/19]], [[40/33]];
A2md: [[14/11]];
m3md: [[13/10]];
M3md: [[15/11]];
m4md: [[19/13]], [[22/15]];
M4md: [[20/13]];
d5md: [[11/7]];
P5md: [[33/20]], [[38/23]];
m6md: [[16/9]];
M6md: [[13/7]]
|Scale Signature=4L 3s}}
===Hypohard tunings===
===Hypohard tunings===
Hypohard smitonic tunings (2:1 to 3:1) have generators between 320¢ and 327¢. The major 1-mosstep, or large step, tends to approximate [[8/7]] (231¢) and the major 3-mosstep tends to approximate [[11/8]] (551¢). [[26edo]] approximates these two intervals very well. These JI approximations are associated with [[orgone]] temperament.
Hypohard smitonic tunings (2:1 to 3:1) have generators between 320¢ and 327¢. The major 1-mosstep, or large step, tends to approximate [[8/7]] (231¢) and the major 3-mosstep tends to approximate [[11/8]] (551¢). [[26edo]] approximates these two intervals very well. These JI approximations are associated with [[orgone]] temperament.


Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
Other hypohard edos include [[11edo]] (not shown), [[15edo]] and [[37edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=3/1; 5/2; 7/3|Genchain Extend=3|Notation=NONE}}
{{MOS degrees|Step Ratio=3/1; 5/2; 7/3|JI Ratios=M1md: [[8/7]];
P2md: [[6/5]], [[77/64]];
m3md: [[14/11]];
M3md: [[11/8]];
m4md: [[16/11]];
M4md: [[11/7]];
P5md: [[5/3]];
m6md: [[7/4]];
|Scale Signature=4L 3s}}
===Parahard tunings===
===Parahard tunings===
Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9¢ and 320¢, putting it close to a pure 6/5 (316¢). Stacking six generators and octave-reducing approximates 3/2 (702¢), a diatonic perfect 5th, represented by the diminished 5-mosstep.
Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9¢ and 320¢, putting it close to a pure 6/5 (316¢). Stacking six generators and octave-reducing approximates 3/2 (702¢), a diatonic perfect 5th, represented by the diminished 5-mosstep.
Line 142: Line 111:


Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].
Parahard edos smaller than 53edo include [[15edo]] (not shown), [[19edo]], and [[34edo]].
{{MOS degrees|Scale Signature=4L 3s|Step Ratio=4/1; 7/2; 11/3; 15/4|Genchain Extend=3|Prefix=smi|Notation=NONE}}
{{MOS degrees|Step Ratio=4/1; 7/2; 11/3; 15/4|JI Ratios=m1md: [[25/24]], [[26/25]];
M1md: [[15/13]];
P2md: [[6/5]];
A2md: [[4/3]];
m3md: [[5/4]];
M3md: [[18/13]];
m4md: [[13/9]];
M4md: [[8/5]];
d5md: [[3/2]];
P5md: [[5/3]];
m6md: [[26/15]];
M6md: [[25/13]]
|Scale Signature=4L 3s}}
==Modes==
==Modes==
{{MOS modes|Scale Signature=4L 3s|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}}
Alexandru Ianu ([[User:Ayceman|Ayceman]])<ref>Description of ''Sylvian Moon Dance'' mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.</ref> has proposed the following mode names relating to the Almsivi in Morrowind (TES):
==Scales==


=== Subset and superset scales ===
{{MOS modes|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic|Scale Signature=4L 3s}}
4L 3s has a parent scale of [[1L 3s]], a tetratonic scale, meaning 1L 3s is a subset. 4L 3s also has two child scales, which are supersets of 4L 3s:


* [[7L 4s]], a smitonic chromatic scale produced using soft-of-basic step ratios.
===Scale degrees===
* [[4L 7s]], a smitonic chromatic scale produced using hard-of-basic step ratios.
{{MOS mode degrees|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic|Scale Signature=4L 3s}}


==Scales==
=== Subset and superset scales===
4L 3s has a parent scale of [[3L 1s]], a tetratonic scale, meaning 1L 3s is a subset. 4L 3s also has two child scales, which are supersets of 4L 3s:
*[[7L 4s]], a smitonic chromatic scale produced using soft-of-basic step ratios.
*[[4L 7s]], a smitonic chromatic scale produced using hard-of-basic step ratios.
11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.
11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.
===Scala files===
===Scala files===
*[[Orgone7]]
*[[Orgone7]]
*[[Cata7]]
*[[Cata7]]
Line 170: Line 152:
8/3: [[Superkleismic]];
8/3: [[Superkleismic]];
11/3: [[Hanson]]/[[keemun]];
11/3: [[Hanson]]/[[keemun]];
6/1: [[Oolong]]/[[myna]]↓;
6/1: [[Oolong]]/[[myna]]↓}}
2/1: (Generators smaller than this are proper)}}
==Music==
==Music==
''(add music)''
*[[City of the Asleep]], [https://cityoftheasleep.bandcamp.com/album/an-amputated-elliptic-knob-of-the-cryptocurve-regenerates "An Amputated Elliptic Knob of the Cryptocurve Regenerates"] (Various orgone edos)
*[[User:Ks26|ks26]], [https://www.youtube.com/watch?v=AEnEYk3X1as Ghost Bridge] (11edo)
*[[User:Ayceman|Alexandru Ianu]], [https://youtu.be/81uZbsmbet8 Sylvian Moon Dance] (11edo) ([[:File:Sylvian_Moon_Dance.pdf|sheet music]])
*[[File:Sixix Fugue.mp3|256x256px]] A fugue in [[18edo]] smitonic functional harmony (WIP)


== See also ==
==References==
Approaches:
<references />
*[[4L 3s/Inthar's approach]]

Revision as of 01:50, 23 May 2024

The following is a draft for a proposed rewrite of the following page: 4L 3s

The primary changes are as follows: see what the page looks like with proposed changes (scale characteristics section) and quickstart guide

The original page can be compared with this page here.

This page has a quickstart guide.
Information on how to start composing or playing can be found at the page linked above.
↖ 3L 2s ↑ 4L 2s 5L 2s ↗
← 3L 3s 4L 3s 5L 3s →
↙ 3L 4s ↓ 4L 4s 5L 4s ↘ 
┌╥╥┬╥┬╥┬┐
│║║│║│║││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLs
sLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 5\7 to 3\4 (857.1 ¢ to 900.0 ¢)
Dark 1\4 to 2\7 (300.0 ¢ to 342.9 ¢)
TAMNAMS information
Name smitonic
Prefix smi-
Abbrev. smi
Related MOS scales
Parent 3L 1s
Sister 3L 4s
Daughters 7L 4s, 4L 7s
Neutralized 1L 6s
2-Flought 11L 3s, 4L 10s
Equal tunings
Equalized (L:s = 1:1) 5\7 (857.1 ¢)
Supersoft (L:s = 4:3) 18\25 (864.0 ¢)
Soft (L:s = 3:2) 13\18 (866.7 ¢)
Semisoft (L:s = 5:3) 21\29 (869.0 ¢)
Basic (L:s = 2:1) 8\11 (872.7 ¢)
Semihard (L:s = 5:2) 19\26 (876.9 ¢)
Hard (L:s = 3:1) 11\15 (880.0 ¢)
Superhard (L:s = 4:1) 14\19 (884.2 ¢)
Collapsed (L:s = 1:0) 3\4 (900.0 ¢)

4L 3s, named smitonic in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 4 large steps and 3 small steps, repeating every octave. Generators that produce this scale range from 857.1 ¢ to 900 ¢, or from 300 ¢ to 342.9 ¢. 4L 3s can be seen as a warped diatonic scale, where one large step of diatonic (5L 2s) is replaced with a small step.

Name

TAMNAMS suggests the temperament-agnostic name smitonic smy-TON-ik /smaɪˈtɒnɪk/ for this scale. The name is derived from 'sharp minor third', since the central range for the dark generator (320¢ to 333.3¢) is significantly sharp of 6/5 (just minor 3rd, 315.6¢).

Notation

This article assumes TAMNAMS for naming step ratios, intervals, and scale degrees, and diamond-MOS notation for note names.

Intervals and degrees

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 (0-mosstep and 0-mosdegree) for the unison, per TAMNAMS. Ordinal names, such as mos-1st for the unison, are discouraged for non-diatonic MOS scales.

Being a moment-of-symmetry scale, every interval class of 4L 3s, except for the unison and octave, has two varieties – large and small – whose relative qualities are denoted as major or minor, or augmented, perfect, and diminished for the generators.

Intervals of 4L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-smistep Perfect 0-smistep P0smis 0 0.0 ¢
1-smistep Minor 1-smistep m1smis s 0.0 ¢ to 171.4 ¢
Major 1-smistep M1smis L 171.4 ¢ to 300.0 ¢
2-smistep Perfect 2-smistep P2smis L + s 300.0 ¢ to 342.9 ¢
Augmented 2-smistep A2smis 2L 342.9 ¢ to 600.0 ¢
3-smistep Minor 3-smistep m3smis L + 2s 300.0 ¢ to 514.3 ¢
Major 3-smistep M3smis 2L + s 514.3 ¢ to 600.0 ¢
4-smistep Minor 4-smistep m4smis 2L + 2s 600.0 ¢ to 685.7 ¢
Major 4-smistep M4smis 3L + s 685.7 ¢ to 900.0 ¢
5-smistep Diminished 5-smistep d5smis 2L + 3s 600.0 ¢ to 857.1 ¢
Perfect 5-smistep P5smis 3L + 2s 857.1 ¢ to 900.0 ¢
6-smistep Minor 6-smistep m6smis 3L + 3s 900.0 ¢ to 1028.6 ¢
Major 6-smistep M6smis 4L + 2s 1028.6 ¢ to 1200.0 ¢
7-smistep Perfect 7-smistep P7smis 4L + 3s 1200.0 ¢

Note names

For this article, note names are based on diamond-MOS notation, where the naturals JKLMNOP are applied to the step pattern LsLsLsL and the accidentals & (pronounced "am" or "amp") and @ (pronounced "at") are used to represent sharps and flats respectively. Thus, the basic gamut for 4L 3s is the following:

J, J&/K@, K, L, L&/M@, M, N, N&/O@, O, P, P&/J@, J

Theory

Low harmonic entropy scales

There are two notable harmonic entropy minima:

  • Kleismic temperament, in which the generator is 6/5 and 6 of them make a 3/1.
  • Myna temperament, in which the generator is also 6/5 but 10 of them make a 6/1, resulting in the intervals 4/3 and 3/2 being absent.

Temperament interpretations

Main article: 4L 3s/Temperaments

4L 3s has the following temperament interpretations:

  • Sixix, with generators around 338.6¢.
  • Orgone, with generators around 323.4¢.
  • Kleismic, with generators around 317¢.

Other temperaments, such as amity and myna, require more than 7 pitches to contain the concordant chords optimized by these temperaments. If restricted to a rank-2 approach, a MODMOS or a larger MOS gamut is necessary to access these pitches.

Tuning ranges

Simple tunings

The basic tuning for 4L 3s has a large and small step size of 2 and 1 respectively, which is supported by 11edo. Other small edos include 15edo and 18edo.

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 11edo (Basic, L:s = 2:1) 15edo (Hard, L:s = 3:1) 18edo (Soft, L:s = 3:2) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 1 109.1 1 80 2 133.3
Major 1-smidegree 2 218.2 3 240 3 200 8/7
Perfect 2-smidegree 3 327.3 4 320 5 333.3 6/5, 77/64
Augmented 2-smidegree 4 436.4 6 480 6 400
Minor 3-smidegree 4 436.4 5 400 7 466.7 14/11
Major 3-smidegree 5 545.5 7 560 8 533.3 11/8
Minor 4-smidegree 6 654.5 8 640 10 666.7 16/11
Major 4-smidegree 7 763.6 10 800 11 733.3 11/7
Diminished 5-smidegree 7 763.6 9 720 12 800
Perfect 5-smidegree 8 872.7 11 880 13 866.7 5/3
Minor 6-smidegree 9 981.8 12 960 15 1000 7/4
Major 6-smidegree 10 1090.9 14 1120 16 1066.7
Perfect 7-smidegree (octave) 11 1200 15 1200 18 1200 2/1 (exact)

Parasoft tunings

Parasoft smitonic tunings (4:3 to 3:2) can be considered "meantone smitonic" since it has the following features of meantone diatonic tunings:

  • The major 1-mosstep, or large step, is around 10/9 to 9/8, thus making it a "meantone".
  • The augmented 2-mosstep is around the size of a meantone-sized major 3rd and can be used as a stand-in for such.

These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702¢), and they have otherwise fairly convincing versions of both diatonic structure and tertian harmony, provided you frequently modify using the comma-like chromas. For this reason, parasoft might be the most accessible smitonic tuning range.

Edos include 18edo, 25edo, and 43edo. Some key considerations include:

  • 18edo can be used to make the large and small steps more distinct, or can be considered a distorted 19edo diatonic.
    • 18edo has a major 1-mosstep that is close to 9/8 (203¢).
    • 18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700¢) by 33.3¢.
    • 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
  • The augmented 2-mosstep of 25edo is very close to 5/4 (386¢).
  • The various interval flavors separated by a chroma shows that parasoft smitonic is a useful cluster MOS. However, many of these intervals lack simple JI interpretations.
User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 18edo (Soft, L:s = 3:2) 25edo (Supersoft, L:s = 4:3) 43edo (L:s = 7:5) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Augmented 0-smidegree 1 66.7 1 48 2 55.8
Diminished 1-smidegree 1 66.7 2 96 3 83.7
Minor 1-smidegree 2 133.3 3 144 5 139.5 13/12
Major 1-smidegree 3 200 4 192 7 195.3 9/8, 10/9
Augmented 1-smidegree 4 266.7 5 240 9 251.2
Diminished 2-smidegree 4 266.7 6 288 10 279.1
Perfect 2-smidegree 5 333.3 7 336 12 334.9 17/14, 40/33
Augmented 2-smidegree 6 400 8 384 14 390.7 5/4
2× Augmented 2-smidegree 7 466.7 9 432 16 446.5
Diminished 3-smidegree 6 400 9 432 15 418.6
Minor 3-smidegree 7 466.7 10 480 17 474.4 21/16
Major 3-smidegree 8 533.3 11 528 19 530.2 19/14, 34/25
Augmented 3-smidegree 9 600 12 576 21 586 7/5
Diminished 4-smidegree 9 600 13 624 22 614 10/7
Minor 4-smidegree 10 666.7 14 672 24 669.8 28/19, 25/17
Major 4-smidegree 11 733.3 15 720 26 725.6 32/21
Augmented 4-smidegree 12 800 16 768 28 781.4
2× Diminished 5-smidegree 11 733.3 16 768 27 753.5
Diminished 5-smidegree 12 800 17 816 29 809.3 8/5
Perfect 5-smidegree 13 866.7 18 864 31 865.1 28/17, 33/20
Augmented 5-smidegree 14 933.3 19 912 33 920.9
Diminished 6-smidegree 14 933.3 20 960 34 948.8
Minor 6-smidegree 15 1000 21 1008 36 1004.7 16/9, 9/5
Major 6-smidegree 16 1066.7 22 1056 38 1060.5 24/13
Augmented 6-smidegree 17 1133.3 23 1104 40 1116.3
Diminished 7-smidegree 17 1133.3 24 1152 41 1144.2
Perfect 7-smidegree (octave) 18 1200 25 1200 43 1200 2/1 (exact)

Hyposoft tunings

Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327¢ and 333¢. By analogy of parasoft tunings being called "meantone smitonic", these tunings can be considered "neogothic smitonic" or "archy smitonic".

Edos include 11edo (not shown), 18edo, and 29edo.

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 18edo (Soft, L:s = 3:2) 29edo (Semisoft, L:s = 5:3) Approx. JI Ratios
Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 1/1 (exact)
Minor 1-smidegree 2 133.3 3 124.1 14/13
Major 1-smidegree 3 200 5 206.9 9/8
Perfect 2-smidegree 5 333.3 8 331 23/19, 40/33
Augmented 2-smidegree 6 400 10 413.8 14/11
Minor 3-smidegree 7 466.7 11 455.2 13/10
Major 3-smidegree 8 533.3 13 537.9 15/11
Minor 4-smidegree 10 666.7 16 662.1 19/13, 22/15
Major 4-smidegree 11 733.3 18 744.8 20/13
Diminished 5-smidegree 12 800 19 786.2 11/7
Perfect 5-smidegree 13 866.7 21 869 33/20, 38/23
Minor 6-smidegree 15 1000 24 993.1 16/9
Major 6-smidegree 16 1066.7 26 1075.9 13/7
Perfect 7-smidegree (octave) 18 1200 29 1200 2/1 (exact)

Hypohard tunings

Hypohard smitonic tunings (2:1 to 3:1) have generators between 320¢ and 327¢. The major 1-mosstep, or large step, tends to approximate 8/7 (231¢) and the major 3-mosstep tends to approximate 11/8 (551¢). 26edo approximates these two intervals very well. These JI approximations are associated with orgone temperament.

Other hypohard edos include 11edo (not shown), 15edo and 37edo.

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 15edo (Hard, L:s = 3:1) 26edo (Semihard, L:s = 5:2) 37edo (L:s = 7:3) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 1 80 2 92.3 3 97.3
Major 1-smidegree 3 240 5 230.8 7 227 8/7
Perfect 2-smidegree 4 320 7 323.1 10 324.3 6/5, 77/64
Augmented 2-smidegree 6 480 10 461.5 14 454.1
Minor 3-smidegree 5 400 9 415.4 13 421.6 14/11
Major 3-smidegree 7 560 12 553.8 17 551.4 11/8
Minor 4-smidegree 8 640 14 646.2 20 648.6 16/11
Major 4-smidegree 10 800 17 784.6 24 778.4 11/7
Diminished 5-smidegree 9 720 16 738.5 23 745.9
Perfect 5-smidegree 11 880 19 876.9 27 875.7 5/3
Minor 6-smidegree 12 960 21 969.2 30 973 7/4
Major 6-smidegree 14 1120 24 1107.7 34 1102.7
Perfect 7-smidegree (octave) 15 1200 26 1200 37 1200 2/1 (exact)

Parahard tunings

Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9¢ and 320¢, putting it close to a pure 6/5 (316¢). Stacking six generators and octave-reducing approximates 3/2 (702¢), a diatonic perfect 5th, represented by the diminished 5-mosstep.

This range contains very accurate edos such as 53edo and 72edo, and has very accurate approximations to many low-overtone JI intervals, namely basic 5-limit ratios and some ratios involving 13. However, 4L 3s only has one interval of 3/2, so it's suggested to use a larger MOS, such as 4L 7s, to achieve 5-limit harmony.

These JI approximations are associated with kleismic temperament, though the 2.3.5.13 extension described here is called cata.

Parahard edos smaller than 53edo include 15edo (not shown), 19edo, and 34edo.

User:MOS degrees is deprecated. Please use Template:MOS tunings instead.
Scale degree of 4L 3s
Scale degree 19edo (Superhard, L:s = 4:1) 34edo (L:s = 7:2) 53edo (L:s = 11:3) 72edo (L:s = 15:4) Approx. JI Ratios
Steps Cents Steps Cents Steps Cents Steps Cents
Perfect 0-smidegree (unison) 0 0 0 0 0 0 0 0 1/1 (exact)
Minor 1-smidegree 1 63.2 2 70.6 3 67.9 4 66.7 25/24, 26/25
Major 1-smidegree 4 252.6 7 247.1 11 249.1 15 250 15/13
Perfect 2-smidegree 5 315.8 9 317.6 14 317 19 316.7 6/5
Augmented 2-smidegree 8 505.3 14 494.1 22 498.1 30 500 4/3
Minor 3-smidegree 6 378.9 11 388.2 17 384.9 23 383.3 5/4
Major 3-smidegree 9 568.4 16 564.7 25 566 34 566.7 18/13
Minor 4-smidegree 10 631.6 18 635.3 28 634 38 633.3 13/9
Major 4-smidegree 13 821.1 23 811.8 36 815.1 49 816.7 8/5
Diminished 5-smidegree 11 694.7 20 705.9 31 701.9 42 700 3/2
Perfect 5-smidegree 14 884.2 25 882.4 39 883 53 883.3 5/3
Minor 6-smidegree 15 947.4 27 952.9 42 950.9 57 950 26/15
Major 6-smidegree 18 1136.8 32 1129.4 50 1132.1 68 1133.3 25/13
Perfect 7-smidegree (octave) 19 1200 34 1200 53 1200 72 1200 2/1 (exact)

Modes

Alexandru Ianu (Ayceman)[1] has proposed the following mode names relating to the Almsivi in Morrowind (TES):


Modes of 4L 3s
UDP Cyclic
order		 Step
pattern
6|0 1 LLsLsLs
5|1 6 LsLLsLs
4|2 4 LsLsLLs
3|3 2 LsLsLsL
2|4 7 sLLsLsL
1|5 5 sLsLLsL
0|6 3 sLsLsLL

Scale degrees

Scale degrees of the modes of 4L 3s
UDP Cyclic
order 		Step
pattern 		Scale degree (smidegree)
0 1 2 3 4 5 6 7
6|0 1 LLsLsLs Perf. Maj. Aug. Maj. Maj. Perf. Maj. Perf.
5|1 6 LsLLsLs Perf. Maj. Perf. Maj. Maj. Perf. Maj. Perf.
4|2 4 LsLsLLs Perf. Maj. Perf. Maj. Min. Perf. Maj. Perf.
3|3 2 LsLsLsL Perf. Maj. Perf. Maj. Min. Perf. Min. Perf.
2|4 7 sLLsLsL Perf. Min. Perf. Maj. Min. Perf. Min. Perf.
1|5 5 sLsLLsL Perf. Min. Perf. Min. Min. Perf. Min. Perf.
0|6 3 sLsLsLL Perf. Min. Perf. Min. Min. Dim. Min. Perf.

Scales

Subset and superset scales

4L 3s has a parent scale of 3L 1s, a tetratonic scale, meaning 1L 3s is a subset. 4L 3s also has two child scales, which are supersets of 4L 3s:

  • 7L 4s, a smitonic chromatic scale produced using soft-of-basic step ratios.
  • 4L 7s, a smitonic chromatic scale produced using hard-of-basic step ratios.

11edo, the equalized form of both 7L 4s and 4L 7s, is also a superset of 4L 3s.

Scala files

Scale tree

Template:Scale tree

Music

References

  1. ↑ Description of Sylvian Moon Dance mentioning the naming proposal https://musescore.com/user/36772625/scores/6700443 – The theme relates to the mystical nature of the Tribunal and TES lore, which fits smitonic.
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