5L 3s: Difference between revisions
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{{Interwiki | |||
| en = 5L 3s | |||
| de = | |||
| es = | |||
| ja = | |||
| ko = 5L3s (Korean) | |||
}} | |||
{{Infobox MOS | |||
| Neutral = 2L 6s | |||
}} | |||
: ''For the tritave-equivalent MOS structure with the same step pattern, see [[5L 3s (3/1-equivalent)]].'' | |||
{{MOS intro}} | |||
5L 3s can be seen as a [[Warped diatonic|warped diatonic scale]], because it has one extra small step compared to diatonic ([[5L 2s]]). | |||
== Name == | |||
{{TAMNAMS name}} 'Oneiro' is sometimes used as a shortened form. | |||
'Father' is sometimes also used to denote 5L 3s, but it's a misnomer, as [[father]] is technically an abstract [[regular temperament]] (although a very inaccurate one), not a generator range. There are father tunings which generate 3L 5s. A more correct but still not quite correct name would be 'father[8]' or 'father octatonic'. "Father" is also vague regarding the number of notes, because optimal generators for it also generate [[3L 2s]]. | |||
== Scale properties == | |||
& | === Intervals === | ||
{{MOS intervals}} | |||
=== Generator chain === | |||
{{MOS genchain}} | |||
=== Modes === | |||
{{MOS mode degrees}} | |||
==== Proposed mode names ==== | |||
The following names have been proposed for the modes of 5L 3s, and are named after cities in the Dreamlands. | |||
{{MOS modes | |||
| Mode Names= | |||
Dylathian $ | |||
Ilarnekian $ | |||
Celephaïsian $ | |||
Ultharian $ | |||
Mnarian $ | |||
Kadathian $ | |||
Hlanithian $ | |||
Sarnathian $ | |||
| Collapsed=1 | |||
}} | |||
== Tunings== | |||
=== Simple tunings === | |||
The simplest tuning for 5L 3s correspond to 13edo, 18edo, and 21edo, with step ratios 2:1, 3:1, and 3:2, respectively. | |||
{{MOS tunings|JI Ratios=Int Limit: 30; Prime Limit: 19; Tenney Height: 7.7}} | |||
=== Hypohard tunings === | |||
[[Hypohard]] oneirotonic tunings have step ratios between 2:1 and 3:1 and can be considered "meantone oneirotonic", sharing the following features with [[meantone]] diatonic tunings: | |||
* The large step is a "meantone", around the range of [[10/9]] to [[9/8]]. | |||
* The major 2-mosstep is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third. | |||
With step ratios between 5:2 and 2:1, the minor 2-mosstep is close to [[7/6]]. | |||
EDOs that are in the hypohard range include [[13edo]], [[18edo]], and [[31edo]], and are associated with [[5L 3s/Temperaments#A-Team|A-Team]] temperament. | |||
* 13edo has characteristically small 1-mossteps of about 185{{c}}. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all hypohard tunings. | |||
* 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3{{c}}, a perfect 5-mosstep) and falling fifths (666.7{{c}}, a major 4-mosstep) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry. | |||
* 31edo can be used to make the major 2-mosstep a near-just 5/4. | |||
* [[44edo]] (generator {{nowrap|17\44 {{=}} 463.64{{c}}}}), [[57edo]] (generator {{nowrap|22\57 {{=}} 463.16{{c}}}}), and [[70edo]] (generator 27\70 {{=}} 462.857{{c}}}}) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8. | |||
{{MOS tunings|Step Ratios=Hypohard|JI Ratios=Subgroup: 2.5.9.21; Int Limit:40; Complements Only: 1|Tolerance=15}} | |||
=== Hyposoft tunings === | |||
[[Hyposoft]] oneirotonic tunings have step ratios between 3:2 and 2:1, which remains relatively unexplored. In these tunings, | |||
* The large step of oneirotonic tends to be intermediate in size between [[10/9]] and [[11/10]]; the small step size is a semitone close to [[17/16]], about 92{{c}} to 114{{c}}. | |||
* The major 2-mosstep (made of two large steps) in these tunings tends to be more of a neutral third, ranging from 6\21 (342{{c}}) to 4\13 (369{{c}}). | |||
* [[21edo]]'s P1-L1ms-L2ms-L4ms approximates 9:10:11:13 better than the corresponding 13edo chord does. 21edo will serve those who like the combination of neogothic minor thirds (285.71{{c}}) and Baroque diatonic semitones (114.29{{c}}, close to quarter-comma meantone's 117.11{{c}}). | |||
* [[34edo]]'s 9:10:11:13 is even better. | |||
This set of JI identifications is associated with [[5L 3s/Temperaments#Petrtri|petrtri]] temperament. (P1-M1ms-P3ms could be said to approximate 5:11:13 in all soft-of-basic tunings, which is what "basic" [[petrtri]] temperament is.) | |||
{{MOS tunings | |||
| Step Ratios = Hyposoft | |||
| JI Ratios = | |||
1/1; | |||
16/15; | |||
10/9; 11/10; | |||
13/11; 20/17; | |||
11/9; | |||
5/4; | |||
13/10; | |||
18/13; 32/23; | |||
13/9; 23/16; | |||
20/13; | |||
8/5; | |||
18/11; | |||
22/13; 17/10; | |||
9/5; | |||
15/8; | |||
2/1 | |||
}} | |||
=== Parasoft and ultrasoft tunings === | |||
The range of oneirotonic tunings of step ratio between 6:5 and 3:2 is closely related to [[porcupine]] temperament; these tunings equate three oneirotonic large steps to a diatonic perfect fourth, i.e. they equate the oneirotonic large step to a [[porcupine]] generator. The chord 10:11:13 is very well approximated in 29edo. | |||
{{MOS tunings | |||
| Step Ratios = 6/5; 3/2; 4/3 | |||
| JI Ratios = | |||
1/1; | |||
14/13; | |||
11/10; | |||
9/8; | |||
15/13; | |||
13/11; | |||
14/11; | |||
13/10; | |||
4/3; | |||
15/11; | |||
7/5; | |||
10/7; | |||
22/15; | |||
3/2; | |||
20/13; | |||
11/7; | |||
22/13; | |||
26/15; | |||
16/9; | |||
20/11; | |||
13/7; | |||
2/1 | |||
}} | |||
=== Parahard tunings === | |||
23edo oneiro combines the sound of neogothic tunings like [[46edo]] and the sounds of "superpyth" and "semaphore" scales. This is because 23edo oneirotonic has a large step of 208.7¢, same as [[46edo]]'s neogothic major second, and is both a warped [[22edo]] [[superpyth]] [[diatonic]] and a warped [[24edo]] [[semaphore]] [[semiquartal]] (and both nearby scales are [[superhard]] MOSes). | |||
{{MOS tunings | |||
| JI Ratios = | |||
1/1; | |||
21/17; | |||
17/16; | |||
14/11; | |||
6/5; | |||
21/16; | |||
21/17; | |||
34/21; | |||
32/21; | |||
5/3; | |||
11/7; | |||
32/17; | |||
34/21; | |||
2/1 | |||
| Step Ratios = 4/1 | |||
}} | |||
=== Ultrahard tunings === | |||
{{Main|5L 3s/Temperaments#Buzzard}} | |||
[[Buzzard]] is a rank-2 temperament in the [[Step ratio|pseudocollapsed]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum. | |||
In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]] and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well. | |||
Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic. | |||
{{MOS tunings | |||
| JI Ratios = | |||
1/1; | |||
8/7; | |||
13/10; | |||
21/16; | |||
3/2; | |||
12/7, 22/13; | |||
26/15; | |||
49/25, 160/81; | |||
2/1 | |||
| Step Ratios = 7/1; 10/1; 12/1 | |||
| Tolerance = 30 | |||
}} | |||
== Approaches == | |||
* [[5L 3s/Temperaments]] | |||
== Samples == | |||
[[File:The Angels' Library edo.mp3]] [[:File:The Angels' Library edo.mp3|The Angels' Library]] by [[Inthar]] in the Sarnathian (23233233) mode of 21edo oneirotonic ([[:File:The Angels' Library Score.pdf|score]]) | |||
[[File:13edo Prelude in J Oneirominor.mp3]] | |||
[[WT13C]] [[:File:13edo Prelude in J Oneirominor.mp3|Prelude II (J Oneirominor)]] ([[:File:13edo Prelude in J Oneirominor Score.pdf|score]]) – Simple two-part Baroque piece. It stays in oneirotonic even though it modulates to other keys a little. | |||
[[File:13edo_1MC.mp3]] | |||
(13edo, first 30 seconds is in J Celephaïsian) | |||
[[File:A Moment of Respite.mp3]] | |||
(13edo, L Ilarnekian) | |||
[[File:Lunar Approach.mp3]] | |||
(by [[Igliashon Jones]], 13edo, J Celephaïsian) | |||
=== 13edo Oneirotonic Modal Studies === | |||
* [[File:Inthar-13edo Oneirotonic Studies 1 Dylathian.mp3]]: Tonal Study in Dylathian | |||
* [[File:Inthar-13edo Oneirotonic Studies 2 Ultharian.mp3]]: Tonal Study in Ultharian | |||
* [[File:Inthar-13edo Oneirotonic Studies 3 Hlanithian.mp3]]: Tonal Study in Hlanithian | |||
* [[File:Inthar-13edo Oneirotonic Studies 4 Illarnekian.mp3]]: Tonal Study in Ilarnekian | |||
* [[File:Inthar-13edo Oneirotonic Studies 5 Mnarian.mp3]]: Tonal Study in Mnarian | |||
* [[File:Inthar-13edo Oneirotonic Studies 6 Sarnathian.mp3]]: Tonal Study in Sarnathian | |||
* [[File:Inthar-13edo Oneirotonic Studies 7 Celephaisian.mp3]]: Tonal Study in Celephaïsian | |||
* [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian | |||
== Scale tree == | |||
{{MOS tuning spectrum | |||
| 13/8 = Golden oneirotonic (458.3592{{c}}) | |||
| 13/5 = Golden A-Team (465.0841{{c}}) | |||
}} | |||
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A --> | |||
[[Category:Pages with internal sound examples]] | |||