User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
m Added links to comma pages and added this page to category "temperament collections"
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,263 edits
m Reorganised subheadings, added to-do info
Line 18: Line 18:
Normalised subgroup bases: '''2.3.11.89'''
Normalised subgroup bases: '''2.3.11.89'''


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


TE Generator Tunings (cents)
TE Generator Tunings (cents)
Line 88: Line 85:


⟨0.511, 1.196, 6.223, -13.002]
⟨0.511, 1.196, 6.223, -13.002]


POTE Generator Tunings (cents)
POTE Generator Tunings (cents)
Line 119: Line 114:
|TE Error
|TE Error
|1.179689 cents/octave
|1.179689 cents/octave
|}
|}Unison Vectors
 
=== Vectors and ET sequence ===
Unison Vectors
* [-3, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
* [-3, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
* [0, -5, 0, 2⟩ (7921:7776 - [[7921/7776|Attic comma]])
* [0, -5, 0, 2⟩ (7921:7776 - [[7921/7776|Attic comma]])
Line 132: Line 124:


(* val for 89 is lowered)
(* val for 89 is lowered)
=== Temperament data (normalised bases) ===
''Todo: please fill out this section''


=== Example MOS scale: Floor[17] ===
=== Example MOS scale: Floor[17] ===
Line 160: Line 155:
Normalised subgroup bases: '''2.5.11.89'''
Normalised subgroup bases: '''2.5.11.89'''


=== Mappings ===
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 209: Line 204:
|}
|}


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


Line 258: Line 253:
|TE Error
|TE Error
|1.078398 cents/octave
|1.078398 cents/octave
|}
|}Unison Vectors
 
=== Vectors and ET sequence ===
Unison Vectors
* [-5, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
* [-5, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
* [0, 3, 0, -2⟩ (8000:7921 - [[8000/7921|Incisor comma]])
* [0, 3, 0, -2⟩ (8000:7921 - [[8000/7921|Incisor comma]])
Line 271: Line 263:


(* vals for 55 and 89 are raised)
(* vals for 55 and 89 are raised)
=== Temperament data (normalised bases) ===
''Todo: please fill out this section''


=== Example MOS scale: Teefs[19] ===
=== Example MOS scale: Teefs[19] ===
Line 301: Line 296:
Normalised subgroup bases: '''2.3.31.89'''
Normalised subgroup bases: '''2.3.31.89'''


=== Mappings ===
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 350: Line 345:
|}
|}


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


Line 369: Line 364:


⟨0.853, -1.050, -5.200, 2.022]
⟨0.853, -1.050, -5.200, 2.022]


POTE Generator Tunings (cents)
POTE Generator Tunings (cents)
Line 400: Line 393:
|TE Error
|TE Error
|0.646730 cents/octave
|0.646730 cents/octave
|}
|}Unison Vectors
 
=== Vectors and ET sequence ===
Unison Vectors
* [7, 0, 1, -2⟩ (7936:7921 - [[7936/7921|Lily comma]])
* [7, 0, 1, -2⟩ (7936:7921 - [[7936/7921|Lily comma]])
* [-9, 1, 2, -1⟩ (2883:2848 - [[2883/2848|Lilac comma]])
* [-9, 1, 2, -1⟩ (2883:2848 - [[2883/2848|Lilac comma]])
Line 413: Line 403:


(* val for 62 is lowered)
(* val for 62 is lowered)
=== Temperament data (normalised bases) ===
''Todo: please fill out this section''


=== Example MOS scale: Lylla[19] ===
=== Example MOS scale: Lylla[19] ===
Line 445: Line 438:
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 ===
=== Temperament data (raw bases) ===
Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
{| class="wikitable"
Line 494: Line 487:
|}
|}


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


Line 545: Line 538:
|}
|}


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


Line 557: Line 550:


(* val for 89 is raised)
(* val for 89 is raised)
=== Temperament data (normalised bases) ===
''Todo: please fill out this section''


=== Example MOS scale: Rocket[19] ===
=== Example MOS scale: Rocket[19] ===
Line 588: Line 584:
[[Category:MOS scales]]
[[Category:MOS scales]]
[[Category:Temperament collections]]
[[Category:Temperament collections]]
[[Category:Todo:expand]]

Revision as of 04:49, 18 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

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


Optimal ET sequence: 7, 17, 24, 41*

(* val for 89 is lowered)

Temperament data (normalised bases)

Todo: please 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

Music

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


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

(* vals for 55 and 89 are raised)

Temperament data (normalised bases)

Todo: please fill out this section

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

Music

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


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

(* val for 62 is lowered)

Temperament data (normalised bases)

Todo: please 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

Music

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: please 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

Music

Retrieved from "https://en.xen.wiki/index.php?title=User:BudjarnLambeth/Batch_89_temperaments&oldid=117072"