User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions
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* [3, -6, 1, 1⟩ (979:972) | * [3, -6, 1, 1⟩ (979:972) | ||
* [-6, 7, -2, 0⟩ (243:242) | * [-6, 7, -2, 0⟩ (243:242) | ||
{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }} | {{Optimal ET sequence|legend=1| 7, 17, 24, 41* }} | ||
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* [-5, 4, -1, -1⟩ (1000:979) | * [-5, 4, -1, -1⟩ (1000:979) | ||
* [-5, -2, -1, 3⟩ (704969:704000) | * [-5, -2, -1, 3⟩ (704969:704000) | ||
{{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }} | {{Optimal ET sequence|legend=1| 5*, 6, 13, 19, 32 }} | ||
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* [-16, 1, 1, 1⟩ (8277:8192) | * [-16, 1, 1, 1⟩ (8277:8192) | ||
* [-2, 1, 3, -3⟩ (714984:704969) | * [-2, 1, 3, -3⟩ (714984:704969) | ||
{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }} | {{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129* }} | ||
Revision as of 22:46, 13 June 2023
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 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
Mappings
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 and POTE tunings
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 |
Vectors and ET sequence
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)
Optimal ET sequence: 7, 17, 24, 41*
(* val for 89 is lowered)
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
Teefs
Raw subgroup bases: 2.20.55.89
Normalised subgroup bases: 2.5.11.89
Mappings
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 and POTE tunings
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 |
Vectors and ET sequence
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)
Optimal ET sequence: 5*, 6, 13, 19, 32
(* vals for 55 and 89 are raised)
Example MOS scale: Teefs[19]
- 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
Raw subgroup bases: 2.12.62.89
Normalised subgroup bases: 2.3.31.89
Mappings
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 and POTE tunings
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 |
Vectors and ET sequence
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)
Optimal ET sequence: 2, 13, 15, 17, 19, 36, 55, 129*
(* val for 62 is lowered)
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
Rocket
Raw subgroup bases: 2.18.72.89
Normalised subgroup bases: 2.9+.9-.89 (contains a dual harmonic 9)
Mappings
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 and POTE tunings
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 |
Vectors and ET sequence
Unison Vectors
- [-2, -1, 1, 0⟩ (1:1)
- [2, 1, -1, 0⟩ (1:1)
- [-6, 3, 0, -1⟩ (729:712)
- [-8, 2, 1, -1⟩ (729:712)
Optimal ET sequence: 4*, 5*, 6, 13, 19
(* val for 89 is raised)
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