@@ Line 1: / Line 1: @@
+{{Technical data page}}<br><br>
 {{novelty}}
-These temperaments were documented in honour of the members of Batch 89, as depicted in ''Guardians of the Galaxy Vol. 3'' (2023).
+{{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 ==
@@ Line 13: / Line 17: @@
 * 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 ==
@@ Line 19: / Line 24: @@
 Normalised subgroup bases: '''2.3.11.89'''
-Related temperaments: '''[[Neutral]]'''
+Related temperaments: [[Neutral]]
 === Temperament data (raw bases) ===
@@ Line 103: / Line 109: @@
 Unison Vectors
-* [-3, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
+* [-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]])
@@ Line 112: / Line 118: @@
 (* val for 89 is lowered)
 === Temperament data (normalised bases) ===
 Equal Temperament Mappings
@@ Line 199: / Line 205: @@
 Unison Vectors
-* [-3, 0, -1, 1⟩ (89:88)
+* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
-* [-1, 5, -2, 0⟩ (243:242)
+* [-1, 5, -2, 0⟩ (243:242) - ([[243/242|Rastma]])
-* [-2, -5, 1, 1⟩ (979:972)
+* [-2, -5, 1, 1⟩ (979:972) - ([[979/972|Basement comma]])
-* [-5, -5, 0, 2⟩ (7921:7776)
+* [-5, -5, 0, 2⟩ (7921:7776) - ([[7921/7776|Attic comma]])
-{{Optimal ET sequence|legend=1| 7, 17, 24, 41* }}
-(* val for 89 is lowered)
 === Example MOS scale: Floor[17] ===
+Rotations of this scale are still considered the same scale.
 * 56.430
@@ Line 233: / Line 236: @@
-Cosmic
+Cosmic (approximated from [[32afdo]])
 * 498.382
 * 702.129
@@ Line 239: / Line 242: @@
 * 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 ===
-* ''[https://youtu.be/YHbBJOHdD_E Improvisation in Floor(17) in Scale Workshop]'' by [[Budjarn Lambeth]]
+* ''[https://www.youtube.com/watch?v=YHbBJOHdD_E Improvisation in Floor(17) in Scale Workshop]'' by [[Budjarn Lambeth]] (Jun 2023)
 == Teefs ==
@@ Line 249: / Line 275: @@
 Normalised subgroup bases: '''2.5.11.89'''
-Related temperaments: '''[[Bug]]'''
+Related temperaments: [[Bug]]
 === Temperament data (raw bases) ===
@@ Line 333: / Line 360: @@
 Unison Vectors
-* [-5, 1, -1, 1⟩ (89:88 - [[89/88|Sky comma]])
+* [-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]])
@@ Line 342: / Line 369: @@
 (* vals for 55 and 89 are raised)
 === Temperament data (normalised bases) ===
 Equal Temperament Mappings
@@ Line 429: / Line 456: @@
 Unison Vectors
-* [-3, 0, -1, 1⟩ (89:88)
+* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
-* [0, 3, -2, 0⟩ (125:121)
+* [0, 3, -2, 0⟩ (125:121) - ([[125/121|Jug comma]])
-* [3, 3, -1, -1⟩ (1000:979)
+* [3, 3, -1, -1⟩ (1000:979) - ([[1000/979|Canine comma]])
-* [6, 3, 0, -2⟩ (8000:7921)
+* [6, 3, 0, -2⟩ (8000:7921) - ([[8000/7921|Incisor comma]])
-{{Optimal ET sequence|legend=1| 5, 6, 13, 19, 32 }}
+=== 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.
-{{Todo|inline=yes|comment=Check whether any vals are lowered or raised}}
+* 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
-=== Example MOS scale: Teefs[32] ===
-* 39.979
+'''Subsets'''
-* 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'''
+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
-Cosmic
-* 489.562
-* 711.337
-* 785.262
-* 1013.070
-* 1200.899
 === Music ===
 == Lylla ==
@@ Line 492: / Line 526: @@
 Normalised subgroup bases: '''2.3.31.89'''
-Related temperaments: '''[[Bluebirds]]'''
+Related temperaments: [[Bluebirds]]
 === Temperament data (raw bases) ===
 Equal Temperament Mappings
 {| class="wikitable"
@@ Line 578: / Line 614: @@
 * [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|Lime comma]])
+* [-16, 1, 1, 1⟩ (8277:8192 - [[8277/8192|Lilly pilly comma]])
 * [-2, 1, 3, -3⟩ (714984:704969 - [[714984/704969|Lightyear comma]])
@@ Line 585: / Line 621: @@
 (* val for 62 is lowered)
 === Temperament data (normalised bases) ===
 Equal Temperament Mappings
 {| class="wikitable"
@@ Line 670: / Line 708: @@
 Unison Vectors
-* [-5, 1, 2, -1⟩ (2883:2848)
+* [-5, 1, 2, -1⟩ (2883:2848) - ([[2883/2848|Lilac comma]])
-* [8, 0, 1, -2⟩ (7936:7921)
+* [8, 0, 1, -2⟩ (7936:7921) - ([[7936/7921|Lily comma]])
-* [-13, 1, 1, 1⟩ (8277:8192)
+* [-13, 1, 1, 1⟩ (8277:8192) - ([[8277/8192|Lilly pilly comma]])
-* [-18, 2, 3, 0⟩ (268119:262144)
+* [-18, 2, 3, 0⟩ (268119:262144) - ([[268119/262144|Lutra comma]])
-{{Optimal ET sequence|legend=1| 2, 13, 15, 17, 19, 36, 55, 129 }}
-{{todo|inline=yes|comment=Check whether any vals are lowered or raised}}
 === 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
@@ Line 706: / Line 741: @@
-Cosmic
+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
@@ Line 715: / Line 759: @@
 === Music ===
-* ''[https://youtu.be/kcXcSIWOWaI Improvisation in Lylla(19) in Scale Workshop]'' by [[Budjarn Lambeth]]
+* ''[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]]'''
+Related temperaments: [[Lu]], [[Deutone]]
 === Temperament data (raw bases) ===
 Equal Temperament Mappings
 {| class="wikitable"
@@ Line 836: / Line 884: @@
 (* val for 89 is raised)
 === Temperament data (normalised bases) ===
-{{todo|inline=yes|comment=Fill out this section}}
+{{todo|complete list|inline=yes|comment=Fill out this section}}
 === Example MOS scale: Rocket[19] ===
+Rotations of this scale are still considered the same scale.
 * 60.544
@@ Line 866: / Line 916: @@
-Cosmic
+Cosmic (approximated from [[32afdo]])
 * 509.908
 * 691.541
@@ Line 872: / Line 922: @@
 * 1011.298
 * 1201.449
+Minor Hexatonic (approximated from [[12edo]])
+* 190.151
+* 319.757
+* 509.908
+* 691.541
+* 1011.298
+* 1201.449
 === Music ===
-[[Category:17-tone scales]]
+* ''[https://www.youtube.com/watch?v=_NepcrTf9ng The Wound]'' - [[Budjarn Lambeth]] (Nov 2024)
-[[Category:19-tone scales]]
-[[Category:89-limit]]
+== Bonus scales: the Batch 89 JI scales ==
-[[Category:Listen]]
+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.
-[[Category:MOS scales]]
-[[Category:Subgroup temperaments]]
+=== Otonal Batch 89 scale ===
-[[Category:Temperament collections]]
+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

User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions