User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions

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Documented four temperaments that I discovered
 
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
 
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Line 1: Line 1:
{{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 8: Line 13:
Each of the temperaments also includes the 89th harmonic, representing their shared trauma and hardship, and how they gave each other the strength to endure and transcend it.
Each of the temperaments also includes the 89th harmonic, representing their shared trauma and hardship, and how they gave each other the strength to endure and transcend it.


The other two harmonics were selected based on the characters' names. The reason for using their ''names'' as a basis, is because choosing their own name was these characters' most symbolic act of asserting their individuality, it was an undeniable demonstration that they had souls capable of creativity. Souls not created by the hands that made them, but by the hands that guided those hands. Thus, it's fitting that the ''names'' they chose should be immortalised in these temperaments:
The other two harmonics were selected based on the characters' names. The reason for using their ''names'' as a basis, is because choosing their own name was these characters' most symbolic act of asserting their individuality, it was an undeniable demonstration that they had souls capable of creativity. Souls which did not come from, nor belong to, their makers, but which were, and are, their own. Thus, it's fitting that the ''names'' they chose should be immortalised in these temperaments:


* 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.  


== Teefs (2.20.55.89) ==
 
== Floor ==
Raw subgroup bases: '''2.6.66.89'''
 
Normalised subgroup bases: '''2.3.11.89'''
 
Related temperaments: [[Neutral]]
 
 
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
!
!
!2
!2
!20
!6
!55
!66
!89
!89
!
!
|-
|-
|[ ⟨
|[ ⟨
|13
|7
|56
|18
|75
|42
|84
|45
|]
|]
|-
|-
|⟨
|⟨
|6
|17
|26
|44
|35
|103
|39
|110
|] ⟩
|] ⟩
|}
|}


Reduced Mapping
Reduced Mapping
Line 43: Line 56:
!
!
!2
!2
!20
!6
!55
!66
!89
!89
!
!
Line 50: Line 63:
|[ ⟨
|[ ⟨
|1
|1
|2
|4
|4
|5
|5
|6
|]
|]
|-
|-
Line 58: Line 71:
|0
|0
|2
|2
|7
|5
|5
|3
|] ⟩
|] ⟩
|}
|}
Line 66: Line 79:
TE Generator Tunings (cents)
TE Generator Tunings (cents)


⟨1200.8989, 187.8292]
⟨1200.5110, 351.0646]




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


⟨73.92353, 39.98217]
⟨34.45745, 56.42993]




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


⟨1200.899, 5179.254, 6943.641, 7768.881]
⟨1200.511, 3103.151, 7259.496, 7757.878]




TE Mistunings (cents)
TE Mistunings (cents)


⟨0.899, -7.060, 6.009, -1.999]
⟨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, 187.6886]
⟨1200.9365, 350.5869]




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


⟨73.86819, 39.95225]
⟨44.70571, 52.23509]




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


⟨1200.000, 5175.377, 6938.443, 7763.066]
⟨1200.936, 1902.110, 4154.807, 7757.617]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨-0.000, -10.936, 0.812, -7.814]
⟨0.936, 0.155, 3.489, -13.263]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.305923
|0.558811
|-
|-
|Adjusted Error
|Adjusted Error
|6.983419 cents
|7.996249 cents
|-
|-
|TE Error
|TE Error
|1.078398 cents/octave
|1.234802 cents/octave
|}
|}


Line 117: Line 205:
Unison Vectors
Unison Vectors


* [-5, 1, -1, 1⟩ (89:88)
* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
* [0, 3, 0, -2⟩ (8000:7921)
* [-1, 5, -2, 0⟩ (243:242) - ([[243/242|Rastma]])
* [-5, 4, -1, -1⟩ (1000:979)
* [-2, -5, 1, 1⟩ (979:972) - ([[979/972|Basement comma]])
* [-5, -2, -1, 3⟩ (704969:704000)
* [-5, -5, 0, 2⟩ (7921:7776) - ([[7921/7776|Attic comma]])
 
 
=== Example MOS scale: Floor[17] ===
Rotations of this scale are still considered the same scale.
 
* 56.430
* 147.317
* 203.747
* 294.634
* 351.065
* 407.495
* 498.382
* 554.812
* 645.699
* 702.129
* 793.016
* 849.446
* 905.877
* 996.764
* 1053.194
* 1144.081
* 1200.511
 
 
'''Subsets'''
 


=== Example MOS scale: Teefs[19] ===
Cosmic (approximated from [[32afdo]])
* 498.382
* 702.129
* 793.016
* 996.764
* 1200.511


* 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


== Lylla (2.12.62.89) ==
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 ===
 
* ''[https://www.youtube.com/watch?v=YHbBJOHdD_E Improvisation in Floor(17) in Scale Workshop]'' by [[Budjarn Lambeth]] (Jun 2023)
 
 
== Teefs ==
Raw subgroup bases: '''2.20.55.89'''
 
Normalised subgroup bases: '''2.5.11.89'''
 
Related temperaments: [[Bug]]
 
 
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
!
!
!2
!2
!12
!20
!62
!55
!89
!89
!
!
|-
|-
|[ ⟨
|[ ⟨
|19
|13
|68
|56
|113
|75
|123
|84
|]
|]
|-
|-
|⟨
|⟨
|17
|6
|61
|26
|101
|35
|110
|39
|] ⟩
|] ⟩
|}
|}


Reduced Mapping
Reduced Mapping
Line 174: Line 307:
!
!
!2
!2
!12
!20
!62
!55
!89
!89
!
!
Line 181: Line 314:
|[ ⟨
|[ ⟨
|1
|1
|5
|4
|5
|5
|6
|6
Line 188: Line 321:
|⟨
|⟨
|0
|0
| -3
|2
|2
|1
|5
|3
|] ⟩
|] ⟩
|}
|}
Line 197: Line 330:
TE Generator Tunings (cents)
TE Generator Tunings (cents)


⟨1200.8527, 567.7861]
⟨1200.8989, 187.8292]




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


⟨45.54316, 19.73721]
⟨73.92353, 39.98217]




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


⟨1200.853, 4300.905, 7139.836, 7772.902]
⟨1200.899, 5179.254, 6943.641, 7768.881]




TE Mistunings (cents)
TE Mistunings (cents)


⟨0.853, -1.050, -5.200, 2.022]
⟨0.899, -7.060, 6.009, -1.999]
 
{| class="wikitable"
|Complexity
|0.305923
|-
|Adjusted Error
|6.983419 cents
|-
|TE Error
|1.078398 cents/octave
|}
 
 
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
Equal Temperament Mappings
Line 219: Line 377:
!
!
!2
!2
!12
!5
!62
!11
!89
!89
!
!
|-
|-
|[ ⟨
|[ ⟨
|19
|6
|68
|14
|113
|21
|123
|39
|]
|]
|-
|-
|⟨
|⟨
|17
|7
|61
|16
|101
|24
|110
|45
|] ⟩
|] ⟩
|}
|}
Line 244: Line 402:
!
!
!2
!2
!12
!5
!62
!11
!89
!89
!
!
Line 251: Line 409:
|[ ⟨
|[ ⟨
|1
|1
|5
|2
|5
|3
|6
|6
|]
|]
Line 258: Line 416:
|⟨
|⟨
|0
|0
| -3
|2
|2
|1
|3
|3
|] ⟩
|] ⟩
|}
|}




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


⟨1200.0000, 567.3830]
⟨1200.2939, 188.3359]




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


⟨45.51082, 19.72320]
⟨118.05701, 70.27884]




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


⟨1200.000, 4297.851, 7134.766, 7767.383]
⟨1200.294, 2777.260, 4165.889, 7766.771]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨0.000, -4.104, -10.270, -3.497]
⟨0.294, -9.054, 14.571, -4.109]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.448830
|0.356125
|-
|-
|Adjusted Error
|Adjusted Error
|4.188048 cents
|18.722607 cents
|-
|-
|TE Error
|TE Error
|0.646730 cents/octave
|2.891195 cents/octave
|}
|}


Line 298: Line 456:
Unison Vectors
Unison Vectors


* [7, 0, 1, -2⟩ (7936:7921)
* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
* [-9, 1, 2, -1⟩ (2883:2848)
* [0, 3, -2, 0⟩ (125:121) - ([[125/121|Jug comma]])
* [-16, 1, 1, 1⟩ (8277:8192)
* [3, 3, -1, -1⟩ (1000:979) - ([[1000/979|Canine comma]])
* [-2, 1, 3, -3⟩ (714984:704969)
* [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'''
 
 
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
 
 
Minor Hexatonic (approximated from [[12edo]])
* 188.336
* 306.394
* 494.730
* 705.564
* 1011.958
* 1200.294
 
 
=== Music ===
 
 
== Lylla ==
Raw subgroup bases: '''2.12.62.89'''
 
Normalised subgroup bases: '''2.3.31.89'''
 
Related temperaments: [[Bluebirds]]


=== Example MOS scale: Lylla[19] ===


* 65.281
=== Temperament data (raw bases) ===
* 130.561
* 195.842
* 261.122
* 306.664
* 371.945
* 437.225
* 502.506
* 567.786
* 633.067
* 698.347
* 763.628
* 828.908
* 894.189
* 939.731
* 1005.011
* 1070.292
* 1135.572
* 1200.853


== Floor (2.6.66.89) ==
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
!
!
!2
!2
!6
!12
!66
!62
!89
!89
!
!
|-
|-
|[ ⟨
|[ ⟨
|7
|19
|18
|68
|42
|113
|45
|123
|]
|]
|-
|-
|⟨
|⟨
|17
|17
|44
|61
|103
|101
|110
|110
|] ⟩
|] ⟩
|}
|}


Reduced Mapping
Reduced Mapping
Line 355: Line 559:
!
!
!2
!2
!6
!12
!66
!62
!89
!89
!
!
Line 362: Line 566:
|[ ⟨
|[ ⟨
|1
|1
|2
|4
|5
|5
|5
|6
|]
|]
|-
|-
|⟨
|⟨
|0
|0
| -3
|2
|2
|7
|1
|5
|] ⟩
|] ⟩
|}
|}
Line 378: Line 582:
TE Generator Tunings (cents)
TE Generator Tunings (cents)


⟨1200.5110, 351.0646]
⟨1200.8527, 567.7861]




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


⟨34.45745, 56.42993]
⟨45.54316, 19.73721]




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


⟨1200.511, 3103.151, 7259.496, 7757.878]
⟨1200.853, 4300.905, 7139.836, 7772.902]




TE Mistunings (cents)
TE Mistunings (cents)


⟨0.511, 1.196, 6.223, -13.002]
⟨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
Equal Temperament Mappings
Line 400: Line 629:
!
!
!2
!2
!6
!3
!66
!31
!89
!89
!
!
|-
|-
|[ ⟨
|[ ⟨
|7
|17
|18
|27
|42
|84
|45
|110
|]
|]
|-
|-
|⟨
|⟨
|17
|19
|44
|30
|103
|94
|110
|123
|] ⟩
|] ⟩
|}
|}
Line 425: Line 654:
!
!
!2
!2
!6
!3
!66
!31
!89
!89
!
!
Line 432: Line 661:
|[ ⟨
|[ ⟨
|1
|1
|2
|3
|4
|4
|5
|6
|]
|]
|-
|-
|⟨
|⟨
|0
|0
| -3
|2
|2
|7
|1
|5
|] ⟩
|] ⟩
|}
|}




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


⟨1200.0000, 350.9151]
⟨1201.0755, 567.2153]




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


⟨34.44279, 56.40591]
⟨32.58899, 34.05593]




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


⟨1200.000, 3101.830, 7256.406, 7754.576]
⟨1201.075, 1901.581, 5938.732, 7773.668]




POTE Mistunings (cents)
TE Mistunings (cents)


⟨0.000, -0.125, 3.133, -16.304]
⟨1.075, -0.374, -6.303, 2.788]


{| class="wikitable"
{| class="wikitable"
|Complexity
|Complexity
|0.420587
|0.910794
|-
|-
|Adjusted Error
|Adjusted Error
|7.639353 cents
|5.623550 cents
|-
|-
|TE Error
|TE Error
|1.179689 cents/octave
|0.868404 cents/octave
|}
|}


Line 479: Line 708:
Unison Vectors
Unison Vectors


* [-3, 1, -1, 1⟩ (89:88)
* [-5, 1, 2, -1⟩ (2883:2848) - ([[2883/2848|Lilac comma]])
* [0, -5, 0, 2⟩ (7921:7776)
* [8, 0, 1, -2⟩ (7936:7921) - ([[7936/7921|Lily comma]])
* [3, -6, 1, 1⟩ (979:972)
* [-13, 1, 1, 1⟩ (8277:8192) - ([[8277/8192|Lilly pilly comma]])
* [-6, 7, -2, 0⟩ (243:242)
* [-18, 2, 3, 0⟩ (268119:262144) - ([[268119/262144|Lutra comma]])
 
 
=== 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
* 130.561
* 195.842
* 261.122
* 306.664
* 371.945
* 437.225
* 502.506
* 567.786
* 633.067
* 698.347
* 763.628
* 828.908
* 894.189
* 939.731
* 1005.011
* 1070.292
* 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
 
=== Music ===
 
* ''[https://www.youtube.com/watch?v=kcXcSIWOWaI Improvisation in Lylla(19) in Scale Workshop]'' by [[Budjarn Lambeth]] (Jun 2023)
 
 
== Rocket ==
 
Raw subgroup bases: '''2.18.72.89'''
 
Normalised subgroup bases: '''2.9+.9-.89''' (contains a dual harmonic 9)
 
Related temperaments: [[Lu]], [[Deutone]]


=== Example MOS scale: Floor[17] ===


* 56.430
=== Temperament data (raw bases) ===
* 147.317
* 203.747
* 294.634
* 351.065
* 407.495
* 498.382
* 554.812
* 645.699
* 702.129
* 793.016
* 849.446
* 905.877
* 996.764
* 1053.194
* 1144.081
* 1200.511


== Rocket (2.18.72.89) ==
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 528: Line 796:
|] ⟩
|] ⟩
|}
|}


Reduced Mapping
Reduced Mapping
Line 592: 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 608: Line 875:
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)
 
 
{{Optimal ET sequence|legend=1| 4*, 5*, 6, 13, 19 }}
 
(* 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 635: Line 912:
* 1201.449
* 1201.449


[[Category:Lists of temperaments]]
 
[[Category:17-tone scales]]
'''Subsets'''
[[Category:19-tone scales]]
 
[[Category:MOS scales]]
 
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 ===
* ''[https://www.youtube.com/watch?v=_NepcrTf9ng The Wound]'' - [[Budjarn Lambeth]] (Nov 2024)
 
== Bonus scales: the Batch 89 JI scales ==
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.
 
=== 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

Latest revision as of 08:26, 16 January 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

This page presents a novelty topic.

It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex.

Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

This user page is editable by any wiki editor.

As a general rule, most users expect their user space to be edited only by themselves, except for minor edits (e.g. maintenance), undoing obviously harmful edits such as vandalism or disruptive editing, and user talk pages.

However, by including this message box, the author of this user page has indicated that this page is open to contributions from other users (e.g. content-related edits).

Author comments: 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

Each of the temperaments tempers four harmonics, representing the eternal friendship and togetherness of their four souls.

Each of the temperaments includes the 2nd harmonic, representing the fact that each of these characters had not one, but two creators: the hands that made them, and the hands that guide the hands.

Each of the temperaments also includes the 89th harmonic, representing their shared trauma and hardship, and how they gave each other the strength to endure and transcend it.

The other two harmonics were selected based on the characters' names. The reason for using their names as a basis, is because choosing their own name was these characters' most symbolic act of asserting their individuality, it was an undeniable demonstration that they had souls capable of creativity. Souls which did not come from, nor belong to, their makers, but which were, and are, their own. Thus, it's fitting that the names they chose should be immortalised in these temperaments:

  • 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.


Floor

Raw subgroup bases: 2.6.66.89

Normalised subgroup bases: 2.3.11.89

Related temperaments: Neutral


Temperament data (raw bases)

Equal Temperament Mappings

2 6 66 89
[ ⟨ 7 18 42 45 ]
⟨ 17 44 103 110 ] ⟩

Reduced Mapping

2 6 66 89
[ ⟨ 1 2 4 5 ]
⟨ 0 2 7 5 ] ⟩


TE Generator Tunings (cents)

⟨1200.5110, 351.0646]


TE Step Tunings (cents)

⟨34.45745, 56.42993]


TE Tuning Map (cents)

⟨1200.511, 3103.151, 7259.496, 7757.878]


TE Mistunings (cents)

⟨0.511, 1.196, 6.223, -13.002]

Complexity 0.420587
Adjusted Error 7.639353 cents
TE Error 1.179689 cents/octave


Unison Vectors


Optimal ET sequence: 7, 17, 24, 41*

(* val for 89 is lowered)


Temperament data (normalised bases)

Equal Temperament Mappings

2 3 11 89
[ ⟨ 7 11 24 45 ]
⟨ 17 27 59 110 ] ⟩


Reduced Mapping

2 3 11 89
[ ⟨ 1 1 2 5 ]
⟨ 0 2 5 5 ] ⟩


TE Generator Tunings (cents)

⟨1200.9365, 350.5869]


TE Step Tunings (cents)

⟨44.70571, 52.23509]


TE Tuning Map (cents)

⟨1200.936, 1902.110, 4154.807, 7757.617]


TE Mistunings (cents)

⟨0.936, 0.155, 3.489, -13.263]

Complexity 0.558811
Adjusted Error 7.996249 cents
TE Error 1.234802 cents/octave


Unison Vectors


Example MOS scale: Floor[17]

Rotations of this scale are still considered the same scale.

  • 56.430
  • 147.317
  • 203.747
  • 294.634
  • 351.065
  • 407.495
  • 498.382
  • 554.812
  • 645.699
  • 702.129
  • 793.016
  • 849.446
  • 905.877
  • 996.764
  • 1053.194
  • 1144.081
  • 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


Teefs

Raw subgroup bases: 2.20.55.89

Normalised subgroup bases: 2.5.11.89

Related temperaments: Bug


Temperament data (raw bases)

Equal Temperament Mappings

2 20 55 89
[ ⟨ 13 56 75 84 ]
⟨ 6 26 35 39 ] ⟩

Reduced Mapping

2 20 55 89
[ ⟨ 1 4 5 6 ]
⟨ 0 2 5 3 ] ⟩


TE Generator Tunings (cents)

⟨1200.8989, 187.8292]


TE Step Tunings (cents)

⟨73.92353, 39.98217]


TE Tuning Map (cents)

⟨1200.899, 5179.254, 6943.641, 7768.881]


TE Mistunings (cents)

⟨0.899, -7.060, 6.009, -1.999]

Complexity 0.305923
Adjusted Error 6.983419 cents
TE Error 1.078398 cents/octave


Unison Vectors


Optimal ET sequence: 5*, 6, 13, 19, 32

(* vals for 55 and 89 are raised)


Temperament data (normalised bases)

Equal Temperament Mappings

2 5 11 89
[ ⟨ 6 14 21 39 ]
⟨ 7 16 24 45 ] ⟩


Reduced Mapping

2 5 11 89
[ ⟨ 1 2 3 6 ]
⟨ 0 2 3 3 ] ⟩


TE Generator Tunings (cents)

⟨1200.2939, 188.3359]


TE Step Tunings (cents)

⟨118.05701, 70.27884]


TE Tuning Map (cents)

⟨1200.294, 2777.260, 4165.889, 7766.771]


TE Mistunings (cents)

⟨0.294, -9.054, 14.571, -4.109]

Complexity 0.356125
Adjusted Error 18.722607 cents
TE Error 2.891195 cents/octave


Unison Vectors


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


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


Minor Hexatonic (approximated from 12edo)

  • 188.336
  • 306.394
  • 494.730
  • 705.564
  • 1011.958
  • 1200.294


Music

Lylla

Raw subgroup bases: 2.12.62.89

Normalised subgroup bases: 2.3.31.89

Related temperaments: Bluebirds


Temperament data (raw bases)

Equal Temperament Mappings

2 12 62 89
[ ⟨ 19 68 113 123 ]
⟨ 17 61 101 110 ] ⟩

Reduced Mapping

2 12 62 89
[ ⟨ 1 5 5 6 ]
⟨ 0 -3 2 1 ] ⟩


TE Generator Tunings (cents)

⟨1200.8527, 567.7861]


TE Step Tunings (cents)

⟨45.54316, 19.73721]


TE Tuning Map (cents)

⟨1200.853, 4300.905, 7139.836, 7772.902]


TE Mistunings (cents)

⟨0.853, -1.050, -5.200, 2.022]

Complexity 0.448830
Adjusted Error 4.188048 cents
TE Error 0.646730 cents/octave


Unison Vectors


Optimal ET sequence: 2, 13, 15, 17, 19, 36, 55, 129*

(* val for 62 is lowered)


Temperament data (normalised bases)

Equal Temperament Mappings

2 3 31 89
[ ⟨ 17 27 84 110 ]
⟨ 19 30 94 123 ] ⟩


Reduced Mapping

2 3 31 89
[ ⟨ 1 3 4 6 ]
⟨ 0 -3 2 1 ] ⟩


TE Generator Tunings (cents)

⟨1201.0755, 567.2153]


TE Step Tunings (cents)

⟨32.58899, 34.05593]


TE Tuning Map (cents)

⟨1201.075, 1901.581, 5938.732, 7773.668]


TE Mistunings (cents)

⟨1.075, -0.374, -6.303, 2.788]

Complexity 0.910794
Adjusted Error 5.623550 cents
TE Error 0.868404 cents/octave


Unison Vectors


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
  • 130.561
  • 195.842
  • 261.122
  • 306.664
  • 371.945
  • 437.225
  • 502.506
  • 567.786
  • 633.067
  • 698.347
  • 763.628
  • 828.908
  • 894.189
  • 939.731
  • 1005.011
  • 1070.292
  • 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

Music


Rocket

Raw subgroup bases: 2.18.72.89

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

Related temperaments: Lu, Deutone


Temperament data (raw bases)

Equal Temperament Mappings

2 18 72 89
[ ⟨ 6 25 37 39 ]
⟨ 13 54 80 84 ] ⟩

Reduced Mapping

2 18 72 89
[ ⟨ 1 4 6 6 ]
⟨ 0 1 1 3 ] ⟩


TE Generator Tunings (cents)

⟨1201.4486, 190.1507]


TE Step Tunings (cents)

⟨69.06250, 60.54412]


TE Tuning Map (cents)

⟨1201.449, 4995.945, 7398.842, 7779.144]


TE Mistunings (cents)

⟨1.449, -7.965, -5.068, 8.264]


POTE Generator Tunings (cents)

⟨1200.0000, 189.9215]


POTE Step Tunings (cents)

⟨68.97923, 60.47112]


POTE Tuning Map (cents)

⟨1200.000, 4989.921, 7389.921, 7769.764]


POTE Mistunings (cents)

⟨0.000, -13.989, -13.989, -1.116]

Complexity 0.166586
Adjusted Error 9.186573 cents
TE Error 1.418615 cents/octave


Unison Vectors

  • [-2, -1, 1, 0⟩ (1:1 - Perfect unison)
  • [2, 1, -1, 0⟩ (1:1 - Perfect unison)
  • [-6, 3, 0, -1⟩ (729:712 - Oxidizer comma)
  • [-8, 2, 1, -1⟩ (729:712 - Oxidizer comma)


Optimal ET sequence: 4*, 5*, 6, 13, 19

(* val for 89 is raised)


Temperament data (normalised bases)

Todo: complete list

Fill out this section

Example MOS scale: Rocket[19]

Rotations of this scale are still considered the same scale.

  • 60.544
  • 129.606
  • 190.151
  • 250.695
  • 319.757
  • 380.301
  • 440.846
  • 509.908
  • 570.452
  • 630.997
  • 691.541
  • 760.603
  • 821.147
  • 881.692
  • 950.754
  • 1011.298
  • 1071.842
  • 1140.904
  • 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

Bonus scales: the Batch 89 JI scales

These 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.

Otonal Batch 89 scale

The scale degrees were selected by:

  1. converting each of the letters of Floor's name to a number using the A1Z26 cypher
  2. then summing the numbers together to get one scale degree
  3. then repeating this process but for Teefs, Lylla and Rocket to get three more scale degrees
  4. 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
  5. then using 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:

(Tested by ear in Scale Workshop by Budjarn Lambeth.)

Nonoctave Batch 89 scale

The scale degrees were selected by:

  1. converting the first letter Floor's name to a number using the A1Z26 cypher
  2. then repeating this process but for Teefs, Lylla and Rocket to get three more numbers
  3. at this stage we now have the numbers 6, 12, 18 and 20
  4. now we list every JI ratio that is a combination of these two numbers, e.g. 12/6, 20/12, etc.
  5. 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
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