5L 3s: Difference between revisions

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|-
|-
! Mode
! Mode
![[Modal UDP Notation|UDP]]
! [[Modal UDP Notation|UDP]]
! Name
! Name
|-
|-
| LLsLLsLs
| LLsLLsLs
|<nowiki>7|0</nowiki>
| 7{{pipe}}0
| Dylathian
| Dylathian
|-
|-
| LLsLsLLs
| LLsLsLLs
|<nowiki>6|1</nowiki>
| 6{{pipe}}1
| Ilarnekian
| Ilarnekian
|-
|-
| LsLLsLLs
| LsLLsLLs
| |<nowiki>5|2</nowiki>
| 5{{pipe}}2
| Celephaïsian
| Celephaïsian
|-
|-
| LsLLsLsL
| LsLLsLsL
|<nowiki>4|3</nowiki>
| 4{{pipe}}3
| Ultharian
| Ultharian
|-
|-
| LsLsLLsL
| LsLsLLsL
|<nowiki>3|4</nowiki>
| 3{{pipe}}4
| Mnarian
| Mnarian
|-
|-
| sLLsLLsL
| sLLsLLsL
|<nowiki>2|5</nowiki>
| 2{{pipe}}5
| Kadathian
| Kadathian
|-
|-
| sLLsLsLL
| sLLsLsLL
|<nowiki>1|6</nowiki>
| 1{{pipe}}6
| Hlanithian
| Hlanithian
|-
|-
| sLsLLsLL
| sLsLLsLL
|<nowiki>0|7</nowiki>
| 0{{pipe}}7
| Sarnathian
| Sarnathian
|}
|}
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|}
|}


===Hypohard===
=== Hypohard ===
[[Hypohard]] oneirotonic tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1.  
[[Hypohard]] oneirotonic tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1.  


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|-
|-
!
!
![[13edo]] (basic)
! [[13edo]] (basic)
![[18edo]] (hard)
! [[18edo]] (hard)
![[31edo]] (semihard)
! [[31edo]] (semihard)
|-
|-
| generator (g)
| generator (g)
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{| class="wikitable right-2 right-3 right-4 sortable "
{| class="wikitable right-2 right-3 right-4 sortable "
|-
|-
! class="unsortable" |Degree
! class="unsortable" | Degree
! Size in 13edo (basic)
! Size in 13edo (basic)
! Size in 18edo (hard)
! Size in 18edo (hard)
! Size in 31edo (semihard)
! Size in 31edo (semihard)
! class="unsortable" |Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! class="unsortable" | Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref>
! #Gens up
! #Gens up
|- style="background-color: #eaeaff;"
|- style="background-color: #eaeaff;"
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<references />
<references />


===Hyposoft===
=== Hyposoft ===
[[Hyposoft]] oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings remains relatively unexplored. In these tunings,  
[[Hyposoft]] oneirotonic tunings (with generator between 8\21 and 5\13) have step ratios between 3/2 and 2/1. The 8\21-to-5\13 range of oneirotonic tunings 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¢ to 114¢.
* 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¢ to 114¢.
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{| class="wikitable right-2 right-3 sortable "
{| class="wikitable right-2 right-3 sortable "
|-
|-
! class="unsortable" |Degree
! class="unsortable" | Degree
! Size in 21edo (soft)
! Size in 21edo (soft)
! Size in 34edo (semisoft)
! Size in 34edo (semisoft)
! class="unsortable" |Approximate ratios
! class="unsortable" | Approximate ratios
! #Gens up
! #Gens up
|- style="background-color: #eaeaff;"
|- style="background-color: #eaeaff;"
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|}
|}


===Parasoft to ultrasoft tunings===
=== Parasoft to ultrasoft tunings ===
The range of oneirotonic tunings of step ratio between 6/5 and 3/2 (thus in the [[parasoft]] to [[ultrasoft]] range) may be of interest because it 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. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] The chord 10:11:13 is very well approximated in 29edo.
The range of oneirotonic tunings of step ratio between 6/5 and 3/2 (thus in the [[parasoft]] to [[ultrasoft]] range) may be of interest because it 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. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] The chord 10:11:13 is very well approximated in 29edo.


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| 4\37, 129.73
| 4\37, 129.73
|}
|}
==== Intervals====
==== Intervals====
The intervals of the extended generator chain (-15 to +15 generators) are as follows in various softer-than-soft oneirotonic tunings.
The intervals of the extended generator chain (-15 to +15 generators) are as follows in various softer-than-soft oneirotonic tunings.
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===Parahard===
===Parahard===
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).
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).
====Intervals====
====Intervals====
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various oneirotonic tunings close to [[23edo]].  
The intervals of the extended generator chain (-12 to +12 generators) are as follows in various oneirotonic tunings close to [[23edo]].  
{| class="wikitable right-2 right-3 sortable "
{| class="wikitable right-2 right-3 sortable "
|-
|-
! class="unsortable" |Degree
! class="unsortable" | Degree
! Size in 23edo (superhard)
! Size in 23edo (superhard)
! class="unsortable" |Approximate ratios (23edo)
! class="unsortable" | Approximate ratios (23edo)
! #Gens up
! #Gens up
|- style="background-color: #eaeaff;"
|- style="background-color: #eaeaff;"
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|}
|}


===Ultrahard===
=== Ultrahard ===
[[Buzzard]] is an oneirotonic rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum.
[[Buzzard]] is an oneirotonic rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the only [[harmonic entropy]] minimum of the oneirotonic spectrum.


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! Size in 63edo
! Size in 63edo
! Size in POTE tuning
! Size in POTE tuning
! class="unsortable" |Approximate ratios
! class="unsortable" | Approximate ratios
! #Gens up
! #Gens up
|-
|-
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* [[5L 3s/Temperaments]]
* [[5L 3s/Temperaments]]


==Samples==
== 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: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]])


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* [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian
* [[File:Inthar-13edo Oneirotonic Studies 8 Kadathian.mp3]]: Tonal Study in Kadathian


==Scale tree==
== Scale tree ==
Generator ranges:
Generator ranges:
* Bright generator: 450 cents (3\8) to 480 cents (2\5)
* Bright generator: 450 cents (3\8) to 480 cents (2\5)
* Dark generator: 720 cents (3\5) to 750 cents (5\8)
* Dark generator: 720 cents (3\5) to 750 cents (5\8)


{| class="wikitable center-all"
{{Scale tree}}
! colspan="6" |Bright generator
!Cents
!L
!s
!L/s
!Comments
|-
| 3\8 || || || || || || 450.000 ||1||1||1.000||
|-
| || || || || || 17\45 || 453.333 ||6||5||1.200||
|-
| || || || || 14\37 || || 454.054 ||5||4||1.250||
|-
| || || || || || 25\66 || 454.545 ||9||7||1.286||
|-
| || || || 11\29 || || || 455.172 ||4||3||1.333||
|-
| || || || || || 30\79 || 455.696 ||11||8||1.375||
|-
| || || || || 19\50 || || 456.000 ||7||5||1.400||
|-
| || || || || || 27\71 || 456.338 ||10||7||1.429||
|-
| || || 8\21 || || || || 457.143 ||3||2||1.500||
|-
| || || || || || 29\76 || 457.895 ||11||7||1.571||
|-
| || || || || 21\55 || || 458.182 ||8||5||1.600||
|-
| || || || || || 34\89 || 458.427 ||13||8||1.625||Golden oneirotonic (458.3592¢)
|-
| || || || 13\34 || || || 458.824 ||5||3||1.667||
|-
| || || || || || 31\81 || 459.259 ||12||7||1.714||
|-
| || || || || 18\47 || || 459.574 ||7||4||1.750||
|-
| || || || || || 23\60 || 460.000 ||9||5||1.800||
|-
| || 5\13 || || || || || 461.538 ||2||1||2.000||Basic oneirotonic <br>(generators smaller than this are proper)
|-
| || || || || || 22\57 || 463.158 ||9||4||2.250||
|-
| || || || || 17\44 || || 463.636 ||7||3||2.333||
|-
| || || || || || 29\75 || 464.000 ||12||5||2.400||
|-
| || || || 12\31 || || || 464.516 ||5||2||2.500||
|-
| || || || || || 31\80 || 465.000 ||13||5||2.600||Golden A-Team (465.0841¢)
|-
| || || || || 19\49 || || 465.306 ||8||3||2.667||
|-
| || || || || || 26\67 || 465.672 ||11||4||2.750||
|-
| || || 7\18 || || || || 466.667 ||3||1||3.000||
|-
| || || || || || 23\59 || 467.797 ||10||3||3.333||
|-
| || || || || 16\41 || || 468.293 ||7||2||3.500||
|-
| || || || || || 25\64 || 468.750 ||11||3||3.667||
|-
| || || || 9\23 || || || 469.565 ||4||1||4.000||
|-
| || || || || || 20\51 || 470.588 ||9||2||4.500||
|-
| || || || || 11\28 || || 471.429 ||5||1||5.000||
|-
| || || || || || 13\33 || 472.727 ||6||1||6.000||
|-
| 2\5 || || || || || || 480.000 ||1||0||→ inf||
|}


[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
[[Category:Oneirotonic| ]] <!-- sort order in category: this page shows above A -->
[[Category:Pages with internal sound examples]]
[[Category:Pages with internal sound examples]]
[[Category:8-tone scales]]
[[Category:8-tone scales]]