User:BudjarnLambeth/Batch 89 temperaments

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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

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]

POTE Generator Tunings (cents)

⟨1200.0000, 350.9151]

POTE Step Tunings (cents)

⟨34.44279, 56.40591]

POTE Tuning Map (cents)

⟨1200.000, 3101.830, 7256.406, 7754.576]

POTE Mistunings (cents)

⟨0.000, -0.125, 3.133, -16.304]

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)

Todo: fill out this section

Example MOS scale: Floor[17]

• 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

• 498.382
• 702.129
• 793.016
• 996.764
• 1200.511

Music

• Improvisation in Floor(17) in Scale Workshop by Budjarn Lambeth

Teefs

Raw subgroup bases: 2.20.55.89

Normalised subgroup bases: 2.5.11.89

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]

POTE Generator Tunings (cents)

⟨1200.0000, 187.6886]

POTE Step Tunings (cents)

⟨73.86819, 39.95225]

POTE Tuning Map (cents)

⟨1200.000, 5175.377, 6938.443, 7763.066]

POTE Mistunings (cents)

⟨-0.000, -10.936, 0.812, -7.814]

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)

Todo: fill out this section

Example MOS scale: Teefs[32]

• 39.979
• 73.925
• 113.904
• 147.850
• 187.829
• 227.808
• 261.754
• 301.733
• 335.679
• 375.658
• 415.637
• 449.583
• 489.562
• 523.508
• 563.487
• 597.433
• 637.412
• 677.391
• 711.337
• 751.316
• 785.262
• 825.241
• 865.220
• 899.166
• 939.145
• 973.091
• 1013.070
• 1053.049
• 1086.995
• 1126.974
• 1160.920
• 1200.899

Subsets

• 489.562
• 711.337
• 785.262
• 1013.070
• 1200.899

Lylla

Raw subgroup bases: 2.12.62.89

Normalised subgroup bases: 2.3.31.89

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]

POTE Generator Tunings (cents)

⟨1200.0000, 567.3830]

POTE Step Tunings (cents)

⟨45.51082, 19.72320]

POTE Tuning Map (cents)

⟨1200.000, 4297.851, 7134.766, 7767.383]

POTE Mistunings (cents)

⟨0.000, -4.104, -10.270, -3.497]

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)

Todo: fill out this section

Example MOS scale: Lylla[19]

• 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

• 502.506
• 698.347
• 828.908
• 1005.011
• 1200.853

Music

• Improvisation in Lylla(19) in Scale Workshop by Budjarn Lambeth

Rocket

Raw subgroup bases: 2.18.72.89

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

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: fill out this section

Example MOS scale: Rocket[19]

• 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

• 509.908
• 691.541
• 821.147
• 1011.298
• 1201.449