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{{Technical data page}}<br><br>
{{novelty}}
{{Editable user page|Feel free to add examples of music made with these temperaments, and feel free to add any new scales, approaches or other concepts you develop based on these ideas.}}
These temperaments were documented in honour of the members of Batch 89, as depicted in the 2023 film ''Guardians of the Galaxy Vol. 3''. The temperaments were first documented in 2023.
== Methodology ==
== Methodology ==
These temperaments were documented in honour of the members of Batch 89, as depicted in ''Guardians of the Galaxy Vol. 3'' (2023).
Each of the temperaments tempers four harmonics, representing the eternal friendship and togetherness of their four souls.
Each of the temperaments tempers four harmonics, representing the eternal friendship and togetherness of their four souls.


Line 12: Line 17:
* One harmonic was chosen by converting the first letter of the character's name to a number using the A1Z26 cypher, and using that number.
* One harmonic was chosen by converting the first letter of the character's name to a number using the A1Z26 cypher, and using that number.
* The other was chosen by converting each of the letters of the character's name to a number using the A1Z26 cypher, and then summing the numbers together.  
* The other was chosen by converting each of the letters of the character's name to a number using the A1Z26 cypher, and then summing the numbers together.  


== Floor ==
== Floor ==
Line 18: Line 24:
Normalised subgroup bases: '''2.3.11.89'''
Normalised subgroup bases: '''2.3.11.89'''


=== Mappings ===
Related temperaments: [[Neutral]]
 
 
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 66: Line 75:
|] ⟩
|] ⟩
|}
|}
=== TE and POTE tunings ===




Line 87: Line 94:
TE Mistunings (cents)
TE Mistunings (cents)


⟨0.511, 1.196, 6.223, -13.002]
⟨0.511, 1.196, 6.223, -13.002]  
 
{| class="wikitable"
|Complexity
|0.420587
|-
|Adjusted Error
|7.639353 cents
|-
|TE Error
|1.179689 cents/octave
|}
 
 
Unison Vectors
* [-3, 1, -1, 1⟩ (89:88 - [[89/88|Tailwind comma]])
* [0, -5, 0, 2⟩ (7921:7776 - [[7921/7776|Attic comma]])
* [3, -6, 1, 1⟩ (979:972 - [[979/972|Basement comma]])
* [-6, 7, -2, 0⟩ (243:242 - [[243/242|Rastma]])
 
 
{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }}
 
(* val for 89 is lowered)
 
 
=== Temperament data (normalised bases) ===
 
Equal Temperament Mappings
{| class="wikitable"
!
!2
!3
!11
!89
!
|-
|[ ⟨
|7
|11
|24
|45
|]
|-
|⟨
|17
|27
|59
|110
|] ⟩
|}
 


Reduced Mapping
{| class="wikitable"
!
!2
!3
!11
!89
!
|-
|[ ⟨
|1
|1
|2
|5
|]
|-
|⟨
|0
|2
|5
|5
|] ⟩
|}




POTE Generator Tunings (cents)
TE Generator Tunings (cents)


⟨1200.0000, 350.9151]
⟨1200.9365, 350.5869]




POTE Step Tunings (cents)
TE Step Tunings (cents)


⟨34.44279, 56.40591]
⟨44.70571, 52.23509]




POTE Tuning Map (cents)
TE Tuning Map (cents)


⟨1200.000, 3101.830, 7256.406, 7754.576]
⟨1200.936, 1902.110, 4154.807, 7757.617]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨0.000, -0.125, 3.133, -16.304]
⟨0.936, 0.155, 3.489, -13.263]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.420587
|0.558811
|-
|-
|Adjusted Error
|Adjusted Error
|7.639353 cents
|7.996249 cents
|-
|-
|TE Error
|TE Error
|1.179689 cents/octave
|1.234802 cents/octave
|}
|}


=== Vectors and ET sequence ===
 
Unison Vectors
Unison Vectors
* [-3, 1, -1, 1⟩ (89:88)
* [0, -5, 0, 2⟩ (7921:7776)
* [3, -6, 1, 1⟩ (979:972)
* [-6, 7, -2, 0⟩ (243:242)


* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
* [-1, 5, -2, 0⟩ (243:242) - ([[243/242|Rastma]])
* [-2, -5, 1, 1⟩ (979:972) - ([[979/972|Basement comma]])
* [-5, -5, 0, 2⟩ (7921:7776) - ([[7921/7776|Attic comma]])


{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }}
(* val for 89 is lowered)


=== Example MOS scale: Floor[17] ===
=== Example MOS scale: Floor[17] ===
Rotations of this scale are still considered the same scale.


* 56.430
* 56.430
Line 152: Line 231:
* 1144.081
* 1144.081
* 1200.511
* 1200.511
'''Subsets'''
Cosmic (approximated from [[32afdo]])
* 498.382
* 702.129
* 793.016
* 996.764
* 1200.511
Major (approximated from [[12edo]])
(rotate to get its modes e.g. minor)
* 203.747
* 407.494
* 498.381
* 702.129
* 905.876
* 1109.624
* 1200.511
Minor Hexatonic
* 203.747
* 294.634
* 498.382
* 702.129
* 996.764
* 1200.511


=== Music ===
=== Music ===
* ''[https://www.youtube.com/watch?v=YHbBJOHdD_E Improvisation in Floor(17) in Scale Workshop]'' by [[Budjarn Lambeth]] (Jun 2023)


== Teefs ==
== Teefs ==
Line 160: Line 275:
Normalised subgroup bases: '''2.5.11.89'''
Normalised subgroup bases: '''2.5.11.89'''


=== Mappings ===
Related temperaments: [[Bug]]
 
 
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 209: Line 327:
|}
|}


=== TE and POTE tunings ===
 
TE Generator Tunings (cents)
TE Generator Tunings (cents)


Line 229: Line 347:
⟨0.899, -7.060, 6.009, -1.999]
⟨0.899, -7.060, 6.009, -1.999]


{| class="wikitable"
|Complexity
|0.305923
|-
|Adjusted Error
|6.983419 cents
|-
|TE Error
|1.078398 cents/octave
|}


POTE Generator Tunings (cents)


⟨1200.0000, 187.6886]
Unison Vectors
* [-5, 1, -1, 1⟩ (89:88 - [[89/88|Tailwind comma]])
* [0, 3, 0, -2⟩ (8000:7921 - [[8000/7921|Incisor comma]])
* [-5, 4, -1, -1⟩ (1000:979 - [[1000/979|Canine comma]])
* [-5, -2, -1, 3⟩ (704969:704000 - [[704969/704000|Molar comma]])
 
 
{{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }}
 
(* vals for 55 and 89 are raised)
 
 
=== Temperament data (normalised bases) ===
 
Equal Temperament Mappings
{| class="wikitable"
!
!2
!5
!11
!89
!
|-
|[ ⟨
|6
|14
|21
|39
|]
|-
|⟨
|7
|16
|24
|45
|] ⟩
|}
 
 
Reduced Mapping
{| class="wikitable"
!
!2
!5
!11
!89
!
|-
|[ ⟨
|1
|2
|3
|6
|]
|-
|⟨
|0
|2
|3
|3
|] ⟩
|}
 
 
TE Generator Tunings (cents)
 
⟨1200.2939, 188.3359]




POTE Step Tunings (cents)
TE Step Tunings (cents)


⟨73.86819, 39.95225]
⟨118.05701, 70.27884]




POTE Tuning Map (cents)
TE Tuning Map (cents)


⟨1200.000, 5175.377, 6938.443, 7763.066]
⟨1200.294, 2777.260, 4165.889, 7766.771]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨-0.000, -10.936, 0.812, -7.814]
⟨0.294, -9.054, 14.571, -4.109]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.305923
|0.356125
|-
|-
|Adjusted Error
|Adjusted Error
|6.983419 cents
|18.722607 cents
|-
|-
|TE Error
|TE Error
|1.078398 cents/octave
|2.891195 cents/octave
|}
|}


=== Vectors and ET sequence ===
 
Unison Vectors
Unison Vectors
* [-5, 1, -1, 1⟩ (89:88)
* [0, 3, 0, -2⟩ (8000:7921)
* [-5, 4, -1, -1⟩ (1000:979)
* [-5, -2, -1, 3⟩ (704969:704000)


* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
* [0, 3, -2, 0⟩ (125:121) - ([[125/121|Jug comma]])
* [3, 3, -1, -1⟩ (1000:979) - ([[1000/979|Canine comma]])
* [6, 3, 0, -2⟩ (8000:7921) - ([[8000/7921|Incisor comma]])
=== Example inflected MOS scale: UFO scale ===
An [[inflected MOS]] of the Teefs[19] [[MOS scale]]. Also a subset of the Teefs[51] MOS scale, and it can be approximated closely by [[51edo]]. Rotations of this scale are still considered the same scale.
* 47.780
* 92.776
* 188.336
* 210.834
* 258.614
* 306.394
* 399.170
* 494.730
* 542.510
* 657.784
* 705.564
* 801.124
* 893.900
* 941.680
* 989.460
* 1011.958
* 1107.518
* 1152.514
* 1200.294
'''Subsets'''


{{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }}


(* vals for 55 and 89 are raised)
Cosmic (approximated from [[32afdo]])
* 494.730
* 705.564
* 801.124
* 1011.958
* 1200.294
 
 
Major (approximated from [[12edo]])
 
(rotate to get its modes e.g. minor)
* 188.336
* 399.170
* 494.730
* 705.564
* 893.900
* 1107.518
* 1200.294
 


=== Example MOS scale: Teefs[19] ===
Minor Hexatonic (approximated from [[12edo]])
* 188.336
* 306.394
* 494.730
* 705.564
* 1011.958
* 1200.294


* 73.924
* 113.906
* 187.829
* 261.753
* 301.735
* 375.658
* 449.582
* 489.564
* 563.488
* 637.411
* 711.335
* 751.317
* 825.241
* 899.164
* 939.146
* 1013.070
* 1086.993
* 1126.975
* 1200.899


=== Music ===
=== Music ===


== Lylla ==
== Lylla ==
Line 301: Line 526:
Normalised subgroup bases: '''2.3.31.89'''
Normalised subgroup bases: '''2.3.31.89'''


=== Mappings ===
Related temperaments: [[Bluebirds]]
 
 
=== Temperament data (raw bases) ===
 
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 350: Line 579:
|}
|}


=== TE and POTE tunings ===
 
TE Generator Tunings (cents)
TE Generator Tunings (cents)


Line 370: Line 599:
⟨0.853, -1.050, -5.200, 2.022]
⟨0.853, -1.050, -5.200, 2.022]


{| class="wikitable"
|Complexity
|0.448830
|-
|Adjusted Error
|4.188048 cents
|-
|TE Error
|0.646730 cents/octave
|}
Unison Vectors
* [7, 0, 1, -2⟩ (7936:7921 - [[7936/7921|Lily comma]])
* [-9, 1, 2, -1⟩ (2883:2848 - [[2883/2848|Lilac comma]])
* [-16, 1, 1, 1⟩ (8277:8192 - [[8277/8192|Lilly pilly comma]])
* [-2, 1, 3, -3⟩ (714984:704969 - [[714984/704969|Lightyear comma]])
{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }}
(* val for 62 is lowered)
=== Temperament data (normalised bases) ===
Equal Temperament Mappings
{| class="wikitable"
!
!2
!3
!31
!89
!
|-
|[ ⟨
|17
|27
|84
|110
|]
|-
|⟨
|19
|30
|94
|123
|] ⟩
|}
Reduced Mapping
{| class="wikitable"
!
!2
!3
!31
!89
!
|-
|[ ⟨
|1
|3
|4
|6
|]
|-
|⟨
|0
| -3
|2
|1
|] ⟩
|}




POTE Generator Tunings (cents)
TE Generator Tunings (cents)


⟨1200.0000, 567.3830]
⟨1201.0755, 567.2153]




POTE Step Tunings (cents)
TE Step Tunings (cents)


⟨45.51082, 19.72320]
⟨32.58899, 34.05593]




POTE Tuning Map (cents)
TE Tuning Map (cents)


⟨1200.000, 4297.851, 7134.766, 7767.383]
⟨1201.075, 1901.581, 5938.732, 7773.668]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨0.000, -4.104, -10.270, -3.497]
⟨1.075, -0.374, -6.303, 2.788]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.448830
|0.910794
|-
|-
|Adjusted Error
|Adjusted Error
|4.188048 cents
|5.623550 cents
|-
|-
|TE Error
|TE Error
|0.646730 cents/octave
|0.868404 cents/octave
|}
|}


=== Vectors and ET sequence ===
 
Unison Vectors
Unison Vectors
* [7, 0, 1, -2⟩ (7936:7921)
* [-9, 1, 2, -1⟩ (2883:2848)
* [-16, 1, 1, 1⟩ (8277:8192)
* [-2, 1, 3, -3⟩ (714984:704969)


* [-5, 1, 2, -1⟩ (2883:2848) - ([[2883/2848|Lilac comma]])
* [8, 0, 1, -2⟩ (7936:7921) - ([[7936/7921|Lily comma]])
* [-13, 1, 1, 1⟩ (8277:8192) - ([[8277/8192|Lilly pilly comma]])
* [-18, 2, 3, 0⟩ (268119:262144) - ([[268119/262144|Lutra comma]])


{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }}
(* val for 62 is lowered)


=== Example MOS scale: Lylla[19] ===
=== Example MOS scale: Lylla[19] ===
Rotations of this scale are still considered the same scale. Note the 829 cent interval, a solid approximation of [[acoustic phi]].


* 65.281
* 65.281
Line 434: Line 735:
* 1070.292
* 1070.292
* 1135.572
* 1135.572
* 1200.853
'''Subsets'''
Cosmic (approximated from [[32afdo]])
* 502.506
* 698.347
* 828.908
* 1005.011
* 1200.853
Minor Hexatonic (approximated from [[12edo]])
* 195.842
* 306.664
* 502.506
* 698.347
* 1005.011
* 1200.853
* 1200.853


=== Music ===
=== Music ===


* ''Improvisation in Lylla[19] in Scale Workshop'' by Budjarn https://youtu.be/kcXcSIWOWaI
* ''[https://www.youtube.com/watch?v=kcXcSIWOWaI Improvisation in Lylla(19) in Scale Workshop]'' by [[Budjarn Lambeth]] (Jun 2023)
 


== Rocket ==
== Rocket ==
Raw subgroup bases: '''2.18.72.89'''
Raw subgroup bases: '''2.18.72.89'''


Normalised subgroup bases: '''2.9+.9-.89''' (contains a dual harmonic 9)
Normalised subgroup bases: '''2.9+.9-.89''' (contains a dual harmonic 9)


=== Mappings ===
Related temperaments: [[Lu]], [[Deutone]]
 
 
=== Temperament data (raw bases) ===
 
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 494: Line 821:
|}
|}


=== TE and POTE tunings ===
 
TE Generator Tunings (cents)
TE Generator Tunings (cents)


Line 532: Line 859:
POTE Mistunings (cents)
POTE Mistunings (cents)


⟨0.000, -13.989, -13.989, -1.116]
⟨0.000, -13.989, -13.989, -1.116]  


{| class="wikitable"
{| class="wikitable"
Line 545: Line 872:
|}
|}


=== Vectors and ET sequence ===
 
Unison Vectors
Unison Vectors


* [-2, -1, 1, 0⟩ (1:1)
* [-2, -1, 1, 0⟩ (1:1 - [[1/1|Perfect unison]])
* [2, 1, -1, 0⟩ (1:1)
* [2, 1, -1, 0⟩ (1:1 - Perfect unison)
* [-6, 3, 0, -1⟩ (729:712)
* [-6, 3, 0, -1⟩ (729:712 - [[729/712|Oxidizer comma]])
* [-8, 2, 1, -1⟩ (729:712)
* [-8, 2, 1, -1⟩ (729:712 - Oxidizer comma)




Line 557: Line 884:


(* val for 89 is raised)
(* val for 89 is raised)
=== Temperament data (normalised bases) ===
{{todo|complete list|inline=yes|comment=Fill out this section}}


=== Example MOS scale: Rocket[19] ===
=== Example MOS scale: Rocket[19] ===
Rotations of this scale are still considered the same scale.


* 60.544
* 60.544
Line 579: Line 911:
* 1140.904
* 1140.904
* 1201.449
* 1201.449
'''Subsets'''
Cosmic (approximated from [[32afdo]])
* 509.908
* 691.541
* 821.147
* 1011.298
* 1201.449
Minor Hexatonic (approximated from [[12edo]])
* 190.151
* 319.757
* 509.908
* 691.541
* 1011.298
* 1201.449


=== Music ===
=== Music ===
[[Category:17-tone scales]]
* ''[https://www.youtube.com/watch?v=_NepcrTf9ng The Wound]'' - [[Budjarn Lambeth]] (Nov 2024)
[[Category:19-tone scales]]
 
[[Category:89-limit]]
== Bonus scales: the Batch 89 JI scales ==
[[Category:Listen]]
These [[just intonation|just intonation scales]] were documented in honour of the members of Batch 89, as depicted in the 2023 film ''Guardians of the Galaxy Vol. 3''. The scales were first documented in 2026.
[[Category:Lists of temperaments]]
 
[[Category:MOS scales]]
=== Otonal Batch 89 scale ===
The scale degrees were selected by:
# ''converting each of the letters of Floor's name to a number using the A1Z26 cypher''
# ''then summing the numbers together to get one scale degree''
# ''then repeating this process but for Teefs, Lylla and Rocket to get three more scale degrees''
# ''then adding the octave, so that identical copies of the scale are infinitely reflected up and down the pitch spectrum, reflecting that these characters will be together forever''
# ''then using {{w|negative harmony}} to change the scale from utonal to otonal, to reflect how the characters found wonder even in a dark situation and used it to make the galaxy a brighter place''
 
This results in the following scale:
* 110/89
* 124/89
* 132/89
* 144/89
* 178/89
 
Which is a subset of [[89afdo]] (''see [[afdo]]'').
 
==== Edo approximations ====
 
Edos with nice-sounding approximations of this scale include:
* [[14edo]]: 4 3 1 2 4
* [[17edo]]: 5 3 2 2 5
* [[20edo]]: 6 4 1 3 6
* [[21edo]]: 6 4 2 3 6
* [[23edo]]: 7 4 2 3 7 ''(closest to JI until 65edo)''
* [[24edo]]: 7 4 3 3 7
* [[26edo]]: 8 4 1 3 8
* [[27edo]]: 8 5 2 4 8
* [[30edo]]: 9 5 3 4 9
* [[31edo]]: 9 6 3 4 9
* [[34edo]]: 10 6 3 5 10
* [[37edo]]: 11 7 3 5 11
* [[40edo]]: 12 7 4 5 12
* [[44edo]]: 13 8 4 6 13
* [[46edo]]: 14 8 4 6 14
* [[53edo]]: 16 9 5 7 16
* [[60edo]]: 18 9 5 8 18
* [[65edo]]: 20 11 6 8 20
 
(Tested by ear in [[Scale Workshop]] by [[Budjarn Lambeth]].)
 
=== Nonoctave Batch 89 scale ===
The scale degrees were selected by:
# ''converting the first letter Floor's name to a number using the A1Z26 cypher''
# ''then repeating this process but for Teefs, Lylla and Rocket to get three more numbers''
# ''at this stage we now have the numbers 6, 12, 18 and 20''
# ''now we list every JI ratio that is a combination of these two numbers, e.g. 12/6, 20/12, etc.''
# ''then we sort these in order from the smallest interval to the largest, using the largest as the scale [[period]]''
 
This results in the following scale:
* 20/18
* 18/12
* 20/12
* 12/6
* 18/6
* 20/6
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth/Batch_89_temperaments"