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5L 3s

Revision as of 04:06, 27 March 2021 by Inthar (talk | contribs) (→Intervals: belongs in main petrtri page)
For the tritave-equivalent MOS structure with the same step pattern, see 5L 3s (tritave-equivalent).
↖ 4L 2s ↑ 5L 2s 6L 2s ↗
← 4L 3s 5L 3s 6L 3s →
↙ 4L 4s ↓ 5L 4s 6L 4s ↘ 
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└┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLs
sLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\8 to 2\5 (450.0 ¢ to 480.0 ¢)
Dark 3\5 to 5\8 (720.0 ¢ to 750.0 ¢)
TAMNAMS information
Name oneirotonic
Prefix oneiro-
Abbrev. onei
Related MOS scales
Parent 3L 2s
Sister 3L 5s
Daughters 8L 5s, 5L 8s
Neutralized 2L 6s
2-Flought 13L 3s, 5L 11s
Equal tunings
Equalized (L:s = 1:1) 3\8 (450.0 ¢)
Supersoft (L:s = 4:3) 11\29 (455.2 ¢)
Soft (L:s = 3:2) 8\21 (457.1 ¢)
Semisoft (L:s = 5:3) 13\34 (458.8 ¢)
Basic (L:s = 2:1) 5\13 (461.5 ¢)
Semihard (L:s = 5:2) 12\31 (464.5 ¢)
Hard (L:s = 3:1) 7\18 (466.7 ¢)
Superhard (L:s = 4:1) 9\23 (469.6 ¢)
Collapsed (L:s = 1:0) 2\5 (480.0 ¢)

5L 3s or oneirotonic (/oʊnaɪrəˈtɒnɪk/ oh-ny-rə-TON-ik or /ənaɪrə-/ ə-ny-rə-) refers to the structure of octave-equivalent MOS scales with generators ranging from 2\5 (two degrees of 5edo = 480¢) to 3\8 (three degrees of 8edo = 450¢). In the case of 8edo, L and s are the same size; in the case of 5edo, s becomes so small it disappears (and all that remains are the five equal L's). The name oneirotonic (from Greek oneiros 'dream') was coined by Cryptic Ruse after the Dreamlands in H.P. Lovecraft's Dream Cycle mythos.

Oneirotonic is a distorted diatonic, because it has one extra small step compared to diatonic (5L 2s): for example, the Ionian diatonic mode LLsLLLs can be distorted to the Dylathian oneirotonic mode LLsLLsLs.

Any edo with an interval between 450¢ and 480¢ has an oneirotonic scale. 13edo is the smallest edo with a (non-degenerate) 5L3s oneirotonic scale and thus is the most commonly used oneirotonic tuning.

5L 3s has a pentatonic MOS subset 3L 2s (SLSLL), and in this context we call this the oneiro-pentatonic. When viewed as a chord (with undetermined voicing) we call it the Oneiro Core Pentad. (Note: 3L 5s scales also have 3L 2s subsets.)

In terms of regular temperaments, there are at least two melodically viable ways to interpret oneirotonic (see also Tuning ranges):

  1. When the generator is between 457.14¢ (8\21) and 461.54¢ (5\13): Petrtri (13&21, a 2.5.9.11.13.17 temperament that mainly approximates the harmonic series chord 5:9:11:13)
  2. When the generator is between 461.54¢ (5\13) and 466.67¢ (7\18): A-Team (13&18, a 2.9.5.21 temperament where two major mosseconds or "whole tones" approximate a 5/4 classical major third)

In a sense, these two temperaments represent the middle of the oneirotonic spectrum (with the step ratio (L/s) ranging from 3/2 to 3/1); 13edo represents both temperaments, with a step ratio of 2/1. This is analogous to how in the diatonic spectrum, the 19edo-to-17edo-range has the least extreme ratio of large to small step sizes, with 12edo representing both meantone (19edo to 12edo) and pythagorean/neogothic (12edo to 17edo).

More extreme oneirotonic temperaments include:

  • Tridec (a 2.3.7/5.11/5.13/5 subgroup temperament that approximates 5:7:11:13:15), when the generator is between 453.33¢ (17\45) and 457.14¢ (8\21). These have near-equal step ratios of 6/5 to 3/2.
  • Buzzard, when the generator is between 471.42¢ (11\28) and 480¢ (2\5). While this is a harmonically accurate temperament, with 4 generators reaching 3/2 and -3 generators 7/4, it is relatively weak melodically, as the optimum size of the small steps is around 20-25 cents, making it difficult to distinguish from equal pentatonic.

In the past, 5L 3s has been viewed as a MOS of the low-accuracy 5-limit temperament father. This viewpoint is increasingly considered obsolete, but "father" is still sometimes used for both the 5L 3s oneirotonic and the 3L 2s oneiro-pentatonic.

Notation

The notation used in this article is J Ultharian (LsLLsLsL) = JKLMNOPQJ, with reference pitch N = 261.6255653 Hz, unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".) Ultharian has been chosen as the default mode because we want to carry over the diatonic idea of sharpening the second-to-last degree to get the leading tone for minor keys and the sharpened "Vmaj", and we also have the "sharp V" for the oneiromajor tonality by default.

The chain of oneirofourths becomes: ... P@ K@ N@ Q L O J M P K N Q& L& O& ...

Thus the 13edo gamut is as follows:

J/Q& J&/K@ K/L@ L/K& L&/M@ M M&/N@ N/O@ O/N& O&/P@ P Q Q&/J@ J

The 18edo gamut is notated as follows:

J Q&/K@ J&/L@ K L K&/M@ L& M N@ M&/O@ N O P@ O& P Q P&/J@ Q@ J

The 21edo gamut:

J J& K@ K K&/L@ L L& M@ M M& N@ N N&/O@ O O& P@ P P&/Q@ Q Q& J@ J

Scale tree

generator tetrachord g in cents 2g 3g 4g Comments
2\5 1 0 1 480.000 960.000 240.00 720.000
21\53 10 1 10 475.472 950.943 226.415 701.887 Vulture/Buzzard is around here
19\48 9 1 9 475 950 225 700
17\43 8 1 8 474.419 948.837 223.256 697.674
15\38 7 1 7 473.684 947.368 221.053 694.737
13\33 6 1 6 472.727 945.455 218.181 690.909
11\28 5 1 5 471.429 942.857 214.286 685.714
9\23 4 1 4 469.565 939.130 208.696 678.261 L/s = 4
16\41 7 2 7 468.293 936.585 204.878 673.171 Barbad is around here
7\18 3 1 3 466.667 933.333 200.000 666.667 L/s = 3
A-Team starts around here...
19\49 8 3 8 465.306 930.612 195.918 661.2245
50\129 21 8 21 465.116 930.233 195.349 660.465
131\338 55 21 55 465.089 930.1775 195.266 660.335
212\547 89 34 89 465.082 930.1645 195.247 660.329
81\209 34 13 34 465.072 930.1435 195.215 660.287
31\80 13 5 13 465 930 195 660
12\31 5 2 5 464.516 929.032 193.549 658.065
5\13 2 1 2 461.538 923.077 184.615 646.154 ...and ends here
Boundary of propriety (generators smaller than this are proper)
Petrtri starts here...
13\34 5 3 5 458.824 917.647 176.471 635.294
34\89 13 8 13 458.427 916.854 175.281 633.708
89\233 34 21 34 458.369 916.738 175.107 633.473
233\610 89 55 89 458.361 916.721 175.082 633.443 Golden oneirotonic; generator is 2 octaves minus logarithmic phi
144\377 55 34 55 458.355 916.711 175.066 633.422
55\144 21 13 21 458.333 916.666 175 633.333
21\55 8 5 8 458.182 916.364 174.545 632.727
8\21 3 2 3 457.143 914.286 171.429 628.571 ...and ends here
Optimum rank range (L/s=3/2) oneirotonic
11\29 4 3 4 455.172 910.345 165.517 620.690 Tridec is around here
14\37 5 4 5 454.054 908.108 162.162 616.216
17\45 6 5 6 453.333 906.667 160 613.333
20\53 7 6 7 452.83 905.66 158.491 611.321
23\61 8 7 8 452.459 904.918 157.377 609.836
26\69 9 8 9 452.174 904.348 156.522 608.696
29\77 10 9 10 451.948 903.896 155.844 607.792
3\8 1 1 1 450.000 900.000 150.000 600.000

Tuning ranges

A-Team (13&18)

Main article: A-Team

Petrtri (13&21)

Main article: Petrtri

Tridec (29&37)

In the broad sense, Tridec can be viewed as any oneirotonic tuning that equates three oneirotonic large steps to a 4/3 perfect fourth, i.e. equates the oneirotonic large step to a porcupine generator. [This identification may come in handy since many altered oneirotonic modes have three consecutive large steps.] Based on the JI interpretations of the 29edo and 37edo tunings, it can in fact be viewed as a 2.3.7/5.11/5.13/5 temperament, i.e. a non-over-1 temperament that approximates the chord 5:7:11:13:15. Since it is the same as Petrtri when you only care about the 9:10:11:13 (R-M2-M3-M5), it can be regarded as a flatter variant of Petrtri (analogous to how septimal meantone and flattone are the same when you only consider how it maps 8:9:10:12).

The optimal generator is 455.2178¢, which is very close to 29edo's 11\29 (455.17¢), but we could accept any generator between 17\45 (453.33¢) and 8\21 (457.14¢), if we stipulate that the 3/2 has to be between 7edo's fifth and 5edo's fifth.

Based on the EDOs that support it, Tridec is essentially the same as 13-limit Ammonite.

The sizes of the generator, large step and small step of oneirotonic are as follows in various tridec tunings.

21edo 29edo 37edo Optimal (POTE) tuning JI intervals represented (2.3.7/5.11/5.13/5 subgroup)
generator (g) 8\21, 457.14 11\29, 455.17 14\37, 454.05 455.22 13/10
L (3g - octave) 3\21, 171.43 4\29, 165.52 5\37, 162.16 165.65 11/10
s (-5g + 2 octaves) 2\21, 114.29 3\29, 124.14 4\37, 129.73 123.91 14/13, 15/14

Buzzard (48&53)

In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. 23edo, 28edo and 33edo can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between A-Team and true Buzzard in terms of harmonies. 38edo & 43edo are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but 48edo is where it really comes into it's own in terms of harmonies, providing not only an excellent 3/2, but also 7/4 and archipelago harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.

Beyond that, it's a question of which intervals you want to favor. 53edo has an essentially perfect 3/2, 58edo gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while 63edo does the same for the basic 4:6:7 triad. You could in theory go up to 83edo if you want to favor the 7/4 above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.

The sizes of the generator, large step and small step of oneirotonic are as follows in various buzzard tunings.

38edo 53edo 63edo Optimal (POTE) tuning JI intervals represented (2.3.5.7.13 subgroup)
generator (g) 15\38, 473.68 21\53, 475.47 25\63, 476.19 475.69 3/2 21/16
L (3g - octave) 7/38, 221.04 10/53, 226.41 12/63, 228.57 227.07 8/7
s (-5g + 2 octaves) 1/38 31.57 1/53 22.64 1/63 19.05 21.55 55/54 81/80 91/90

Intervals

Generators Notation (1/1 = J) Octatonic interval category name Generators Notation of 2/1 inverse Octatonic interval category name
The 8-note MOS has the following intervals (from some root):
0 J perfect unison 0 J octave
1 M perfect oneirofourth (aka minor fourth, falling fourth) -1 O perfect oneirosixth (aka major fifth, rising fifth)
2 P major oneiroseventh -2 L minor oneirothird
3 K major oneirosecond -3 Q minor oneiroeighth
4 N major oneirofifth (aka minor fifth, falling fifth) -4 N@ minor oneirofifth (aka major fourth, rising fourth)
5 Q& major oneiroeighth -5 K@ minor oneirosecond
6 L& major oneirothird -6 P@ minor oneiroseventh
7 O& augmented oneirosixth -7 M@ diminished oneirofourth
The chromatic 13-note MOS (either 5L 8s or 8L 5s) also has the following intervals (from some root):
8 J& augmented unison -8 J@ diminished octave
9 M& augmented oneirofourth -9 O@ diminished oneirosixth
10 P& augmented oneiroseventh -10 L@ diminished oneirothird
11 K& augmented oneirosecond -11 Q@ diminished oneiroeighth
12 N& augmented oneirofifth -12 N@@ diminished oneirofifth

Key signatures

Flat keys:

  • J@ Oneirominor, L@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@, Q@
  • M@ Oneirominor, O@ Oneiromajor = N@, K@, P@, M@, J@, O@, L@
  • P@ Oneirominor, J@ Oneiromajor = N@, K@, P@, M@, J@, O@
  • K@ Oneirominor, M@ Oneiromajor = N@, K@, P@, M@, J@
  • N@ Oneirominor, P@ Oneiromajor = N@, K@, P@, M@
  • Q Oneirominor, K@ Oneiromajor = N@, K@, P@
  • L Oneirominor, N@ Oneiromajor = N@, K@
  • O Oneirominor, Q Oneiromajor = N@

All-natural key signature:

  • J Oneirominor, L Oneiromajor = no sharps or flats

Sharp keys:

  • M Oneirominor, O Oneiromajor = Q&
  • P Oneirominor, J Oneiromajor = Q&, L&
  • K Oneirominor, M Oneiromajor = Q&, L&, O&
  • N Oneirominor, P Oneiromajor = Q&, L&, O&, J&
  • Q& Oneirominor, K Oneiromajor = Q&, L&, O&, J&, M&
    • Enharmonic with J@ Oneirominor, L@ Oneiromajor in 13edo
  • L& Oneirominor, N Oneiromajor = Q&, L&, O&, J&, M&, P&
    • Enharmonic with M@ Oneirominor, O@ Oneiromajor in 13edo
  • O& Oneirominor, Q& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&
    • Enharmonic with P@ Oneirominor, J@ Oneiromajor in 13edo
  • J& Oneirominor, L& Oneiromajor = Q&, L&, O&, J&, M&, P&, K&, N&
    • Enharmonic with K@ Oneirominor, M@ Oneiromajor in 13edo

Modes

Oneirotonic modes are named after cities in the Dreamlands. (The names are by Cryptic Ruse.)

  1. Dylathian (də-LA(H)TH-iən): LLSLLSLS
  2. Illarnekian (ill-ar-NEK-iən): LLSLSLLS
  3. Celephaïsian (kel-ə-FAY-zhən): LSLLSLLS
  4. Ultharian (ul-THA(I)R-iən): LSLLSLSL
  5. Mnarian (mə-NA(I)R-iən): LSLSLLSL
  6. Kadathian (kə-DA(H)TH-iən): SLLSLLSL
  7. Hlanithian (lə-NITH-iən): SLLSLSLL
  8. Sarnathian (sar-NA(H)TH-iən): SLSLLSLL

The modes on the white keys JKLMNOPQJ are:

  • J Ultharian
  • K Hlanithian
  • L Illarnekian
  • M Mnarian
  • N Sarnathian
  • O Celephaïsian
  • P Kadathian
  • Q Dylathian
Table of modes (based on J, from brightest to darkest)
Mode 1 2 3 4 5 6 7 8 (9)
Dylathian J K L& M N O& P Q& (J)
Illarnekian J K L& M N O P Q& (J)
Celephaïsian J K L M N O P Q& (J)
Ultharian J K L M N O P Q (J)
Mnarian J K L M N@ O P Q (J)
Kadathian J K@ L M N@ O P Q (J)
Hlanithian J K@ L M N@ O P@ Q (J)
Sarnathian J K@ L M@ N@ O P@ Q (J)


Ana modes

We call modes (see oneirotonic modes) with a major mos5th ana modes (from Greek for 'up'), because the sharper 5th degree functions as a flattened melodic fifth when moving from the tonic up. The ana modes of the MOS are the 4 brightest modes, namely Dylathian, Illarnekian, Celephaïsian and Ultharian.

Kata modes

We call modes with a minor mos5th kata modes (from Greek for 'down'). The kata modes of the MOS are the 4 darkest modes, namely Mnarian, Kadathian, Hlanithian and Sarnathian. In kata modes, the melodically squashed fifth from the tonic downwards is the flatter 5th degree. Kata modes could be used to distort diatonic tropes that start from the tonic and work downwards or work upwards towards the tonic from below it.

Alterations

Archeodim

We call the LSLLLSLS pattern (independently of modal rotation) archeodim, because the "LLL" resembles the archeotonic scale in 13edo and the "LSLSLS" resembles the diminished scale. Archeodim is the most important oneirotonic MODMOS pattern (a MODMOS is a MOS with one or more alterations), because it allows one to evoke certain ana or kata diatonic modes where three whole steps in a row are important (Dorian, Phrygian, Lydian or Mixo) in an octatonic context. The MOS would not always be able to do this because it has at most two consecutive large steps. Archeodim modes exist in all oneirotonic tunings, since they use the same large and small steps as the oneirotonic scale itself.

As with the MOS, archeodim has four ana and four kata rotations:

  • Ana:
    • LLLSLSLS: Dylathian &4, Dylydian
    • LLSLSLSL: Illarnekian @8, Illarmixian
    • LSLLLSLS: Celephaïsian &6, Celdorian
    • SLLLSLSL: Ultharian @2, Ulphrygian
  • Kata:
    • LSLSLLLS: Mnarian &8, Mnionian
    • SLSLLLSL: Sarnathian &7, Sardorian
    • LSLSLSLL: Mnarian @7, Mnaeolian
    • SLSLSLLL: Sarnathian @6, Sarlocrian
Table of archeodim modes (based on J)
Mode 1 2 3 4 5 6 7 8 (9)
Dylydian J K L& M& N O& P Q& (J)
Illarmixian J K L& M N O P Q (J)
Celdorian J K L M N O& P Q& (J)
Ulphrygian J K@ L M N O P Q (J)
Mnionian J K L M N@ O P Q& (J)
Sardorian J K@ L M@ N@ O P Q (J)
Mnaeolian J K L M N@ O P@ Q (J)
Sarlocrian J K@ L M@ N@ O@ P@ Q (J)

Other MODMOSes

Other potentially interesting oneirotonic MODMOSes (that do not use half-sharps or half-flats) are:

  • the distorted harmonic minor LSLLSALS (A = aug 2nd = L + chroma)
  • the distorted Freygish SASLSLLS
  • Celephaïsian &4 &6 LsAsLsLs

Pentatonic subsets

Modes of the oneiro-pentatonic 3L 2s MOS:

  1. P1-M2-P4-M5-M7 Oneiro Falling Suspended Pentatonic
  2. P1-M2-P4-P6-M7 Oneiro Rising Suspended Pentatonic
  3. P1-m3-P4-P6-M7 Oneiro Symmetrical Pentatonic
  4. P1-m3-P4-P6-m8 Oneiro Expanding Quartal Pentatonic
  5. P1-m3-m5-P6-m8 Oneiro Diminished Pentatonic

Rank-2 temperaments

Oneirotonic temperaments have a sort of analogy to diatonic temperaments superpyth and meantone in how they treat the large step. In diatonic the large step approximates 9/8 (a very good 9/8 in 12edo), but superpyth has 9/8 ~ 8/7, and meantone has 9/8 ~ 10/9. In oneirotonic the large step tends to approximate 10/9 (and is a very good 10/9 in 13edo which is the oneirotonic analogue to 12edo), but different oneiro temperaments do different things with it. In A-Team (13&18), 10/9 is equated with 9/8, making the major oneirothird a 5/4 (thus is "meantone" in that sense). In both Petrtri (13&21) and Tridec (21&29), 10/9 is equated with 11/10, making the major oneirothird a 11/9; and the perfect oneirofourth is equated to 13/10. So the compressed major triad add2 (R-M2-M3-M5, M5 = major oneirofifth = minor fifth in 13edo) is interpreted as 9:10:11:13 in petrtri, analogous to meantone's 8:9:10:12. Thus Petrtri and Tridec are the same temperament when you only care about the 9:10:11:13, or equivalently the 2.9/5.11/5.13/5 subgroup. This is one reason why Tridec can be viewed as the oneirotonic analogue of flattone: it's a flatter variant of the flat-of-13edo oneiro temperament on the 2.9/5.11/5.13/5 subgroup.

Vulture/Buzzard, in which four generators make a 3/1 (and three generators approximate an octave plus 8/7), is the only harmonic entropy minimum in the oneirotonic range. However, the rest of this region is still rich in notable subgroup temperaments.

Tridec

Subgroup: 2.3.7/5.11/5.13/5

Period: 1\1

Optimal (POTE) generator: 455.2178

EDO generators: 8\21, 11\29, 14\37

Technical data

Comma list: 196/195, 847/845, 1001/1000

Mapping (for 2, 3, 7/5, 11/5, 13/5): [⟨1 5 2 0 1], ⟨0 -9 -4 3 1]]

Mapping generators: ~2, ~13/10

Optimal ET sequence: 21, 29, 37

Intervals

Sortable table of intervals in the Dylathian mode and their Tridec interpretations:

Degree Size in 21edo Size in 29edo Size in 37edo Size in POTE tuning Note name on Q Approximate ratios #Gens up
1 0\21, 0.00 0\29, 0.00 0\37, 0.00 0.00 Q 1/1 0
2 3\21, 171.43 4\29, 165.52 5\37, 163.16 165.65 J 11/10, 10/9 +3
3 6\21, 342.86 8\29, 331.03 10\37, 324.32 331.31 K 11/9, 6/5 +6
4 8\21, 457.14 11\29, 455.17 14\37, 454.05 455.17 L 13/10, 9/7 +1
5 11\21, 628.57 15\29, 620.69 19\37, 616.22 620.87 M 13/9, 10/7 +4
6 14\21, 800.00 19\29, 786.21 23\37, 778.38 786.52 N 11/7 +7
7 16\21, 914.29 22\29, 910.34 28\37, 908.11 910.44 O 22/13 +2
8 19\21, 1085.71 26\29, 1075.86 33\37, 1070.27 1076.09 P 13/7, 28/15 +5

Petrtri

Subgroup: 2.5.9.11.13.17

Period: 1\1

Optimal (POTE) generator: 459.1502

EDO generators: 5\13, 8\21, 13\34

Technical data

Comma list: 100/99, 144/143, 170/169, 221/220

Mapping (for 2, 5, 9, 11, 13, 17): [⟨1 5 7 5 6 6], ⟨0 -7 -10 -4 -6 -5]]

Mapping generators: ~2, ~13/10

Optimal ET sequence: 13, 21, 34

A-Team

Subgroup: 2.5.9.21

Period: 1\1

Optimal (POTE) generator: 464.3865

EDO generators: 5\13, 7\18, 12\31, 17\44

Technical data

Comma list: 81/80, 1029/1024

Mapping (for 2, 5, 9, 21): [⟨1 0 2 4], ⟨0 6 3 1]]

Mapping generators: ~2, ~21/16

Optimal ET sequence: 13, 18, 31, 44

Buzzard

Subgroup: 2.3.5.7

Period: 1\1

Optimal (POTE) generator: ~21/16 = 475.636

EDO generators: 15\38, 17\43, 19\48, 21\53, 23\58, 25\63

Technical data

Commas: 1728/1715, 5120/5103

Map: [<1 0 -6 4|, <0 4 21 -3|]

Mapping generators: ~2, ~21/16

Wedgie: <<4 21 -3 24 -16 -66||

48, 53, 111, 164d, 275d

Badness: 0.0480

Intervals

Sortable table of intervals in the Dylathian mode and their Buzzard interpretations:

Degree Size in 38edo Size in 53edo Size in 63edo Size in POTE tuning Note name on Q Approximate ratios #Gens up
1 0\38, 0.00 0\53, 0.00 0\63, 0.00 0.00 Q 1/1 0
2 7\38, 221.05 10\53, 226.42 12\63, 228.57 227.07 J 8/7 +3
3 14\38, 442.10 20\53, 452.83 24\63, 457.14 453.81 K 13/10, 9/7 +6
4 15\38, 473.68 21\53, 475.47 25\63, 476.19 475.63 L 21/16 +1
5 22\38, 694.73 31\53, 701.89 37\63, 704.76 702.54 M 3/2 +4
6 29\38, 915.78 41\53, 928.30 49\63, 933.33 929.45 N 12/7, 22/13 +7
7 30\38, 947.36 42\53, 950.94 50\63, 952.38 951.27 O 26/15 +2
8 37\38, 1168.42 52\53, 1177.36 62\63, 1180.95 1178.18 P 108/55, 160/81 +5

See also

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