4L 3s: Difference between revisions
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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 name}} | {{TAMNAMS name}} | ||
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== Scale properties == | == Scale properties == | ||
{{MOS scale properties}} | {{MOS scale properties}} | ||
==== Proposed names ==== | ==== Proposed names ==== | ||
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{{MOS modes|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}} | {{MOS modes|Mode Names=Nerevarine; Vivecan; Lorkhanic; Sothic; Kagrenacan; Almalexian; Dagothic}} | ||
==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 it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3. | * [[myna|Myna temperament]], in which the generator is also 6/5 but it takes 10 of them to make a 6/1, meaning that a larger MOS than 4L 3s is required to reach 3/2 or 4/3. | ||
===Temperament interpretations=== | |||
=== Temperament interpretations === | |||
{{main|4L 3s/Temperaments}} | |||
4L 3s has the following temperament interpretations: | 4L 3s has the following temperament interpretations: | ||
*[[Sixix]], with generators around 338. | * [[Sixix]], with generators around 338.6{{c}}. | ||
*[[Orgone]], with generators around 323. | * [[Orgone]], with generators around 323.4{{c}}. | ||
*[[Kleismic]], with generators around | * [[Kleismic]], with generators around 317{{c}}. | ||
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 == | |||
{{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}} | {{Todo|Populate|comment=Populate with JI ratios from prior edits of this page.|inline=1}} | ||
===Simple tunings=== | === Simple tunings === | ||
The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively. | The simplest tunings are those with step ratios 2:1, 3:1, and 3:2, producing 11edo, 15edo, and 18edo, respectively. | ||
{{MOS tunings}} | {{MOS tunings}} | ||
===Parasoft tunings=== | === Parasoft tunings === | ||
Parasoft smitonic tunings can be considered "meantone smitonic" since it has the following features of [[meantone]] diatonic tunings: | Parasoft smitonic tunings 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 ( | These tunings have a major 4-mosstep and minor 4-mosstep that are about equally off a just 3/2 (702{{c}}), 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: | 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 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 ( | ** 18edo has a major 1-mosstep that is close to 9/8 (203{{c}}). | ||
**18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th ( | ** 18edo's major and minor 4-mossteps are both equally off from 12edo's diatonic perfect 5th (700{{c}}) by 33.3{{c}}. | ||
**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 ( | * The augmented 2-mosstep of 25edo is very close to 5/4 (386{{c}}). | ||
{{MOS tunings|Step Ratios=3/2; 7/5; 4/3}} | {{MOS tunings|Step Ratios=3/2; 7/5; 4/3}} | ||
===Hyposoft tunings=== | === Hyposoft tunings === | ||
Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between | Hyposoft smitonic tunings (3:2 to 2:1) are characterized by generators that are a supraminor 3rd, between 327{{c}} and 333{{c}}. 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]]. | ||
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=== Hypohard tunings=== | === Hypohard tunings=== | ||
Hypohard smitonic tunings (2:1 to 3:1) have generators between | Hypohard smitonic tunings (2:1 to 3:1) have generators between 320{{c}} and 327{{c}}. The major 1-mosstep, or large step, tends to approximate [[8/7]] (231{{c}}) and the major 3-mosstep tends to approximate [[11/8]] (551{{c}}). [[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]]. | ||
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{{MOS tunings|Step Ratios=3/1; 5/2; 7/3}} | {{MOS tunings|Step Ratios=3/1; 5/2; 7/3}} | ||
===Parahard tunings=== | === Parahard tunings === | ||
Parahard smitonic tunings (3:1 to 4:1) have generators between 315. | Parahard smitonic tunings (3:1 to 4:1) have generators between 315.9{{c}} and 320{{c}}, putting it close to a pure 6/5 (316{{c}}). Stacking six generators and octave-reducing approximates 3/2 (702{{c}}), 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. | 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. | ||
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{{MOS tunings|Step Ratios=4/1; 11/3; 7/2}} | {{MOS tunings|Step Ratios=4/1; 11/3; 7/2}} | ||
==Scales== | == Scales == | ||
*[[Orgone7]] | * [[Orgone7]] | ||
*[[Cata7]] | * [[Cata7]] | ||
*[[Myna7]] | * [[Myna7]] | ||
== Scale tree== | == Scale tree== | ||
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11/3: [[Hanson]]/[[keemun]]; | 11/3: [[Hanson]]/[[keemun]]; | ||
6/1: [[Oolong]]/[[myna]]↓}} | 6/1: [[Oolong]]/[[myna]]↓}} | ||
==References== | == 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]]) | |||
== References == | |||
<references /> | <references /> | ||
[[Category:Smitonic|*]]<!--Main article--> | [[Category:Smitonic|*]] <!--Main article--> | ||
[[Category:7-tone scales]] | [[Category:7-tone scales]] | ||