Chords of orwell: Difference between revisions

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Below are listed the [[11-odd-limit]] [[dyadic chord]]s of 11-limit [[orwell|orwell temperament]]. Typing the chords requires consideration of the fact that orwell equates certain [[11-odd-limit]] consonances—it conflates [[14/11]] and [[9/7]], [[11/7]] and [[14/9]], [[12/11]] and [[11/10]], and [[11/6]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 9/7 and 11/10 and their inversions. Those requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. If it requires any two of 99/98, 176/175 and 225/224, it is labeled minerva, any two of 99/98, 121/120 or 540/539, big brother, any two of 121/120, 176/175 or 385/384, zeus, any two of 225/224, 385/384 or 540/539, [[undecimal marvel chords|unimarvel]]. If it requires both 99/98 and 385/384 it is labeled orwellian, and if it requires three independent commas among those discussed above, it is labeled orwell. Orwell has [[mos]] of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic has three triads and a tetrad, the nine-note mos is of course much better supplied and with thirteen notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable major triad.
{{Breadcrumb|Orwell}}
Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[orwell|orwell temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of subminor third [[generator]]s above the root.
 
Typing the chords requires consideration of the fact that orwell equates certain [[11-odd-limit]] consonances – it conflates [[14/11]] with [[9/7]], [[11/7]] with [[14/9]], [[12/11]] with [[11/10]], and [[11/6]] with [[20/11]]. If a [[transversal]] can be found which shows the chord to be [[dyadic chord #Essentially tempered dyadic chord|essentially just]], that transversal is listed along with a typing as [[otonal]], [[utonal]], or [[ambitonal]]. Sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is [[dyadic chord #Essentially tempered dyadic chord|essentially tempered]], it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 9/7 and 11/10 over the root.  
 
Those requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. If it requires any two of 99/98, 176/175 and 225/224, it is labeled [[minerva chords|minerva]], any two of 99/98, 121/120 or 540/539, [[big brother chords|big brother]], any two of 121/120, 176/175 or 385/384, [[zeus chords|zeus]], any two of 225/224, 385/384 or 540/539, [[undecimal marvel chords|marvel11]]. If it requires both 99/98 and 385/384 it is labeled [[orwellian chords|orwellian]], and if it requires three independent commas among those discussed above, it is labeled [[orwell chords|orwell]].  
 
Orwell has [[mos]] of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic scale has three triads and a tetrad. The 9-note mos is of course much better supplied, and with 13 notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable [[4:5:6|major triad]].


For diagrams showing how some of these chords might map to a [[keyboard]] such as the Axis-49, see [[Orwell on an isomorphic keyboard]].
For diagrams showing how some of these chords might map to a [[keyboard]] such as the Axis-49, see [[Orwell on an isomorphic keyboard]].
{{Todo|inline=1|cleanup}}


== Triads ==
== Triads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! #
! #
Line 12: Line 17:
! Transversal
! Transversal
! Type
! Type
! As generated
! Comment
! First inversion
! Second inversion
! Odd limit
|-
|-
| 1
| 1
Line 21: Line 23:
| 1–7/6–11/8
| 1–7/6–11/8
| Mothwellsmic
| Mothwellsmic
| 1–7/6–11/8
|  
| 1–7/6–12/7
| 1–16/11–12/7
| 11
|-
|-
| 2
| 2
Line 30: Line 29:
| 1–7/6–8/5
| 1–7/6–8/5
| Keenanismic
| Keenanismic
| 1–7/6–8/5
|  
| 1–11/8–12/7
| 1–5/4–16/11
| 11
|-
|-
| 3
| 3
Line 39: Line 35:
| 1–11/8–8/5
| 1–11/8–8/5
| Keenanismic
| Keenanismic
| 1–11/8–8/5
|  
| 1–7/6–16/11
| 1–5/4–12/7
| 11
|-
|-
| 4
| 4
| 0–2–5
| 0–2–5
| 1–11/8–11/10
| 1–11/10–11/8
| Utonal
| Utonal
| 1–11/10–11/8
|  
| 1–5/4–20/11
| 1–16/11–8/5
| 11
|-
|-
| 5
| 5
| 0–3–5
| 0–3–5
| 1–8/5–11/10
| 1–11/10–8/5
| Otonal
| Otonal
| 1–11/10–8/5
|  
| 1–16/11–20/11
| 1–5/4–11/8
| 11
|-
|-
| 6
| 6
Line 66: Line 53:
| 1–7/6–14/11
| 1–7/6–14/11
| Utonal
| Utonal
| 1–7/6–14/11
|  
| 1–12/11–12/7
| 1–11/7–11/6
| 11
|-
|-
| 7
| 7
| 0–3–6
| 0–3–6
| 1–8/5–9/7
| 1–9/7–8/5
| Marvel
| Marvel
| 1–9/7–8/5
|  
| 1–5/4–14/9
| 1–5/4–8/5
| 9
|-
|-
| 8
| 8
Line 84: Line 65:
| 1–12/11–14/11
| 1–12/11–14/11
| Otonal
| Otonal
| 1–12/11–14/11
|  
| 1–7/6–11/6
| 1–11/7–12/7
| 11
|-
|-
| 9
| 9
Line 93: Line 71:
| 1–7/6–3/2
| 1–7/6–3/2
| Otonal
| Otonal
| 1–7/6–3/2
| [[6:7:9]]
| 1–9/7–12/7
| 1–4/3–14/9
| 9
|-
|-
| 10
| 10
Line 102: Line 77:
| 1–11/8–3/2
| 1–11/8–3/2
| Otonal
| Otonal
| 1–11/8–3/2
|  
| 1–12/11–16/11
| 1–4/3–11/6
| 11
|-
|-
| 11
| 11
Line 111: Line 83:
| 1–12/11–3/2
| 1–12/11–3/2
| Utonal
| Utonal
| 1–12/11–3/2
|  
| 1–11/8–11/6
| 1–4/3–16/11
| 11
|-
|-
| 12
| 12
Line 120: Line 89:
| 1–9/7–3/2
| 1–9/7–3/2
| Utonal
| Utonal
| 1–9/7–3/2
| [[14:18:21|1/(9:7:6)]]
| 1–7/6–14/9
| 1–4/3–12/7
| 9
|-
|-
| 13
| 13
Line 129: Line 95:
| 1–7/6–7/4
| 1–7/6–7/4
| Utonal
| Utonal
| 1–7/6–7/4
| [[14:21:24|1/(12:8:7)]]
| 1–3/2–12/7
| 1–8/7–4/3
| 7
|-
|-
| 14
| 14
Line 138: Line 101:
| 1–11/8–7/4
| 1–11/8–7/4
| Otonal
| Otonal
| 1–11/8–7/4
|  
| 1–14/11–16/11
| 1–8/7–11/7
| 11
|-
|-
| 15
| 15
Line 147: Line 107:
| 1–8/5–7/4
| 1–8/5–7/4
| Valinorsmic
| Valinorsmic
| 1–8/5–7/4
|  
| 1–11/10–5/4
| 1–8/7–20/11
| 11
|-
|-
| 16
| 16
Line 156: Line 113:
| 1–11/10–7/4
| 1–11/10–7/4
| Valinorsmic
| Valinorsmic
| 1–11/10–7/4
|  
| 1–8/5–20/11
| 1–8/7–5/4
| 11
|-
|-
| 17
| 17
Line 165: Line 119:
| 1–14/11–7/4
| 1–14/11–7/4
| Utonal
| Utonal
| 1–14/11–7/4
|  
| 1–11/8–11/7
| 1–8/7–16/11
| 11
|-
|-
| 18
| 18
Line 174: Line 125:
| 1–3/2–7/4
| 1–3/2–7/4
| Otonal
| Otonal
| 1–3/2–7/4
| [[4:6:7]]
| 1–7/6–4/3
| 1–8/7–12/7
| 7
|-
|-
| 19
| 19
| 0–2–10
| 0–2–10
| 1–11/8–6/5
| 1–6/5–11/8
| Keenanismic
| Keenanismic
| 1–6/5–11/8
|  
| 1–8/7–5/3
| 1–16/11–7/4
| 11
|-
|-
| 20
| 20
| 0–3–10
| 0–3–10
| 1–8/5–6/5
| 1–6/5–8/5
| Otonal
| Otonal
| 1–6/5–8/5
| [[4:5:6]]
| 1–4/3–5/3
| 1–5/4–3/2
| 5
|-
|-
| 21
| 21
Line 201: Line 143:
| 1–11/10–6/5
| 1–11/10–6/5
| Otonal
| Otonal
| 1–11/10–6/5
|  
| 1–12/11–20/11
| 1–5/3–11/6
| 11
|-
|-
| 22
| 22
| 0–7–10
| 0–7–10
| 1–3/2–6/5
| 1–6/5–3/2
| Utonal
| Utonal
| 1–6/5–3/2
| [[10:12:15|1/(6:5:4)]]
| 1–5/4–5/3
| 1–4/3–8/5
| 5
|-
|-
| 23
| 23
| 0–8–10
| 0–8–10
| 1–7/4–6/5
| 1–6/5–7/4
| Keenanismic
| Keenanismic
| 1–6/5–7/4
|  
| 1–16/11–5/3
| 1–8/7–11/8
| 11
|-
|-
| 24
| 24
Line 228: Line 161:
| 1–7/6–7/5
| 1–7/6–7/5
| Utonal
| Utonal
| 1–7/6–7/5
| [[30:35:42|1/(7:6:5)]]
| 1–6/5–12/7
| 1–10/7–5/3
| 7
|-
|-
| 25
| 25
| 0–3–11
| 0–3–11
| 1–8/5–7/5
| 1–7/5–8/5
| Otonal
| Otonal
| 1–7/5–8/5
| [[4:5:7]]
| 1–8/7–10/7
| 1–5/4–7/4
| 7
|-
|-
| 26
| 26
Line 246: Line 173:
| 1–11/10–7/5
| 1–11/10–7/5
| Otonal
| Otonal
| 1–11/10–7/5
|  
| 1–14/11–20/11
| 1–10/7–11/7
| 11
|-
|-
| 27
| 27
Line 255: Line 179:
| 1–14/11–7/5
| 1–14/11–7/5
| Utonal
| Utonal
| 1–14/11–7/5
|  
| 1–11/10–11/7
| 1–10/7–20/11
| 11
|-
|-
| 28
| 28
| 0–8–11
| 0–8–11
| 1–7/4–7/5
| 1–7/5–7/4
| Utonal
| Utonal
| 1–7/5–7/4
| [[28:35:40|1/(10:8:7)]]
| 1–5/4–10/7
| 1–8/7–8/5
| 7
|-
|-
| 29
| 29
Line 273: Line 191:
| 1–6/5–7/5
| 1–6/5–7/5
| Otonal
| Otonal
| 1–6/5–7/5
| [[5:6:7]]
| 1–7/6–5/3
| 1–10/7–12/7
| 7
|-
|-
| 30
| 30
Line 282: Line 197:
| 1–7/6–18/11
| 1–7/6–18/11
| Swetismic
| Swetismic
| 1–7/6–18/11
|  
| 1–7/5–12/7
| 1–11/9–10/7
| 11
|-
|-
| 31
| 31
Line 291: Line 203:
| 1–11/8–18/11
| 1–11/8–18/11
| Biyatismic
| Biyatismic
| 1–11/8–18/11
|  
| 1–6/5–16/11
| 1–11/9–5/3
| 11
|-
|-
| 32
| 32
Line 300: Line 209:
| 1–12/11–18/11
| 1–12/11–18/11
| Otonal
| Otonal
| 1–12/11–18/11
|  
| 1–3/2–11/6
| 1–11/9–4/3
| 11
|-
|-
| 33
| 33
Line 309: Line 215:
| 1–9/7–18/11
| 1–9/7–18/11
| Utonal
| Utonal
| 1–9/7–18/11
|  
| 1–14/11–14/9
| 1–11/9–11/7
| 11
|-
|-
| 34
| 34
Line 318: Line 221:
| 1–3/2–18/11
| 1–3/2–18/11
| Utonal
| Utonal
| 1–3/2–18/11
|  
| 1–12/11–4/3
| 1–11/9–11/6
| 11
|-
|-
| 35
| 35
Line 327: Line 227:
| 1–6/5–18/11
| 1–6/5–18/11
| Biyatismic
| Biyatismic
| 1–6/5–18/11
|  
| 1–11/8–5/3
| 1–11/9–16/11
| 11
|-
|-
| 36
| 36
Line 336: Line 233:
| 1–7/5–18/11
| 1–7/5–18/11
| Swetismic
| Swetismic
| 1–7/5–18/11
|  
| 1–7/6–10/7
| 1–11/9–12/7
| 11
|-
|-
| 37
| 37
| 0–2–14
| 0–2–14
| 1–11/8–9/8
| 1–9/8–11/8
| Otonal
| Otonal
| 1–9/8–11/8
|  
| 1–11/9–16/9
| 1–16/11–18/11
| 11
|-
|-
| 38
| 38
| 0–3–14
| 0–3–14
| 1–8/5–9/8
| 1–9/8–8/5
| Marvel
| Marvel
| 1–9/8–8/5
|  
| 1–10/7–16/9
| 1–5/4–7/5
| 9
|-
|-
| 39
| 39
| 0–6–14
| 0–6–14
| 1–9/7–9/8
| 1–9/8–9/7
| Utonal
| Utonal
| 1–9/8–9/7
|  
| 1–8/7–16/9
| 1–14/9–7/4
| 9
|-
|-
| 40
| 40
| 0–7–14
| 0–7–14
| 1–3/2–9/8
| 1–9/8–3/2
| Ambitonal
| Ambitonal
| 1–9/8–3/2
| [[6:8:9]], [[8:9:12]]
| 1–4/3–16/9
| 1–4/3–3/2
| 9
|-
|-
| 41
| 41
| 0–8–14
| 0–8–14
| 1–7/4–9/8
| 1–9/8–7/4
| Otonal
| Otonal
| 1–9/8–7/4
|  
| 1–14/9–16/9
| 1–8/7–9/7
| 9
|-
|-
| 42
| 42
| 0–11–14
| 0–11–14
| 1–7/5–9/8
| 1–9/8–7/5
| Marvel
| Marvel
| 1–9/8–7/5
|  
| 1–5/4–16/9
| 1–10/7–8/5
| 9
|-
|-
| 43
| 43
| 0–12–14
| 0–12–14
| 1–18/11–9/8
| 1–9/8–18/11
| Utonal
| Utonal
| 1–9/8–18/11
|
| 1–16/11–16/9
| 1–11/9–11/8
| 11
|-
|-
| 44
| 44
Line 408: Line 281:
| 1–8/5–9/5
| 1–8/5–9/5
| Otonal
| Otonal
| 1–8/5–9/5
|  
| 1–9/8–5/4
| 1–10/9–16/9
| 9
|-
|-
| 45
| 45
Line 417: Line 287:
| 1–11/10–9/5
| 1–11/10–9/5
| Otonal
| Otonal
| 1–11/10–9/5
|  
| 1–18/11–20/11
| 1–10/9–11/9
| 11
|-
|-
| 46
| 46
Line 426: Line 293:
| 1–9/7–9/5
| 1–9/7–9/5
| Utonal
| Utonal
| 1–9/7–9/5
|  
| 1–7/5–14/9
| 1–10/9–10/7
| 9
|-
|-
| 47
| 47
Line 435: Line 299:
| 1–3/2–9/5
| 1–3/2–9/5
| Utonal
| Utonal
| 1–3/2–9/5
| [[10:15:18|1/(9:6:5)]]
| 1–6/5–4/3
| 1–10/9–5/3
| 9
|-
|-
| 48
| 48
Line 444: Line 305:
| 1–6/5–9/5
| 1–6/5–9/5
| Otonal
| Otonal
| 1–6/5–9/5
| [[6:9:10]]
| 1–3/2–5/3
| 1–10/9–4/3
| 9
|-
|-
| 49
| 49
Line 453: Line 311:
| 1–7/5–9/5
| 1–7/5–9/5
| Otonal
| Otonal
| 1–7/5–9/5
|  
| 1–9/7–10/7
| 1–10/9–14/9
| 9
|-
|-
| 50
| 50
Line 462: Line 317:
| 1–18/11–9/5
| 1–18/11–9/5
| Utonal
| Utonal
| 1–18/11–9/5
|  
| 1–11/10–11/9
| 1–10/9–20/11
| 11
|-
|-
| 51
| 51
Line 471: Line 323:
| 1–9/8–9/5
| 1–9/8–9/5
| Utonal
| Utonal
| 1–9/8–9/5
|  
| 1–8/5–16/9
| 1–10/9–5/4
| 9
|}
|}


== Tetrads ==
== Tetrads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
!  
! Comment
! Example in 22edo
|-
|-
| 1
| 1
Line 490: Line 340:
| 1–7/6–11/8–8/5
| 1–7/6–11/8–8/5
| Orwellian
| Orwellian
| [[File:Orwelltetrad22edo.Mp3]]
|
| [[File:OrwellTetrad22edo.mp3]]
|-
|-
| 2
| 2
| 0–2–3–5
| 0–2–3–5
| 1–11/8–8/5–11/10
| 1–11/10–11/8–8/5
| Keenanismic
| Keenanismic
| [[File:Orwell_0_2_3_5_22edo.Mp3]]
|
| [[File:Orwell_0_2_3_5_22edo.mp3]]
|-
|-
| 3
| 3
| 0–1–3–6
| 0–1–3–6
| 1–7/6–8/5–9/7
| 1–7/6–9/7–8/5
| Unimarvel
| Marvel11
| [[File:Orwell_0_1_3_6_22edo.Mp3]]
|  
| [[File:Orwell_0_1_3_6_22edo.mp3]]
|-
|-
| 4
| 4
| 0–3–5–6
| 0–3–5–6
| 1–8/5–11/10–9/7
| 1–11/10–9/7–8/5
| Unimarvel
| Marvel11
| [[File:Orwell_0_3_5_6_22edo.Mp3]]
|  
| [[File:Orwell_0_3_5_6_22edo.mp3]]
|-
|-
| 5
| 5
Line 514: Line 368:
| 1–7/6–11/8–3/2
| 1–7/6–11/8–3/2
| Big brother
| Big brother
| [[File:Orwell_0_1_2_7_22edo.Mp3]]
|
| [[File:Orwell_0_1_2_7_22edo.mp3]]
|-
|-
| 6
| 6
| 0–2–5–7
| 0–2–5–7
| 1–11/8–11/10–3/2
| 1–11/10–11/8–3/2
| Biyatismic
| Biyatismic
| [[File:Orwell_0_2_5_7_22edo.Mp3]]
|
| [[File:Orwell_0_2_5_7_22edo.mp3]]
|-
|-
| 7
| 7
Line 526: Line 382:
| 1–7/6–9/7–3/2
| 1–7/6–9/7–3/2
| Swetismic
| Swetismic
| [[File:Orwell_0_1_6_7_22edo.Mp3]]
|
| [[File:Orwell_0_1_6_7_22edo.mp3]]
|-
|-
| 8
| 8
Line 532: Line 389:
| 1–11/10–9/7–3/2
| 1–11/10–9/7–3/2
| Big brother
| Big brother
| [[File:Orwell_0_5_6_7_22edo.Mp3]]
|
| [[File:Orwell_0_5_6_7_22edo.mp3]]
|-
|-
| 9
| 9
Line 538: Line 396:
| 1–7/6–11/8–7/4
| 1–7/6–11/8–7/4
| Mothwellsmic
| Mothwellsmic
| [[File:Orwell_0_1_2_8_22edo.Mp3]]
|
| [[File:Orwell_0_1_2_8_22edo.mp3]]
|-
|-
| 10
| 10
Line 544: Line 403:
| 1–7/6–8/5–7/4
| 1–7/6–8/5–7/4
| Zeus
| Zeus
| [[File:Orwell_0_1_3_8_22edo.Mp3]]
|
| [[File:Orwell_0_1_3_8_22edo.mp3]]
|-
|-
| 11
| 11
Line 550: Line 410:
| 1–11/8–8/5–7/4
| 1–11/8–8/5–7/4
| Orwell
| Orwell
| [[File:Orwell_0_2_3_8_22edo.Mp3]]
|
| [[File:Orwell_0_2_3_8_22edo.mp3]]
|-
|-
| 12
| 12
| 0–2–5–8
| 0–2–5–8
| 1–11/8–11/10–7/4
| 1–11/10–11/8–7/4
| Minerva
| Minerva
| [[File:Orwell_0_2_5_8_22edo.Mp3]]
|
| [[File:Orwell_0_2_5_8_22edo.mp3]]
|-
|-
| 13
| 13
| 0–3–5–8
| 0–3–5–8
| 1–8/5–11/10–7/4
| 1–11/10–8/5–7/4
| Valinorsmic
| Valinorsmic
| [[File:Orwell_0_3_5_8_22edo.Mp3]]
|
| [[File:Orwell_0_3_5_8_22edo.mp3]]
|-
|-
| 14
| 14
Line 568: Line 431:
| 1–7/6–14/11–7/4
| 1–7/6–14/11–7/4
| Utonal
| Utonal
| [[File:Orwell_0_1_6_8_22edo.Mp3]]
|
| [[File:Orwell_0_1_6_8_22edo.mp3]]
|-
|-
| 15
| 15
| 0–3–6–8
| 0–3–6–8
| 1–8/5–9/7–7/4
| 1–9/7–8/5–7/4
| Minerva
| Minerva
|
|  
|  
|-
|-
Line 580: Line 445:
| 1–11/10–9/7–7/4
| 1–11/10–9/7–7/4
| Orwell
| Orwell
|
|  
|  
|-
|-
Line 586: Line 452:
| 1–7/6–3/2–7/4
| 1–7/6–3/2–7/4
| Ambitonal
| Ambitonal
| [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]]
|  
|  
|-
|-
Line 592: Line 459:
| 1–11/8–3/2–7/4
| 1–11/8–3/2–7/4
| Otonal
| Otonal
|
|  
|  
|-
|-
Line 598: Line 466:
| 1–11/10–3/2–7/4
| 1–11/10–3/2–7/4
| Zeus
| Zeus
|
|  
|  
|-
|-
Line 604: Line 473:
| 1–9/7–3/2–7/4
| 1–9/7–3/2–7/4
| Mothwellsmic
| Mothwellsmic
|
|  
|  
|-
|-
| 21
| 21
| 0–2–3–10
| 0–2–3–10
| 1–11/8–8/5–6/5
| 1–6/5–11/8–8/5
| Keenanismic
| Keenanismic
|
|  
|  
|-
|-
| 22
| 22
| 0–2–5–10
| 0–2–5–10
| 1–11/8–11/10–6/5
| 1–11/10–6/5–11/8
| Zeus
| Zeus
|
|  
|  
|-
|-
| 23
| 23
| 0–3–5–10
| 0–3–5–10
| 1–8/5–11/10–6/5
| 1–11/10–6/5–8/5
| Otonal
| Otonal
|
|  
|  
|-
|-
| 24
| 24
| 0–2–7–10
| 0–2–7–10
| 1–11/8–3/2–6/5
| 1–6/5–11/8–3/2
| Zeus
| Zeus
|
|  
|  
|-
|-
| 25
| 25
| 0–5–7–10
| 0–5–7–10
| 1–12/11–3/2–6/5
| 1–12/11–6/5–3/2
| Utonal
| Utonal
|
|  
|  
|-
|-
| 26
| 26
| 0–2–8–10
| 0–2–8–10
| 1–11/8–7/4–6/5
| 1–6/5–11/8–7/4
| Orwellian
| Orwellian
|
|  
|  
|-
|-
| 27
| 27
| 0–3–8–10
| 0–3–8–10
| 1–8/5–7/4–6/5
| 1–6/5–8/5–7/4
| Zeus
| Zeus
|
|  
|  
|-
|-
| 28
| 28
| 0–5–8–10
| 0–5–8–10
| 1–11/10–7/4–6/5
| 1–11/10–6/5–7/4
| Zeus
| Zeus
|
|  
|  
|-
|-
| 29
| 29
| 0–7–8–10
| 0–7–8–10
| 1–3/2–7/4–6/5
| 1–6/5–3/2–7/4
| Keenanismic
| Keenanismic
|
|  
|  
|-
|-
| 30
| 30
| 0–1–3–11
| 0–1–3–11
| 1–7/6–8/5–7/5
| 1–7/6–7/5–8/5
| Keenanismic
| Keenanismic
|
|  
|  
|-
|-
| 31
| 31
| 0–3–5–11
| 0–3–5–11
| 1–8/5–11/10–7/5
| 1–11/10–7/5–8/5
| Otonal
| Otonal
|
|  
|  
|-
|-
Line 676: Line 557:
| 1–7/6–14/11–7/5
| 1–7/6–14/11–7/5
| Utonal
| Utonal
|
|  
|  
|-
|-
| 33
| 33
| 0–3–6–11
| 0–3–6–11
| 1–8/5–9/7–7/5
| 1–9/7–7/5–8/5
| Minerva
| Minerva
|
|  
|  
|-
|-
Line 688: Line 571:
| 1–11/10–9/7–7/5
| 1–11/10–9/7–7/5
| Big brother
| Big brother
|
|  
|  
|-
|-
| 35
| 35
| 0–1–8–11
| 0–1–8–11
| 1–7/6–7/4–7/5
| 1–7/6–7/5–7/4
| Utonal
| Utonal
| [[70:84:105:120|1/(12:10:8:7)]]
|  
|  
|-
|-
| 36
| 36
| 0–3–8–11
| 0–3–8–11
| 1–8/5–7/4–7/5
| 1–7/5–8/5–7/4
| Valinorsmic
| Valinorsmic
|
|  
|  
|-
|-
| 37
| 37
| 0–5–8–11
| 0–5–8–11
| 1–11/10–7/4–7/5
| 1–11/10–7/5–7/4
| Minerva
| Minerva
|
|  
|  
|-
|-
| 38
| 38
| 0–6–8–11
| 0–6–8–11
| 1–14/11–7/4–7/5
| 1–14/11–7/5–7/4
| Utonal
| Utonal
|
|  
|  
|-
|-
| 39
| 39
| 0–3–10–11
| 0–3–10–11
| 1–8/5–6/5–7/5
| 1–6/5–7/5–8/5
| Otonal
| Otonal
| [[4:5:6:7]]
|  
|  
|-
|-
Line 724: Line 613:
| 1–11/10–6/5–7/5
| 1–11/10–6/5–7/5
| Otonal
| Otonal
|
|  
|  
|-
|-
| 41
| 41
| 0–8–10–11
| 0–8–10–11
| 1–7/4–6/5–7/5
| 1–6/5–7/5–7/4
| Keenanismic
| Keenanismic
|
|  
|  
|-
|-
Line 736: Line 627:
| 1–7/6–11/8–18/11
| 1–7/6–11/8–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
| 43
| 43
| 0–2–5–12
| 0–2–5–12
| 1–11/8–11/10–18/11
| 1–11/10–11/8–18/11
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 748: Line 641:
| 1–7/6–9/7–18/11
| 1–7/6–9/7–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
Line 754: Line 648:
| 1–12/11–14/11–18/11
| 1–12/11–14/11–18/11
| Otonal
| Otonal
|
|  
|  
|-
|-
Line 760: Line 655:
| 1–7/6–3/2–18/11
| 1–7/6–3/2–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
Line 766: Line 662:
| 1–11/8–3/2–18/11
| 1–11/8–3/2–18/11
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 772: Line 669:
| 1–12/11–3/2–18/11
| 1–12/11–3/2–18/11
| Ambitonal
| Ambitonal
| 11-odd-limit ASS
|  
|  
|-
|-
Line 778: Line 676:
| 1–9/7–3/2–18/11
| 1–9/7–3/2–18/11
| Utonal
| Utonal
|
|  
|  
|-
|-
| 50
| 50
| 0–2–10–12
| 0–2–10–12
| 1–11/8–6/5–18/11
| 1–6/5–11/8–18/11
| Zeus
| Zeus
|
|  
|  
|-
|-
Line 790: Line 690:
| 1–11/10–6/5–18/11
| 1–11/10–6/5–18/11
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
| 52
| 52
| 0–7–10–12
| 0–7–10–12
| 1–3/2–6/5–18/11
| 1–6/5–3/2–18/11
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 802: Line 704:
| 1–7/6–7/5–18/11
| 1–7/6–7/5–18/11
| Swetismic
| Swetismic
|
|  
|  
|-
|-
Line 808: Line 711:
| 1–11/10–7/5–18/11
| 1–11/10–7/5–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
Line 814: Line 718:
| 1–9/7–7/5–18/11
| 1–9/7–7/5–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
Line 820: Line 725:
| 1–6/5–7/5–18/11
| 1–6/5–7/5–18/11
| Big brother
| Big brother
|
|  
|  
|-
|-
| 57
| 57
| 0–2–3–14
| 0–2–3–14
| 1–11/8–8/5–9/8
| 1–9/8–11/8–8/5
| Unimarvel
| Marvel11
|  
|  
|  
|-
|-
| 58
| 58
| 0–3–6–14
| 0–3–6–14
| 1–8/5–9/7–9/8
| 1–9/8–9/7–8/5
| Marvel
| Marvel
|
|  
|  
|-
|-
| 59
| 59
| 0–2–7–14
| 0–2–7–14
| 1–11/8–3/2–9/8
| 1–9/8–11/8–3/2
| Otonal
| Otonal
|
|  
|  
|-
|-
| 60
| 60
| 0–6–7–14
| 0–6–7–14
| 1–9/7–3/2–9/8
| 1–9/8–9/7–3/2
| Utonal
| Utonal
| [[28:36:42:63|1/(9:7:6:4)]]
|  
|  
|-
|-
| 61
| 61
| 0–2–8–14
| 0–2–8–14
| 1–11/8–7/4–9/8
| 1–9/8–11/8–7/4
| Otonal
| Otonal
|
|  
|  
|-
|-
| 62
| 62
| 0–3–8–14
| 0–3–8–14
| 1–8/5–7/4–9/8
| 1–9/8–8/5–7/4
| Minerva
| Minerva
|
|  
|  
|-
|-
| 63
| 63
| 0–6–8–14
| 0–6–8–14
| 1–9/7–7/4–9/8
| 1–9/8–9/7–7/4
| Mothwellsmic
| Mothwellsmic
|
|  
|  
|-
|-
| 64
| 64
| 0–7–8–14
| 0–7–8–14
| 1–3/2–7/4–9/8
| 1–9/8–3/2–7/4
| Otonal
| Otonal
| [[4:6:7:9]]
|  
|  
|-
|-
| 65
| 65
| 0–3–11–14
| 0–3–11–14
| 1–8/5–7/5–9/8
| 1–9/8–7/5–8/5
| Marvel
| Marvel
|
|  
|  
|-
|-
| 66
| 66
| 0–6–11–14
| 0–6–11–14
| 1–9/7–7/5–9/8
| 1–9/8–9/7–7/5
| Minerva
| Minerva
|
|  
|  
|-
|-
| 67
| 67
| 0–8–11–14
| 0–8–11–14
| 1–7/4–7/5–9/8
| 1–9/8–7/5–7/4
| Marvel
| Marvel
|
|  
|  
|-
|-
| 68
| 68
| 0–2–12–14
| 0–2–12–14
| 1–11/8–18/11–9/8
| 1–9/8–11/8–18/11
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
| 69
| 69
| 0–6–12–14
| 0–6–12–14
| 1–9/7–18/11–9/8
| 1–9/8–9/7–18/11
| Utonal
| Utonal
|
|  
|  
|-
|-
| 70
| 70
| 0–7–12–14
| 0–7–12–14
| 1–3/2–18/11–9/8
| 1–9/8–3/2–18/11
| Utonal
| Utonal
|
|  
|  
|-
|-
| 71
| 71
| 0–11–12–14
| 0–11–12–14
| 1–7/5–18/11–9/8
| 1–9/8–7/5–18/11
| Unimarvel
| Marvel11
|  
|  
|  
|-
|-
| 72
| 72
| 0–3–5–17
| 0–3–5–17
| 1–8/5–11/10–9/5
| 1–11/10–8/5–9/5
| Otonal
| Otonal
|
|  
|  
|-
|-
| 73
| 73
| 0–3–6–17
| 0–3–6–17
| 1–8/5–9/7–9/5
| 1–9/7–8/5–9/5
| Marvel
| Marvel
|
|  
|  
|-
|-
Line 928: Line 851:
| 1–11/10–9/7–9/5
| 1–11/10–9/7–9/5
| Swetismic
| Swetismic
|
|  
|  
|-
|-
Line 934: Line 858:
| 1–11/10–3/2–9/5
| 1–11/10–3/2–9/5
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 940: Line 865:
| 1–9/7–3/2–9/5
| 1–9/7–3/2–9/5
| Utonal
| Utonal
| [[70:90:105:126|1/(9:7:6:5)]]
|  
|  
|-
|-
| 77
| 77
| 0–3–10–17
| 0–3–10–17
| 1–8/5–6/5–9/5
| 1–6/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:6:9]]
|  
|  
|-
|-
Line 952: Line 879:
| 1–11/10–6/5–9/5
| 1–11/10–6/5–9/5
| Otonal
| Otonal
|
|  
|  
|-
|-
| 79
| 79
| 0–7–10–17
| 0–7–10–17
| 1–3/2–6/5–9/5
| 1–6/5–3/2–9/5
| Ambitonal
| Ambitonal
| [[10:12:15:18]], [[12:15:18:20]]<br>9-odd-limit ASS
|  
|  
|-
|-
| 80
| 80
| 0–3–11–17
| 0–3–11–17
| 1–8/5–7/5–9/5
| 1–7/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:7:9]]
|  
|  
|-
|-
Line 970: Line 900:
| 1–11/10–7/5–9/5
| 1–11/10–7/5–9/5
| Otonal
| Otonal
|
|  
|  
|-
|-
Line 976: Line 907:
| 1–9/7–7/5–9/5
| 1–9/7–7/5–9/5
| Mothwellsmic
| Mothwellsmic
|
|  
|  
|-
|-
Line 982: Line 914:
| 1–6/5–7/5–9/5
| 1–6/5–7/5–9/5
| Otonal
| Otonal
| [[5:6:7:9]]
|  
|  
|-
|-
Line 988: Line 921:
| 1–11/10–18/11–9/5
| 1–11/10–18/11–9/5
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 994: Line 928:
| 1–9/7–18/11–9/5
| 1–9/7–18/11–9/5
| Utonal
| Utonal
|
|  
|  
|-
|-
Line 1,000: Line 935:
| 1–3/2–18/11–9/5
| 1–3/2–18/11–9/5
| Utonal
| Utonal
|
|  
|  
|-
|-
Line 1,006: Line 942:
| 1–6/5–18/11–9/5
| 1–6/5–18/11–9/5
| Biyatismic
| Biyatismic
|
|  
|  
|-
|-
Line 1,012: Line 949:
| 1–7/5–18/11–9/5
| 1–7/5–18/11–9/5
| Swetismic
| Swetismic
|
|  
|  
|-
|-
| 89
| 89
| 0–3–14–17
| 0–3–14–17
| 1–8/5–9/8–9/5
| 1–9/8–8/5–9/5
| Marvel
| Marvel
|
|  
|  
|-
|-
| 90
| 90
| 0–6–14–17
| 0–6–14–17
| 1–9/7–9/8–9/5
| 1–9/8–9/7–9/5
| Utonal
| Utonal
| [[140:180:252:315|1/(9:7:5:4)]]
|  
|  
|-
|-
| 91
| 91
| 0–7–14–17
| 0–7–14–17
| 1–3/2–9/8–9/5
| 1–9/8–3/2–9/5
| Utonal
| Utonal
| [[20:30:36:45|1/(9:6:5:4)]]
|  
|  
|-
|-
| 92
| 92
| 0–11–14–17
| 0–11–14–17
| 1–7/5–9/8–9/5
| 1–9/8–7/5–9/5
| Marvel
| Marvel
|
|  
|  
|-
|-
| 93
| 93
| 0–12–14–17
| 0–12–14–17
| 1–18/11–9/8–9/5
| 1–9/8–18/11–9/5
| Utonal
| Utonal
|
|  
|  
|}
|}


== Pentads ==
== Pentads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Comment
|-
|-
| 1
| 1
Line 1,057: Line 1,001:
| 1–7/6–11/8–8/5–7/4
| 1–7/6–11/8–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 2
| 2
| 0–2–3–5–8
| 0–2–3–5–8
| 1–11/8–8/5–11/10–7/4
| 1–11/10–11/8–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 3
| 3
| 0–1–3–6–8
| 0–1–3–6–8
| 1–7/6–8/5–9/7–7/4
| 1–7/6–9/7–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 4
| 4
| 0–3–5–6–8
| 0–3–5–6–8
| 1–8/5–11/10–9/7–7/4
| 1–11/10–9/7–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 5
| 5
Line 1,077: Line 1,025:
| 1–7/6–11/8–3/2–7/4
| 1–7/6–11/8–3/2–7/4
| Big brother
| Big brother
|
|-
|-
| 6
| 6
| 0–2–5–7–8
| 0–2–5–7–8
| 1–11/8–11/10–3/2–7/4
| 1–11/10–11/8–3/2–7/4
| Orwell
| Orwell
|
|-
|-
| 7
| 7
Line 1,087: Line 1,037:
| 1–7/6–9/7–3/2–7/4
| 1–7/6–9/7–3/2–7/4
| Big brother
| Big brother
|
|-
|-
| 8
| 8
Line 1,092: Line 1,043:
| 1–11/10–9/7–3/2–7/4
| 1–11/10–9/7–3/2–7/4
| Orwell
| Orwell
|
|-
|-
| 9
| 9
| 0–2–3–5–10
| 0–2–3–5–10
| 1–11/8–8/5–11/10–6/5
| 1–11/10–6/5–11/8–8/5
| Zeus
| Zeus
|
|-
|-
| 10
| 10
| 0–2–5–7–10
| 0–2–5–7–10
| 1–11/8–11/10–3/2–6/5
| 1–11/10–6/5–11/8–3/2
| Zeus
| Zeus
|
|-
|-
| 11
| 11
| 0–2–3–8–10
| 0–2–3–8–10
| 1–11/8–8/5–7/4–6/5
| 1–6/5–11/8–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 12
| 12
| 0–2–5–8–10
| 0–2–5–8–10
| 1–11/8–11/10–7/4–6/5
| 1–11/10–6/5–11/8–7/4
| Orwell
| Orwell
|
|-
|-
| 13
| 13
| 0–3–5–8–10
| 0–3–5–8–10
| 1–8/5–11/10–7/4–6/5
| 1–6/5–11/10–8/5–7/4
| Zeus
| Zeus
|
|-
|-
| 14
| 14
| 0–2–7–8–10
| 0–2–7–8–10
| 1–11/8–3/2–7/4–6/5
| 1–6/5–11/8–3/2–7/4
| Orwell
| Orwell
|
|-
|-
| 15
| 15
| 0–5–7–8–10
| 0–5–7–8–10
| 1–11/10–3/2–7/4–6/5
| 1–11/10–6/5–3/2–7/4
| Zeus
| Zeus
|
|-
|-
| 16
| 16
| 0–1–3–6–11
| 0–1–3–6–11
| 1–7/6–8/5–9/7–7/5
| 1–7/6–9/7–7/5–8/5
| Orwell
| Orwell
|
|-
|-
| 17
| 17
| 0–3–5–6–11
| 0–3–5–6–11
| 1–8/5–11/10–9/7–7/5
| 1–11/10–9/7–7/5
| Orwell
| Orwell
|
|-
|-
| 18
| 18
| 0–1–3–8–11
| 0–1–3–8–11
| 1–7/6–8/5–7/4–7/5
| 1–7/6–7/5–8/5–7/4
| Zeus
| Zeus
|
|-
|-
| 19
| 19
| 0–3–5–8–11
| 0–3–5–8–11
| 1–8/5–11/10–7/4–7/5
| 1–11/10–8/5–7/5–7/4
| Minerva
| Minerva
|
|-
|-
| 20
| 20
| 0–1–6–8–11
| 0–1–6–8–11
| 1–7/6–14/11–7/4–7/5
| 1–7/6–14/11–7/5–7/4
| Utonal
| Utonal
| [[770:924:1155:1320:1680|1/(24:20:16:14:11)]]
|-
|-
| 21
| 21
| 0–3–6–8–11
| 0–3–6–8–11
| 1–8/5–9/7–7/4–7/5
| 1–9/7–7/5–8/5–7/4
| Minerva
| Minerva
|
|-
|-
| 22
| 22
| 0–5–6–8–11
| 0–5–6–8–11
| 1–11/10–9/7–7/4–7/5
| 1–11/10–9/7–7/5–7/4
| Orwell
| Orwell
|
|-
|-
| 23
| 23
| 0–3–5–10–11
| 0–3–5–10–11
| 1–8/5–11/10–6/5–7/5
| 1–11/10–6/5–7/5–8/5
| Otonal
| Otonal
| [[4:5:6:7:11]]
|-
|-
| 24
| 24
| 0–3–8–10–11
| 0–3–8–10–11
| 1–8/5–7/4–6/5–7/5
| 1–6/5–7/5–8/5–7/4
| Zeus
| Zeus
|
|-
|-
| 25
| 25
| 0–5–8–10–11
| 0–5–8–10–11
| 1–11/10–7/4–6/5–7/5
| 1–11/10–6/5–7/5–7/4
| Orwell
| Orwell
|
|-
|-
| 26
| 26
Line 1,182: Line 1,151:
| 1–7/6–11/8–3/2–18/11
| 1–7/6–11/8–3/2–18/11
| Big brother
| Big brother
|
|-
|-
| 27
| 27
| 0–2–5–7–12
| 0–2–5–7–12
| 1–11/8–11/10–3/2–18/11
| 1–11/10–11/8–3/2–18/11
| Biyatismic
| Biyatismic
|
|-
|-
| 28
| 28
Line 1,192: Line 1,163:
| 1–7/6–9/7–3/2–18/11
| 1–7/6–9/7–3/2–18/11
| Big brother
| Big brother
|
|-
|-
| 29
| 29
Line 1,197: Line 1,169:
| 1–11/10–9/7–3/2–18/11
| 1–11/10–9/7–3/2–18/11
| Big brother
| Big brother
|
|-
|-
| 30
| 30
| 0–2–5–10–12
| 0–2–5–10–12
| 1–11/8–11/10–6/5–18/11
| 1–11/10–6/5–11/8–18/11
| Zeus
| Zeus
|
|-
|-
| 31
| 31
| 0–2–7–10–12
| 0–2–7–10–12
| 1–11/8–3/2–6/5–18/11
| 1–6/5–11/8–3/2–18/11
| Zeus
| Zeus
|
|-
|-
| 32
| 32
| 0–5–7–10–12
| 0–5–7–10–12
| 1–11/10–3/2–6/5–18/11
| 1–11/10–6/5–3/2–18/11
| Biyatismic
| Biyatismic
|
|-
|-
| 33
| 33
Line 1,217: Line 1,193:
| 1–7/6–9/7–7/5–18/11
| 1–7/6–9/7–7/5–18/11
| Big brother
| Big brother
|
|-
|-
| 34
| 34
Line 1,222: Line 1,199:
| 1–11/10–9/7–7/5–18/11
| 1–11/10–9/7–7/5–18/11
| Big brother
| Big brother
|
|-
|-
| 35
| 35
Line 1,227: Line 1,205:
| 1–11/10–6/5–7/5–18/11
| 1–11/10–6/5–7/5–18/11
| Big brother
| Big brother
|
|-
|-
| 36
| 36
| 0–2–3–8–14
| 0–2–3–8–14
| 1–11/8–8/5–7/4–9/8
| 1–9/8–11/8–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 37
| 37
| 0–3–6–8–14
| 0–3–6–8–14
| 1–8/5–9/7–7/4–9/8
| 1–9/8–9/7–8/5–7/4
| Minerva
| Minerva
|
|-
|-
| 38
| 38
Line 1,242: Line 1,223:
| 1–11/8–3/2–7/4–9/8
| 1–11/8–3/2–7/4–9/8
| Otonal
| Otonal
| [[4:6:7:9:11]]
|-
|-
| 39
| 39
| 0–6–7–8–14
| 0–6–7–8–14
| 1–9/7–3/2–7/4–9/8
| 1–9/8–9/7–3/2–7/4
| Mothwellsmic
| Mothwellsmic
|
|-
|-
| 40
| 40
| 0–3–6–11–14
| 0–3–6–11–14
| 1–8/5–9/7–7/5–9/8
| 1–9/8–9/7–7/5–8/5
| Minerva
| Minerva
|
|-
|-
| 41
| 41
| 0–3–8–11–14
| 0–3–8–11–14
| 1–8/5–7/4–7/5–9/8
| 1–9/8–7/5–8/5–7/4
| Minerva
| Minerva
|
|-
|-
| 42
| 42
| 0–6–8–11–14
| 0–6–8–11–14
| 1–9/7–7/4–7/5–9/8
| 1–9/8–9/7–7/5–7/4
| Minerva
| Minerva
|
|-
|-
| 43
| 43
| 0–2–7–12–14
| 0–2–7–12–14
| 1–11/8–3/2–18/11–9/8
| 1–9/8–11/8–3/2–18/11
| Biyatismic
| Biyatismic
|
|-
|-
| 44
| 44
| 0–6–7–12–14
| 0–6–7–12–14
| 1–9/7–3/2–18/11–9/8
| 1–9/8–9/7–3/2–18/11
| Utonal
| Utonal
| [[462:693:792:1008:1232|1/(24:16:14:11:9)]]
|-
|-
| 45
| 45
| 0–6–11–12–14
| 0–6–11–12–14
| 1–9/7–7/5–18/11–9/8
| 1–9/8–9/7–7/5–18/11
| Orwell
| Orwell
|
|-
|-
| 46
| 46
| 0–3–5–6–17
| 0–3–5–6–17
| 1–8/5–11/10–9/7–9/5
| 1–11/10–9/7–8/5–9/5
| Unimarvel
| Marvel11
|
|-
|-
| 47
| 47
Line 1,287: Line 1,277:
| 1–11/10–9/7–3/2–9/5
| 1–11/10–9/7–3/2–9/5
| Big brother
| Big brother
|
|-
|-
| 48
| 48
| 0–3–5–10–17
| 0–3–5–10–17
| 1–8/5–11/10–6/5–9/5
| 1–11/10–6/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:6:9:11]]
|-
|-
| 49
| 49
| 0–5–7–10–17
| 0–5–7–10–17
| 1–11/10–3/2–6/5–9/5
| 1–11/10–6/5–3/2–9/5
| Biyatismic
| Biyatismic
|
|-
|-
| 50
| 50
| 0–3–5–11–17
| 0–3–5–11–17
| 1–8/5–11/10–7/5–9/5
| 1–11/10–7/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:7:9:11]]
|-
|-
| 51
| 51
| 0–3–6–11–17
| 0–3–6–11–17
| 1–8/5–9/7–7/5–9/5
| 1–9/7–7/5–8/5–9/5
| Minerva
| Minerva
|
|-
|-
| 52
| 52
Line 1,312: Line 1,307:
| 1–11/10–9/7–7/5–9/5
| 1–11/10–9/7–7/5–9/5
| Big brother
| Big brother
|
|-
|-
| 53
| 53
| 0–3–10–11–17
| 0–3–10–11–17
| 1–8/5–6/5–7/5–9/5
| 1–6/5–7/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:6:7:9]]
|-
|-
| 54
| 54
Line 1,322: Line 1,319:
| 1–11/10–6/5–7/5–9/5
| 1–11/10–6/5–7/5–9/5
| Otonal
| Otonal
| [[5:6:7:9:11]]
|-
|-
| 55
| 55
Line 1,327: Line 1,325:
| 1–11/10–9/7–18/11–9/5
| 1–11/10–9/7–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 56
| 56
Line 1,332: Line 1,331:
| 1–11/10–3/2–18/11–9/5
| 1–11/10–3/2–18/11–9/5
| Biyatismic
| Biyatismic
|
|-
|-
| 57
| 57
Line 1,337: Line 1,337:
| 1–9/7–3/2–18/11–9/5
| 1–9/7–3/2–18/11–9/5
| Utonal
| Utonal
| [[1155:1386:1980:2520:3080|1/(24:20:14:11:9)]]
|-
|-
| 58
| 58
Line 1,342: Line 1,343:
| 1–11/10–6/5–18/11–9/5
| 1–11/10–6/5–18/11–9/5
| Biyatismic
| Biyatismic
|
|-
|-
| 59
| 59
| 0–7–10–12–17
| 0–7–10–12–17
| 1–3/2–6/5–18/11–9/5
| 1–6/5–3/2–18/11–9/5
| Biyatismic
| Biyatismic
|
|-
|-
| 60
| 60
Line 1,352: Line 1,355:
| 1–11/10–7/5–18/11–9/5
| 1–11/10–7/5–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 61
| 61
Line 1,357: Line 1,361:
| 1–9/7–7/5–18/11–9/5
| 1–9/7–7/5–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 62
| 62
Line 1,362: Line 1,367:
| 1–6/5–7/5–18/11–9/5
| 1–6/5–7/5–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 63
| 63
| 0–3–6–14–17
| 0–3–6–14–17
| 1–8/5–9/7–9/8–9/5
| 1–9/8–9/7–8/5–9/5
| Marvel
| Marvel
|
|-
|-
| 64
| 64
| 0–6–7–14–17
| 0–6–7–14–17
| 1–9/7–3/2–9/8–9/5
| 1–9/8–9/7–3/2–9/5
| Utonal
| Utonal
| [[210:252:315:360:560|1/(24:20:16:14:9)]]
|-
|-
| 65
| 65
| 0–3–11–14–17
| 0–3–11–14–17
| 1–8/5–7/5–9/8–9/5
| 1–9/8–7/5–8/5–9/5
| Marvel
| Marvel
|
|-
|-
| 66
| 66
| 0–6–11–14–17
| 0–6–11–14–17
| 1–9/7–7/5–9/8–9/5
| 1–9/8–9/7–7/5–9/5
| Minerva
| Minerva
|
|-
|-
| 67
| 67
| 0–6–12–14–17
| 0–6–12–14–17
| 1–9/7–18/11–9/8–9/5
| 1–9/8–9/7–18/11–9/5
| Utonal
| Utonal
| [[924:1155:1320:2016:2464|1/(20:16:14:11:9)]]
|-
|-
| 68
| 68
| 0–7–12–14–17
| 0–7–12–14–17
| 1–3/2–18/11–9/8–9/5
| 1–9/8–3/2–18/11–9/5
| Utonal
| Utonal
| [[330:396:495:720:880|1/(24:20:16:11:9)]]
|-
|-
| 69
| 69
| 0–11–12–14–17
| 0–11–12–14–17
| 1–7/5–18/11–9/8–9/5
| 1–9/8–7/5–18/11–9/5
| Unimarvel
| Marvel11
|
|}
|}


== Hexads ==
== Hexads ==
{| class="wikitable"
{| class="wikitable center-1"
|-
|-
! #
! #
! Chord
! Generators
! Transversal
! Transversal
! Type
! Type
! Comment
|-
|-
| 1
| 1
| 0–2–3–5–8–10
| 0–2–3–5–8–10
| 1–11/8–8/5–11/10–7/4–6/5
| 1–11/10–6/5–11/8–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 2
| 2
| 0–2–5–7–8–10
| 0–2–5–7–8–10
| 1–11/8–11/10–3/2–7/4–6/5
| 1–11/10–6/5–11/8–3/2–7/4
| Orwell
| Orwell
|
|-
|-
| 3
| 3
| 0–1–3–6–8–11
| 0–1–3–6–8–11
| 1–7/6–8/5–9/7–7/4–7/5
| 1–7/6–9/7–7/5–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 4
| 4
| 0–3–5–6–8–11
| 0–3–5–6–8–11
| 1–8/5–11/10–9/7–7/4–7/5
| 1–11/10–9/7–7/5–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 5
| 5
| 0–3–5–8–10–11
| 0–3–5–8–10–11
| 1–8/5–11/10–7/4–6/5–7/5
| 1–11/10–6/5–7/5–8/5–7/4
| Orwell
| Orwell
|
|-
|-
| 6
| 6
| 0–2–5–7–10–12
| 0–2–5–7–10–12
| 1–11/8–11/10–3/2–6/5–18/11
| 1–11/10–6/5–11/8–3/2–18/11
| Zeus
| Zeus
|
|-
|-
| 7
| 7
| 0–3–6–8–11–14
| 0–3–6–8–11–14
| 1–8/5–9/7–7/4–7/5–9/8
| 1–9/8–9/7–7/5–8/5–7/4
| Minerva
| Minerva
|
|-
|-
| 8
| 8
| 0–3–5–6–11–17
| 0–3–5–6–11–17
| 1–8/5–11/10–9/7–7/5–9/5
| 1–11/10–9/7–7/5–8/5–9/5
| Orwell
| Orwell
|
|-
|-
| 9
| 9
| 0–3–5–10–11–17
| 0–3–5–10–11–17
| 1–8/5–11/10–6/5–7/5–9/5
| 1–11/10–6/5–7/5–8/5–9/5
| Otonal
| Otonal
| [[4:5:6:7:9:11]]
|-
|-
| 10
| 10
Line 1,456: Line 1,479:
| 1–11/10–9/7–3/2–18/11–9/5
| 1–11/10–9/7–3/2–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 11
| 11
| 0–5–7–10–12–17
| 0–5–7–10–12–17
| 1–11/10–3/2–6/5–18/11–9/5
| 1–11/10–6/5–3/2–18/11–9/5
| Biyatismic
| Biyatismic
|
|-
|-
| 12
| 12
Line 1,466: Line 1,491:
| 1–11/10–9/7–7/5–18/11–9/5
| 1–11/10–9/7–7/5–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 13
| 13
Line 1,471: Line 1,497:
| 1–11/10–6/5–7/5–18/11–9/5
| 1–11/10–6/5–7/5–18/11–9/5
| Big brother
| Big brother
|
|-
|-
| 14
| 14
| 0–3–6–11–14–17
| 0–3–6–11–14–17
| 1–8/5–9/7–7/5–9/8–9/5
| 1–9/8–9/7–7/5–8/5–9/5
| Minerva
| Minerva
|
|-
|-
| 15
| 15
| 0–6–7–12–14–17
| 0–6–7–12–14–17
| 1–9/7–3/2–18/11–9/8–9/5
| 1–9/8–9/7–3/2–18/11–9/5
| Utonal
| Utonal
| [[2310:2772:3465:3960:5040:6160|1/(24:20:16:14:11:9)]]
|-
|-
| 16
| 16
| 0–6–11–12–14–17
| 0–6–11–12–14–17
| 1–9/7–7/5–18/11–9/8–9/5
| 1–9/8–9/7–7/5–18/11–9/5
| Orwell
| Orwell
|
|}
|}


Latest revision as of 19:09, 27 January 2026

< Orwell

Below is a complete list of all 11-odd-limit dyadic chords of 11-limit orwell temperament. Note that there are many common chords, for example 8:10:12:15, which are not listed; in this case due to 15/8 not being in the 11-odd-limit. Every chord listed has multiple inversions; only one is listed, that being the inversion where all notes are a nonnegative number of subminor third generators above the root.

Typing the chords requires consideration of the fact that orwell equates certain 11-odd-limit consonances – it conflates 14/11 with 9/7, 11/7 with 14/9, 12/11 with 11/10, and 11/6 with 20/11. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. Sometimes multiple such transversals exist, in which case the chord is a plurichord, and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 9/7 and 11/10 over the root.

Those requiring tempering only by 225/224 are labeled marvel, by 99/98 mothwellsmic, by 121/120 biyatismic, by 176/175 valinorsmic, by 385/384 keenanismic, and by 540/539 swetismic. If it requires any two of 99/98, 176/175 and 225/224, it is labeled minerva, any two of 99/98, 121/120 or 540/539, big brother, any two of 121/120, 176/175 or 385/384, zeus, any two of 225/224, 385/384 or 540/539, marvel11. If it requires both 99/98 and 385/384 it is labeled orwellian, and if it requires three independent commas among those discussed above, it is labeled orwell.

Orwell has mos of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic scale has three triads and a tetrad. The 9-note mos is of course much better supplied, and with 13 notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable major triad.

For diagrams showing how some of these chords might map to a keyboard such as the Axis-49, see Orwell on an isomorphic keyboard.

Triads

# Generators Transversal Type Comment
1 0–1–2 1–7/6–11/8 Mothwellsmic
2 0–1–3 1–7/6–8/5 Keenanismic
3 0–2–3 1–11/8–8/5 Keenanismic
4 0–2–5 1–11/10–11/8 Utonal
5 0–3–5 1–11/10–8/5 Otonal
6 0–1–6 1–7/6–14/11 Utonal
7 0–3–6 1–9/7–8/5 Marvel
8 0–5–6 1–12/11–14/11 Otonal
9 0–1–7 1–7/6–3/2 Otonal 6:7:9
10 0–2–7 1–11/8–3/2 Otonal
11 0–5–7 1–12/11–3/2 Utonal
12 0–6–7 1–9/7–3/2 Utonal 1/(9:7:6)
13 0–1–8 1–7/6–7/4 Utonal 1/(12:8:7)
14 0–2–8 1–11/8–7/4 Otonal
15 0–3–8 1–8/5–7/4 Valinorsmic
16 0–5–8 1–11/10–7/4 Valinorsmic
17 0–6–8 1–14/11–7/4 Utonal
18 0–7–8 1–3/2–7/4 Otonal 4:6:7
19 0–2–10 1–6/5–11/8 Keenanismic
20 0–3–10 1–6/5–8/5 Otonal 4:5:6
21 0–5–10 1–11/10–6/5 Otonal
22 0–7–10 1–6/5–3/2 Utonal 1/(6:5:4)
23 0–8–10 1–6/5–7/4 Keenanismic
24 0–1–11 1–7/6–7/5 Utonal 1/(7:6:5)
25 0–3–11 1–7/5–8/5 Otonal 4:5:7
26 0–5–11 1–11/10–7/5 Otonal
27 0–6–11 1–14/11–7/5 Utonal
28 0–8–11 1–7/5–7/4 Utonal 1/(10:8:7)
29 0–10–11 1–6/5–7/5 Otonal 5:6:7
30 0–1–12 1–7/6–18/11 Swetismic
31 0–2–12 1–11/8–18/11 Biyatismic
32 0–5–12 1–12/11–18/11 Otonal
33 0–6–12 1–9/7–18/11 Utonal
34 0–7–12 1–3/2–18/11 Utonal
35 0–10–12 1–6/5–18/11 Biyatismic
36 0–11–12 1–7/5–18/11 Swetismic
37 0–2–14 1–9/8–11/8 Otonal
38 0–3–14 1–9/8–8/5 Marvel
39 0–6–14 1–9/8–9/7 Utonal
40 0–7–14 1–9/8–3/2 Ambitonal 6:8:9, 8:9:12
41 0–8–14 1–9/8–7/4 Otonal
42 0–11–14 1–9/8–7/5 Marvel
43 0–12–14 1–9/8–18/11 Utonal
44 0–3–17 1–8/5–9/5 Otonal
45 0–5–17 1–11/10–9/5 Otonal
46 0–6–17 1–9/7–9/5 Utonal
47 0–7–17 1–3/2–9/5 Utonal 1/(9:6:5)
48 0–10–17 1–6/5–9/5 Otonal 6:9:10
49 0–11–17 1–7/5–9/5 Otonal
50 0–12–17 1–18/11–9/5 Utonal
51 0–14–17 1–9/8–9/5 Utonal

Tetrads

# Generators Transversal Type Comment Example in 22edo
1 0–1–2–3 1–7/6–11/8–8/5 Orwellian
2 0–2–3–5 1–11/10–11/8–8/5 Keenanismic
3 0–1–3–6 1–7/6–9/7–8/5 Marvel11
4 0–3–5–6 1–11/10–9/7–8/5 Marvel11
5 0–1–2–7 1–7/6–11/8–3/2 Big brother
6 0–2–5–7 1–11/10–11/8–3/2 Biyatismic
7 0–1–6–7 1–7/6–9/7–3/2 Swetismic
8 0–5–6–7 1–11/10–9/7–3/2 Big brother
9 0–1–2–8 1–7/6–11/8–7/4 Mothwellsmic
10 0–1–3–8 1–7/6–8/5–7/4 Zeus
11 0–2–3–8 1–11/8–8/5–7/4 Orwell
12 0–2–5–8 1–11/10–11/8–7/4 Minerva
13 0–3–5–8 1–11/10–8/5–7/4 Valinorsmic
14 0–1–6–8 1–7/6–14/11–7/4 Utonal
15 0–3–6–8 1–9/7–8/5–7/4 Minerva
16 0–5–6–8 1–11/10–9/7–7/4 Orwell
17 0–1–7–8 1–7/6–3/2–7/4 Ambitonal 12:14:18:21, 14:18:21:24
9-odd-limit ASS
18 0–2–7–8 1–11/8–3/2–7/4 Otonal
19 0–5–7–8 1–11/10–3/2–7/4 Zeus
20 0–6–7–8 1–9/7–3/2–7/4 Mothwellsmic
21 0–2–3–10 1–6/5–11/8–8/5 Keenanismic
22 0–2–5–10 1–11/10–6/5–11/8 Zeus
23 0–3–5–10 1–11/10–6/5–8/5 Otonal
24 0–2–7–10 1–6/5–11/8–3/2 Zeus
25 0–5–7–10 1–12/11–6/5–3/2 Utonal
26 0–2–8–10 1–6/5–11/8–7/4 Orwellian
27 0–3–8–10 1–6/5–8/5–7/4 Zeus
28 0–5–8–10 1–11/10–6/5–7/4 Zeus
29 0–7–8–10 1–6/5–3/2–7/4 Keenanismic
30 0–1–3–11 1–7/6–7/5–8/5 Keenanismic
31 0–3–5–11 1–11/10–7/5–8/5 Otonal
32 0–1–6–11 1–7/6–14/11–7/5 Utonal
33 0–3–6–11 1–9/7–7/5–8/5 Minerva
34 0–5–6–11 1–11/10–9/7–7/5 Big brother
35 0–1–8–11 1–7/6–7/5–7/4 Utonal 1/(12:10:8:7)
36 0–3–8–11 1–7/5–8/5–7/4 Valinorsmic
37 0–5–8–11 1–11/10–7/5–7/4 Minerva
38 0–6–8–11 1–14/11–7/5–7/4 Utonal
39 0–3–10–11 1–6/5–7/5–8/5 Otonal 4:5:6:7
40 0–5–10–11 1–11/10–6/5–7/5 Otonal
41 0–8–10–11 1–6/5–7/5–7/4 Keenanismic
42 0–1–2–12 1–7/6–11/8–18/11 Big brother
43 0–2–5–12 1–11/10–11/8–18/11 Biyatismic
44 0–1–6–12 1–7/6–9/7–18/11 Big brother
45 0–5–6–12 1–12/11–14/11–18/11 Otonal
46 0–1–7–12 1–7/6–3/2–18/11 Big brother
47 0–2–7–12 1–11/8–3/2–18/11 Biyatismic
48 0–5–7–12 1–12/11–3/2–18/11 Ambitonal 11-odd-limit ASS
49 0–6–7–12 1–9/7–3/2–18/11 Utonal
50 0–2–10–12 1–6/5–11/8–18/11 Zeus
51 0–5–10–12 1–11/10–6/5–18/11 Biyatismic
52 0–7–10–12 1–6/5–3/2–18/11 Biyatismic
53 0–1–11–12 1–7/6–7/5–18/11 Swetismic
54 0–5–11–12 1–11/10–7/5–18/11 Big brother
55 0–6–11–12 1–9/7–7/5–18/11 Big brother
56 0–10–11–12 1–6/5–7/5–18/11 Big brother
57 0–2–3–14 1–9/8–11/8–8/5 Marvel11
58 0–3–6–14 1–9/8–9/7–8/5 Marvel
59 0–2–7–14 1–9/8–11/8–3/2 Otonal
60 0–6–7–14 1–9/8–9/7–3/2 Utonal 1/(9:7:6:4)
61 0–2–8–14 1–9/8–11/8–7/4 Otonal
62 0–3–8–14 1–9/8–8/5–7/4 Minerva
63 0–6–8–14 1–9/8–9/7–7/4 Mothwellsmic
64 0–7–8–14 1–9/8–3/2–7/4 Otonal 4:6:7:9
65 0–3–11–14 1–9/8–7/5–8/5 Marvel
66 0–6–11–14 1–9/8–9/7–7/5 Minerva
67 0–8–11–14 1–9/8–7/5–7/4 Marvel
68 0–2–12–14 1–9/8–11/8–18/11 Biyatismic
69 0–6–12–14 1–9/8–9/7–18/11 Utonal
70 0–7–12–14 1–9/8–3/2–18/11 Utonal
71 0–11–12–14 1–9/8–7/5–18/11 Marvel11
72 0–3–5–17 1–11/10–8/5–9/5 Otonal
73 0–3–6–17 1–9/7–8/5–9/5 Marvel
74 0–5–6–17 1–11/10–9/7–9/5 Swetismic
75 0–5–7–17 1–11/10–3/2–9/5 Biyatismic
76 0–6–7–17 1–9/7–3/2–9/5 Utonal 1/(9:7:6:5)
77 0–3–10–17 1–6/5–8/5–9/5 Otonal 4:5:6:9
78 0–5–10–17 1–11/10–6/5–9/5 Otonal
79 0–7–10–17 1–6/5–3/2–9/5 Ambitonal 10:12:15:18, 12:15:18:20
9-odd-limit ASS
80 0–3–11–17 1–7/5–8/5–9/5 Otonal 4:5:7:9
81 0–5–11–17 1–11/10–7/5–9/5 Otonal
82 0–6–11–17 1–9/7–7/5–9/5 Mothwellsmic
83 0–10–11–17 1–6/5–7/5–9/5 Otonal 5:6:7:9
84 0–5–12–17 1–11/10–18/11–9/5 Biyatismic
85 0–6–12–17 1–9/7–18/11–9/5 Utonal
86 0–7–12–17 1–3/2–18/11–9/5 Utonal
87 0–10–12–17 1–6/5–18/11–9/5 Biyatismic
88 0–11–12–17 1–7/5–18/11–9/5 Swetismic
89 0–3–14–17 1–9/8–8/5–9/5 Marvel
90 0–6–14–17 1–9/8–9/7–9/5 Utonal 1/(9:7:5:4)
91 0–7–14–17 1–9/8–3/2–9/5 Utonal 1/(9:6:5:4)
92 0–11–14–17 1–9/8–7/5–9/5 Marvel
93 0–12–14–17 1–9/8–18/11–9/5 Utonal

Pentads

# Generators Transversal Type Comment
1 0–1–2–3–8 1–7/6–11/8–8/5–7/4 Orwell
2 0–2–3–5–8 1–11/10–11/8–8/5–7/4 Orwell
3 0–1–3–6–8 1–7/6–9/7–8/5–7/4 Orwell
4 0–3–5–6–8 1–11/10–9/7–8/5–7/4 Orwell
5 0–1–2–7–8 1–7/6–11/8–3/2–7/4 Big brother
6 0–2–5–7–8 1–11/10–11/8–3/2–7/4 Orwell
7 0–1–6–7–8 1–7/6–9/7–3/2–7/4 Big brother
8 0–5–6–7–8 1–11/10–9/7–3/2–7/4 Orwell
9 0–2–3–5–10 1–11/10–6/5–11/8–8/5 Zeus
10 0–2–5–7–10 1–11/10–6/5–11/8–3/2 Zeus
11 0–2–3–8–10 1–6/5–11/8–8/5–7/4 Orwell
12 0–2–5–8–10 1–11/10–6/5–11/8–7/4 Orwell
13 0–3–5–8–10 1–6/5–11/10–8/5–7/4 Zeus
14 0–2–7–8–10 1–6/5–11/8–3/2–7/4 Orwell
15 0–5–7–8–10 1–11/10–6/5–3/2–7/4 Zeus
16 0–1–3–6–11 1–7/6–9/7–7/5–8/5 Orwell
17 0–3–5–6–11 1–11/10–9/7–7/5 Orwell
18 0–1–3–8–11 1–7/6–7/5–8/5–7/4 Zeus
19 0–3–5–8–11 1–11/10–8/5–7/5–7/4 Minerva
20 0–1–6–8–11 1–7/6–14/11–7/5–7/4 Utonal 1/(24:20:16:14:11)
21 0–3–6–8–11 1–9/7–7/5–8/5–7/4 Minerva
22 0–5–6–8–11 1–11/10–9/7–7/5–7/4 Orwell
23 0–3–5–10–11 1–11/10–6/5–7/5–8/5 Otonal 4:5:6:7:11
24 0–3–8–10–11 1–6/5–7/5–8/5–7/4 Zeus
25 0–5–8–10–11 1–11/10–6/5–7/5–7/4 Orwell
26 0–1–2–7–12 1–7/6–11/8–3/2–18/11 Big brother
27 0–2–5–7–12 1–11/10–11/8–3/2–18/11 Biyatismic
28 0–1–6–7–12 1–7/6–9/7–3/2–18/11 Big brother
29 0–5–6–7–12 1–11/10–9/7–3/2–18/11 Big brother
30 0–2–5–10–12 1–11/10–6/5–11/8–18/11 Zeus
31 0–2–7–10–12 1–6/5–11/8–3/2–18/11 Zeus
32 0–5–7–10–12 1–11/10–6/5–3/2–18/11 Biyatismic
33 0–1–6–11–12 1–7/6–9/7–7/5–18/11 Big brother
34 0–5–6–11–12 1–11/10–9/7–7/5–18/11 Big brother
35 0–5–10–11–12 1–11/10–6/5–7/5–18/11 Big brother
36 0–2–3–8–14 1–9/8–11/8–8/5–7/4 Orwell
37 0–3–6–8–14 1–9/8–9/7–8/5–7/4 Minerva
38 0–2–7–8–14 1–11/8–3/2–7/4–9/8 Otonal 4:6:7:9:11
39 0–6–7–8–14 1–9/8–9/7–3/2–7/4 Mothwellsmic
40 0–3–6–11–14 1–9/8–9/7–7/5–8/5 Minerva
41 0–3–8–11–14 1–9/8–7/5–8/5–7/4 Minerva
42 0–6–8–11–14 1–9/8–9/7–7/5–7/4 Minerva
43 0–2–7–12–14 1–9/8–11/8–3/2–18/11 Biyatismic
44 0–6–7–12–14 1–9/8–9/7–3/2–18/11 Utonal 1/(24:16:14:11:9)
45 0–6–11–12–14 1–9/8–9/7–7/5–18/11 Orwell
46 0–3–5–6–17 1–11/10–9/7–8/5–9/5 Marvel11
47 0–5–6–7–17 1–11/10–9/7–3/2–9/5 Big brother
48 0–3–5–10–17 1–11/10–6/5–8/5–9/5 Otonal 4:5:6:9:11
49 0–5–7–10–17 1–11/10–6/5–3/2–9/5 Biyatismic
50 0–3–5–11–17 1–11/10–7/5–8/5–9/5 Otonal 4:5:7:9:11
51 0–3–6–11–17 1–9/7–7/5–8/5–9/5 Minerva
52 0–5–6–11–17 1–11/10–9/7–7/5–9/5 Big brother
53 0–3–10–11–17 1–6/5–7/5–8/5–9/5 Otonal 4:5:6:7:9
54 0–5–10–11–17 1–11/10–6/5–7/5–9/5 Otonal 5:6:7:9:11
55 0–5–6–12–17 1–11/10–9/7–18/11–9/5 Big brother
56 0–5–7–12–17 1–11/10–3/2–18/11–9/5 Biyatismic
57 0–6–7–12–17 1–9/7–3/2–18/11–9/5 Utonal 1/(24:20:14:11:9)
58 0–5–10–12–17 1–11/10–6/5–18/11–9/5 Biyatismic
59 0–7–10–12–17 1–6/5–3/2–18/11–9/5 Biyatismic
60 0–5–11–12–17 1–11/10–7/5–18/11–9/5 Big brother
61 0–6–11–12–17 1–9/7–7/5–18/11–9/5 Big brother
62 0–10–11–12–17 1–6/5–7/5–18/11–9/5 Big brother
63 0–3–6–14–17 1–9/8–9/7–8/5–9/5 Marvel
64 0–6–7–14–17 1–9/8–9/7–3/2–9/5 Utonal 1/(24:20:16:14:9)
65 0–3–11–14–17 1–9/8–7/5–8/5–9/5 Marvel
66 0–6–11–14–17 1–9/8–9/7–7/5–9/5 Minerva
67 0–6–12–14–17 1–9/8–9/7–18/11–9/5 Utonal 1/(20:16:14:11:9)
68 0–7–12–14–17 1–9/8–3/2–18/11–9/5 Utonal 1/(24:20:16:11:9)
69 0–11–12–14–17 1–9/8–7/5–18/11–9/5 Marvel11

Hexads

# Generators Transversal Type Comment
1 0–2–3–5–8–10 1–11/10–6/5–11/8–8/5–7/4 Orwell
2 0–2–5–7–8–10 1–11/10–6/5–11/8–3/2–7/4 Orwell
3 0–1–3–6–8–11 1–7/6–9/7–7/5–8/5–7/4 Orwell
4 0–3–5–6–8–11 1–11/10–9/7–7/5–8/5–7/4 Orwell
5 0–3–5–8–10–11 1–11/10–6/5–7/5–8/5–7/4 Orwell
6 0–2–5–7–10–12 1–11/10–6/5–11/8–3/2–18/11 Zeus
7 0–3–6–8–11–14 1–9/8–9/7–7/5–8/5–7/4 Minerva
8 0–3–5–6–11–17 1–11/10–9/7–7/5–8/5–9/5 Orwell
9 0–3–5–10–11–17 1–11/10–6/5–7/5–8/5–9/5 Otonal 4:5:6:7:9:11
10 0–5–6–7–12–17 1–11/10–9/7–3/2–18/11–9/5 Big brother
11 0–5–7–10–12–17 1–11/10–6/5–3/2–18/11–9/5 Biyatismic
12 0–5–6–11–12–17 1–11/10–9/7–7/5–18/11–9/5 Big brother
13 0–5–10–11–12–17 1–11/10–6/5–7/5–18/11–9/5 Big brother
14 0–3–6–11–14–17 1–9/8–9/7–7/5–8/5–9/5 Minerva
15 0–6–7–12–14–17 1–9/8–9/7–3/2–18/11–9/5 Utonal 1/(24:20:16:14:11:9)
16 0–6–11–12–14–17 1–9/8–9/7–7/5–18/11–9/5 Orwell
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