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| Mapping = 8; 3 4 5 3
| Mapping = 8; 3 4 5 3
| Generators = 7/5
| Generators = 7/5
| Generators tuning = 583.948
| Generators tuning = 583.9
| Optimization method = CWE
| Optimization method = CWE
| MOS scales = [[8L 64s]], [[72L 8s]]
| MOS scales = [[8L 64s]], [[72L 8s]]
| Pergen = (P8/8, P4/3)
| Pergen = (P8/8, P4/3)
| Color name =
| Odd limit 1 = 11 | Mistuning 1 = 1.29 | Complexity 1 = 56
| Odd limit 1 = 11 | Mistuning 1 = 1.286 | Complexity 1 = 56
| Odd limit 2 = 11-limit 15 | Mistuning 2 = 1.47 | Complexity 2 = 64
| Odd limit 2 = 11-limit 15 | Mistuning 2 = 1.473 | Complexity 2 = 64
}}
}}
'''Octoid''' is a [[regular temperament]] which takes a [[period]] of [[8edo|1/8 octave]], which represents [[12/11]], and adds a single [[generator]] which represents [[6/5]], [[7/5]], [[9/7]] or [[11/10]]. It [[tempering out|tempers out]] [[4375/4374]] and [[16875/16807]] in the 7-limit, and [[540/539]], [[1375/1372]], and [[4000/3993]] in the 11-limit.  
'''Octoid''' is a [[regular temperament|temperament]] which takes a [[period]] of 1/8 octave, which represents [[12/11]], and adds a single [[generator]] which represents [[6/5]], [[7/5]], [[9/7]] or [[11/10]]. It [[tempering out|tempers out]] [[4375/4374]] and [[16875/16807]] in the 7-limit, and [[540/539]], [[1375/1372]], and [[4000/3993]] in the 11-limit.  


There are some extensions for the 13-limit including tridecimal octoid {{nowrap|(72 & 224)}} and octopus {{nowrap|(72 & 80)}}.
There are some extensions for the 13-limit including tridecimal octoid {{nowrap|(72 & 224)}} and octopus {{nowrap|(72 & 80)}}.


See [[Ragismic microtemperaments #Octoid]] for technical details.
See [[Stearnsmic clan #Octoid]] for technical details.


== Interval chain ==
== Interval chain ==
Line 101: Line 100:
| [[9/5]]
| [[9/5]]
| 1167.895
| 1167.895
| [[49/25]]
| [[49/25]], [[55/28]]
|-
|-
| 3
| 3
Line 131: Line 130:
| [[15/11]]
| [[15/11]]
| 685.791
| 685.791
|  
| [[49/33]]
| 835.791
| 835.791
|  
|  
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| [[45/44]], [[49/48]]
| [[45/44]], [[49/48]]
| 187.634
| 187.634
|  
| [[49/44]]
| 337.634
| 337.634
|  
|  
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| POTE: ~7/5 = 583.9622{{c}}
| POTE: ~7/5 = 583.9622{{c}}
|}
|}
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo <br>generator
! [[Eigenmonzo|Unchanged interval <br>(eigenmonzo)]]*
! Generator (¢)
! Comments
|-
| 1\8
|
| 150.000
| 8d val, lower bound of 7-odd-limit diamond monotone
|-
| 12\88
|
| 163.636
| 88bcde val, lower bound of 9- and 11-odd-limit diamond monotone
|-
|
| 9/7
| 164.916
|
|-
| 11\80
|
| 165.000
|
|-
|
| 11/10
| 165.004
|
|-
| 32\232
|
| 165.517
| 232d val
|-
|
| 5/3
| 165.641
|
|-
| 21\152
|
| 165.789
|
|-
|
| 11/9
| 165.803
|
|-
|
| 5/4
| 165.922
| 5-odd-limit minimax
|-
| 52\376
|
| 165.957
|
|-
|
| 3/2
| 166.015
| 11-limit 15-odd-limit minimax
|-
| 31\224
|
| 166.071
|
|-
|
| 9/5
| 166.202
| 9- and 11-odd-limit minimax
|-
| 41\296
|
| 166.216
|
|-
|
| 11/8
| 166.227
|
|-
|
| 7/4
| 166.235
| 7-odd-limit minimax
|-
|
| 11/7
| 166.246
|
|-
|
| 7/6
| 166.565
|
|-
| 10\72
|
| 166.667
|
|-
|
| 7/5
| 167.488
|
|-
| 9\64
|
| 168.750
| 64cd val, upper bound of 9- and 11-odd-limit diamond monotone
|-
| 8\56
|
| 171.429
| 56bccdde val, upper bound of 7-odd-limit diamond monotone
|}
<nowiki/>* Besides the octave


== Music ==
== Music ==
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[[Category:Rank-2 temperaments]]
[[Category:Rank-2 temperaments]]
[[Category:Ragismic microtemperaments]]
[[Category:Ragismic microtemperaments]]
[[Category:Mirkwai clan]]
[[Category:Canopic clan]]
[[Category:Stearnsmic clan]]
[[Category:Stearnsmic clan]]
Retrieved from "https://en.xen.wiki/w/Octoid"