@@ 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 105: / 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 201: / Line 205: @@
 Unison Vectors
-* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Sky comma]])
+* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
 * [-1, 5, -2, 0⟩ (243:242) - ([[243/242|Rastma]])
 * [-2, -5, 1, 1⟩ (979:972) - ([[979/972|Basement comma]])
@@ Line 208: / Line 212: @@
 === Example MOS scale: Floor[17] ===
+Rotations of this scale are still considered the same scale.
 * 56.430
@@ Line 231: / Line 236: @@
-Cosmic
+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
@@ Line 241: / Line 267: @@
 === 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)
@@ Line 334: / 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 430: / Line 456: @@
 Unison Vectors
-* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Sky comma]])
+* [-3, 0, -1, 1⟩ (89:88) - ([[89/88|Tailwind comma]])
 * [0, 3, -2, 0⟩ (125:121) - ([[125/121|Jug comma]])
 * [3, 3, -1, -1⟩ (1000:979) - ([[1000/979|Canine comma]])
@@ Line 436: / Line 462: @@
-=== Example inflected MOS scale: Teefs[19] UFO InfMOS ===
+=== Example inflected MOS scale: UFO scale ===
-''See also: [[inflected MOS]].''
+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
@@ Line 463: / Line 489: @@
-Cosmic
+Cosmic (approximated from [[32afdo]])
 * 494.730
 * 705.564
@@ Line 469: / Line 495: @@
 * 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 ===
@@ Line 566: / 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 662: / Line 710: @@
 * [-5, 1, 2, -1⟩ (2883:2848) - ([[2883/2848|Lilac comma]])
 * [8, 0, 1, -2⟩ (7936:7921) - ([[7936/7921|Lily comma]])
-* [-13, 1, 1, 1⟩ (8277:8192) - ([[8277/8192|Lime comma]])
+* [-13, 1, 1, 1⟩ (8277:8192) - ([[8277/8192|Lilly pilly comma]])
 * [-18, 2, 3, 0⟩ (268119:262144) - ([[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
@@ Line 692: / Line 741: @@
-Cosmic
+Cosmic (approximated from [[32afdo]])
 * 502.506
 * 698.347
@@ Line 699: / Line 748: @@
 * 1200.853
+Minor Hexatonic (approximated from [[12edo]])
+* 195.842
+* 306.664
+* 502.506
+* 698.347
+* 1005.011
+* 1200.853
 === 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)
@@ Line 711: / Line 768: @@
 Normalised subgroup bases: '''2.9+.9-.89''' (contains a dual harmonic 9)
-Related temperaments: [[Lu]]
+Related temperaments: [[Lu]], [[Deutone]]
@@ Line 830: / Line 887: @@
 === Temperament data (normalised bases) ===
-{{todo|expand|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 859: / Line 916: @@
-Cosmic
+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
@@ Line 868: / Line 934: @@
 === Music ===
+* ''[https://www.youtube.com/watch?v=_NepcrTf9ng The Wound]'' - [[Budjarn Lambeth]] (Nov 2024)
+== Bonus scales: the Batch 89 JI scales ==
+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.
+=== Otonal Batch 89 scale ===
+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]]''
-[[Category:17-tone scales]]
+This results in the following scale:
-[[Category:19-tone scales]]
+* 20/18
-[[Category:89-limit]]
+* 18/12
-[[Category:Listen]]
+* 20/12
-[[Category:MOS scales]]
+* 12/6
-[[Category:Subgroup temperaments]]
+* 18/6
-[[Category:Temperament collections]]
+* 20/6

User:BudjarnLambeth/Batch 89 temperaments: Difference between revisions