User:BudjarnLambeth/Nimona: Difference between revisions

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Nimona is a 2.15.23 [[Just intonation subgroup|subgroup]] temperament. It has the lowest [[complexity]] of any temperament in the 2.15.23 subgroup (for a target error of 10 [[Cent|cents]]), according to x31eq.com.
'''Nimona''' is a 2.15.23 [[just intonation subgroup|subgroup]] [[temperament]] that [[tempering out|tempers out]] the 2.23 subgroup comma [[529/512]] with the addition of an independent [[generator]] for harmonic [[15/1|15]]. As a result of tempering out 529/512, [[23/16]] is tuned to the semioctave. It has the lowest [[complexity]] of any temperament in the 2.15.23 subgroup for a target error of 10 [[cent]]s, according to [[Graham Breed]]'s [http://x31eq.com/temper/ temeprament finder].  


It was described to celebrate the release of the film ''Nimona''. The 15th and 23rd harmonics represent that the film was first announced in 2015, and was released in 2023. The 2nd harmonic represents that the film had a second chance at life, since it was cancelled by Disney but later picked up and resurrected by Netflix.
It was named by [[Budjarn Lambeth]] in 2023 after the film ''Nimona''. The 15th and 23rd harmonics represent that the film was first announced in 2015, and was released in 2023. The 2nd harmonic represents that the film had a second chance at life, since it was cancelled by Disney but later picked up and resurrected by Netflix.


== Temperament data ==
== Temperament data ==
[[Subgroup]]: 2.15.23


[[Comma list]]: 529/512


Equal Temperament Mappings
{{Mapping|legend=1| 2 0 9 | 0 1 0 }}
{| class="wikitable"
!
!2
!15
!23
!
|-
|[ ⟨
|2
|8
|9
|]
|-
|⟨
|10
|39
|45
|] ⟩
|}


[[Optimal tuning]]s:
* [[CTE]]: ~2 = 1\1, ~15/8 = 1088.2687
* [[CWE]]: ~2 = 1\1, ~15/8 = 1080.1288


Reduced Mapping
{{Optimal ET sequence|legend=1| 2, 6, 8, 10, 38*, 48*, 58* }}
{| class="wikitable"
!
!2
!15
!23
!
|-
|[ ⟨
|2
|8
|9
|]
|-
|⟨
|0
| -1
|0
|] ⟩
|}


<nowiki>*</nowiki> nonpatent val


Unison Vector
== Scales ==
 
* Nimona[18] in TE tuning
[-9, 0, 2⟩ (529:512)
<pre>
 
! nimona18.scl
</br>
Nimona[18] in TE tuning
 
18
{| class="wikitable"
!
|Complexity
104.635
|0.240692
124.232
|-
228.867
|Adjusted Error
248.464
|11.573055 cents
353.099
|-
372.696
|TE Error
477.331
|2.558394 cents/octave
496.928
|}
601.563
 
706.197
== TE tunings ==
725.795
 
830.429
 
850.027
 
954.661
[[Tenney-Euclidean tuning|TE]] Generator Tunings (cents)
974.259
 
1078.893
⟨601.5626, 124.2320]
1097.491
 
1203.125
 
</pre>
TE Step Tunings (cents)
 
⟨-19.59759, 124.23204]
 
 
TE Tuning Map (cents)
 
⟨1203.125, 4688.269, 5414.063]
 
 
TE Mistunings (cents)
 
⟨3.125, -0.000, -14.211]
 
== POTE tunings ==
 
 
 
[[POTE tuning|POTE]] Generator Tunings (cents)
 
⟨600.0000, 123.9093]
 
 
POTE Step Tunings (cents)
 
⟨-19.54668, 123.90934]
 
 
POTE Tuning Map (cents)
 
⟨1200.000, 4676.091, 5400.000]
 
 
POTE Mistunings (cents)
 
⟨0.000, -12.178, -28.274]
 
== Example MOS scale: TE Nimona[18] ==
(Intervals given in cents)


* 104.635
* 124.232
* 228.867
* 248.464
* 353.099
* 372.696
* 477.331
* 496.928
* 601.563
* 706.197
* 725.795
* 830.429
* 850.027
* 954.661
* 974.259
* 1078.893
* 1097.491
* 1203.125
[[Category:23-limit]]
[[Category:Temperaments]]
[[Category:Temperaments]]
[[Category:Subgroup temperaments]]
[[Category:Subgroup temperaments]]
[[Category:18-tone scales]]
[[Category:18-tone scales]]
[[Category:MOS scales]]
[[Category:Tempered scales]]
[[Category:Tempered scales]]
[[Category:Pages with Scala files]]

Revision as of 08:26, 21 April 2024

Nimona is a 2.15.23 subgroup temperament that tempers out the 2.23 subgroup comma 529/512 with the addition of an independent generator for harmonic 15. As a result of tempering out 529/512, 23/16 is tuned to the semioctave. It has the lowest complexity of any temperament in the 2.15.23 subgroup for a target error of 10 cents, according to Graham Breed's temeprament finder.

It was named by Budjarn Lambeth in 2023 after the film Nimona. The 15th and 23rd harmonics represent that the film was first announced in 2015, and was released in 2023. The 2nd harmonic represents that the film had a second chance at life, since it was cancelled by Disney but later picked up and resurrected by Netflix.

Temperament data

Subgroup: 2.15.23

Comma list: 529/512

Mapping: [⟨2 0 9], ⟨0 1 0]]

Optimal tunings:

  • CTE: ~2 = 1\1, ~15/8 = 1088.2687
  • CWE: ~2 = 1\1, ~15/8 = 1080.1288

Optimal ET sequence: 2, 6, 8, 10, 38*, 48*, 58*

* nonpatent val

Scales

  • Nimona[18] in TE tuning
! nimona18.scl
Nimona[18] in TE tuning
18
!
104.635
124.232
228.867
248.464
353.099
372.696
477.331
496.928
601.563
706.197
725.795
830.429
850.027
954.661
974.259
1078.893
1097.491
1203.125
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