# Batch 89 temperaments

**This page presents a novelty topic.** It features ideas which are less likely to find practical applications in xenharmonic music. It may contain numbers that are impractically large, exceedingly complex or chosen arbitrarily.

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

These temperaments were documented in honour of the members of Batch 89, as depicted in *Guardians of the Galaxy Vol. 3* (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

- [-3, 1, -1, 1⟩ (89:88 - Sky comma)
- [0, -5, 0, 2⟩ (7921:7776 - Attic comma)
- [3, -6, 1, 1⟩ (979:972 - Basement comma)
- [-6, 7, -2, 0⟩ (243:242 - Rastma)

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

- [-3, 0, -1, 1⟩ (89:88) - (Sky comma)
- [-1, 5, -2, 0⟩ (243:242) - (Rastma)
- [-2, -5, 1, 1⟩ (979:972) - (Basement comma)
- [-5, -5, 0, 2⟩ (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**

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

- [-5, 1, -1, 1⟩ (89:88 - Sky comma)
- [0, 3, 0, -2⟩ (8000:7921 - Incisor comma)
- [-5, 4, -1, -1⟩ (1000:979 - Canine comma)
- [-5, -2, -1, 3⟩ (704969:704000 - Molar comma)

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

- [-3, 0, -1, 1⟩ (89:88) - (Sky comma)
- [0, 3, -2, 0⟩ (125:121) - (Jug comma)
- [3, 3, -1, -1⟩ (1000:979) - (Canine comma)
- [6, 3, 0, -2⟩ (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

### 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

- [7, 0, 1, -2⟩ (7936:7921 - Lily comma)
- [-9, 1, 2, -1⟩ (2883:2848 - Lilac comma)
- [-16, 1, 1, 1⟩ (8277:8192 - Lime comma)
- [-2, 1, 3, -3⟩ (714984:704969 - Lightyear comma)

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

- [-5, 1, 2, -1⟩ (2883:2848) - (Lilac comma)
- [8, 0, 1, -2⟩ (7936:7921) - (Lily comma)
- [-13, 1, 1, 1⟩ (8277:8192) - (Lime comma)
- [-18, 2, 3, 0⟩ (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

## Rocket

Raw subgroup bases: **2.18.72.89**

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

Related temperaments: Lu

### 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:** expand

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