Heartland: Difference between revisions

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[[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}}
[[Optimal ET sequence]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}}
[[Badness]] (Sintel): 0.615


==== Heartsphere ====
==== Heartsphere ====
Line 24: Line 26:


[[Optimal tuning]] (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~5/4 = 386.0840, ~7/4 = 969.3784, ~13/8 = 840.1616, ~17/16 = 104.5510
[[Optimal tuning]] (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~5/4 = 386.0840, ~7/4 = 969.3784, ~13/8 = 840.1616, ~17/16 = 104.5510
[[Badness]] (Sintel): 15.766


=== 2.3.7.11.19 subgroup temperaments ===
=== 2.3.7.11.19 subgroup temperaments ===
Line 39: Line 43:
[[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}}
[[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}}


[[Badness]]: 0.010707
[[Badness]] (Sintel): 0.529


==== Heartful ====
==== Heartful ====
Line 52: Line 56:
[[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}}
[[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}}


[[Badness]]: 0.019908
[[Badness]] (Sintel): 0.984


==== Doublehearted ====
==== Doublehearted ====
Line 65: Line 69:
[[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}}
[[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}}


[[Badness]]: 0.011318
[[Badness]] (Sintel): 0.560


==== Byhearted ====
==== Byhearted ====
Line 78: Line 82:
[[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}}
[[Optimal ET sequence]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}}


[[Badness]]: 0.018062
[[Badness]] (Sintel): 0.893


=== Full 19-limit temperaments ===
=== Full 19-limit temperaments ===
Line 93: Line 97:


[[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}}
[[Optimal ET sequence]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}}
[[Badness]] (Sintel): 2.294


==== Monkey ====
==== Monkey ====
Line 184: Line 190:
[[Badness]]: 0.016652
[[Badness]]: 0.016652


==== Byhearted ====
==== Weasel ====
{{see also|Tetracot family #Byhearted}}
{{see also|Tetracot family #Weasel}}


[[Subgroup]]: Full 19-limit
[[Subgroup]]: Full 19-limit

Latest revision as of 10:26, 18 January 2026

The heartland is the name given to the collection of temperaments that are children of or related to the heartland temperament, the 2.3.7.11.19 subgroup temperament tempering out both 243/242 and 1083/1078, and its full 19-limit extension, heartsphere. The term "heartland" loosely means "interior part."

For extending the heartland temperament to the 2.3.5.7.11.19 subgroup, it is natural to temper out 361/360, 441/440 or 540/539, which makes a weak extension of the jove temperament. For extending to the 2.3.5.7.11.13.19 subgroup, tempering out 364/363 gives an excellent tuning.

Temperament data

Parent temperaments

Heartland

Subgroup: 2.3.7.11.19

Comma list: 243/242, 1083/1078

Mapping: [⟨1 1 0 2 1], ⟨0 4 0 10 3], ⟨0 0 1 0 1]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~7/4 = 969.3784

Optimal ET sequence: 7, 14, 27e, 34dh, 41, 89, 130

Badness (Sintel): 0.615

Heartsphere

Subgroup: Full 19-limit

Comma list: 243/242, 1083/1078

Mapping: [⟨1 1 0 0 2 0 0 1], ⟨0 4 0 0 10 0 0 3], ⟨0 0 1 0 0 0 0 0], ⟨0 0 0 1 0 0 0 1], ⟨0 0 0 0 0 1 0 0], ⟨0 0 0 0 0 0 1 0]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.2713, ~5/4 = 386.0840, ~7/4 = 969.3784, ~13/8 = 840.1616, ~17/16 = 104.5510

Badness (Sintel): 15.766

2.3.7.11.19 subgroup temperaments

See also: No-fives subgroup temperaments

Hearts

Subgroup: 2.3.7.11.19

Comma list: 243/242, 513/512, 1083/1078

Mapping: [⟨1 1 5 2 6], ⟨0 4 -15 10 -12]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.3413

Optimal ET sequence: 7, 27deh, 34, 41, 89, 130, 219

Badness (Sintel): 0.529

Heartful

Subgroup: 2.3.7.11.19

Comma list: 243/242, 896/891, 1083/1078

Mapping: [⟨1 1 -1 2 0], ⟨0 4 26 10 29]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.8042

Optimal ET sequence: 34dh, 41, 116e, 157e

Badness (Sintel): 0.984

Doublehearted

Subgroup: 2.3.7.11.19

Comma list: 133/132, 243/242, 343/342

Mapping: [⟨1 1 2 2 3], ⟨0 8 11 20 17]]

Optimal tuning (POTE): ~2 = 1＼1, ~19/18 = 87.6684

Optimal ET sequence: 14, 27e, 41

Badness (Sintel): 0.560

Byhearted

Subgroup: 2.3.7.11.19

Comma list: 99/98, 243/242, 363/361

Mapping: [⟨2 2 3 4 5], ⟨0 4 9 10 12]]

Optimal tuning (POTE): ~27/19 = 1＼2, ~21/19 = 174.7347

Optimal ET sequence: 14, 34dh, 48, 110e, 158e

Badness (Sintel): 0.893

Full 19-limit temperaments

Heartlandia (rank 3)

See also: Breed family § Jove

Subgroup: Full 19-limit

Comma list: 171/170, 243/242, 324/323, 364/363, 441/440

Mapping: [⟨1 1 1 2 2 1 3 3], ⟨0 4 0 1 10 23 12 4], ⟨0 0 2 1 0 -1 -1 1]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.3862, ~19/12 = 793.9558

Optimal ET sequence: 14cf, 27effg, 41, 89, 130g

Badness (Sintel): 2.294

Monkey

See also: Tetracot family § Monkey

Subgroup: Full 19-limit

Comma list: 100/99, 105/104, 144/143, 154/153, 170/169, 171/169

Mapping: [⟨1 1 1 5 2 4 6 6], ⟨0 4 9 -15 10 -2 -13 -12]]

Optimal tuning (POTE): ~2 = 1＼1, ~10/9 = 175.6890

Optimal ET sequence: 7, 27deh, 34, 41

Badness: 0.022158

Sesquartia

See also: Schismatic family § Sesquiquartififths

Subgroup: Full 19-limit

Comma list: 243/242, 361/360, 364/363, 441/440, 456/455, 595/594

Mapping: [⟨1 1 7 5 2 -2 -6 6], ⟨0 4 -32 -15 10 39 69 -12]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.4189

Optimal ET sequence: 41, 89g, 130, 171, 301eh

Badness: 0.020466

Heartia

See also: Schismatic family § Sesquiquartififths

Subgroup: Full 19-limit

Comma list: 171/170, 243/242, 256/255, 273/272, 324/323, 441/440

Mapping: [⟨1 1 7 5 2 -2 0 6], ⟨0 4 -32 -15 10 39 28 -12]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.3798

Optimal ET sequence: 41, 89, 130g

Badness: 0.023059

Hearty

See also: Schismatic family § Sesquiquartififths

Subgroup: Full 19-limit

Comma list: 221/220, 243/242, 361/360, 364/363, 441/440, 456/455

Mapping: [⟨1 1 7 5 2 -2 13 6], ⟨0 4 -32 -15 10 39 -61 -12]]

Optimal tuning (POTE): ~2 = 1＼1, ~21/19 = 175.3766

Optimal ET sequence: 41g, 89, 130, 609ceefggh

Badness: 0.022816

Bunya

See also: Tetracot family § Bunya

Subgroup: Full 19-limit

Comma list: 100/99, 120/119, 144/143, 170/169, 190/189, 225/224

Mapping: [⟨1 1 1 -1 2 4 6 0], ⟨0 4 9 26 10 -2 -13 29]]

Optimal tuning (POTE): ~2 = 1＼1, ~10/9 = 175.9529

Optimal ET sequence: 34dh, 41, 75e

Badness: 0.019460

Octacot

See also: Tetracot family § Octacot

Subgroup: Full 19-limit

Comma list: 100/99, 120/119, 133/132, 144/143, 154/153, 189/187

Mapping: [⟨1 1 1 2 2 4 3 3], ⟨0 8 18 11 20 -4 15 17]]

Optimal tuning (POTE): ~2 = 1＼1, ~18/17 = 88.1109

Optimal ET sequence: 14c, 27eg, 41, 68egg, 109efgg

Badness: 0.016652

Weasel

See also: Tetracot family § Weasel

Subgroup: Full 19-limit

Comma list: 50/49, 78/77, 85/84, 99/98, 135/133, 243/242

Mapping: [⟨2 2 2 3 4 3 7 5], ⟨0 4 9 9 10 15 4 12]]

Optimal tuning (POTE): ~7/5 = 1＼2, ~21/19 = 175.6965

Optimal ET sequence: 14cf, 34dh, 48f, 82dh

Badness: 0.021029

Interval lattice

Interval lattice of heartland

740.3¢
915.6¢
1090.9¢
66.1¢
241.4¢ 		14/11
416.7¢
591.9¢ 		14/9
767.2¢ 		19/11
942.5¢ 		21/11
1117.8¢ 		19/18
93.0¢ 		7/6
268.3¢
443.6¢
618.8¢ 		19/12
794.1¢ 		7/4
969.4¢
1144.6¢
119.9¢ 		19/16
295.2¢ 		21/16
470.5¢
16/11
647.3¢
822.6¢ 		16/9
997.8¢
1173.1¢ 		12/11
148.4¢
323.6¢ 		4/3
498.9¢ 		28/19
674.2¢ 		18/11
849.5¢ 		38/21
1024.7¢ 		1/1
0.0¢ 		21/19
175.3¢ 		11/9
350.5¢ 		19/14
525.8¢ 		3/2
701.1¢
876.4¢ 		11/6
1051.6¢
26.9¢ 		9/8
202.2¢
377.4¢ 		11/8
552.7¢
32/21
729.5¢ 		32/19
904.8¢
1080.1¢
55.4¢ 		8/7
230.6¢ 		24/19
405.9¢
581.2¢
756.4¢ 		12/7
931.7¢ 		36/19
1107.0¢ 		22/21
82.2¢ 		22/19
257.5¢ 		9/7
432.8¢
608.1¢ 		11/7
783.3¢
958.6¢
1133.9¢
109.1¢
284.4¢
459.7¢

Scales

Heartland has 13, 27 and 41-tone MV3 scales, with 1L6m6s, 7L7m13s and 7L7m27s respectively.

Chords

Below are listed 21-odd-limit essentially tempered chords of the heartland temperament. Chords requiring tempering only by 243/242 are labeled rastmic, by 1083/1078 bihendrix, and by 3971/3969 heartlandismic. Those requiring any two of these commas are labeled heartland.

Triads

# Transversal Steps Type Odd limit
1 1-11/9-3/2 11/9-11/9-4/3 rastmic 11-odd-limit
2 1-9/8-11/9 9/8-12/11-18/11 rastmic 11-odd-limit
3 1-12/11-11/9 12/11-9/8-18/11 rastmic 11-odd-limit
4 1-19/14-11/6 19/14-19/14-12/11 bihendrix 19-odd-limit
5 1-7/6-19/14 7/6-22/19-28/19 bihendrix 19-odd-limit
6 1-22/19-19/14 22/19-7/6-28/19 bihendrix 19-odd-limit
7 1-11/9-9/7 11/9-22/21-14/9 rastmic 21-odd-limit
8 1-22/21-9/7 22/21-11/9-14/9 rastmic 21-odd-limit
9 1-11/9-19/14 11/9-21/19-28/19 bihendrix 21-odd-limit
10 1-21/19-19/14 21/19-11/9-28/19 bihendrix 21-odd-limit
11 1-22/19-9/7 22/19-21/19-14/9 bihendrix 21-odd-limit
12 1-21/19-9/7 21/19-22/19-14/9 bihendrix 21-odd-limit
13 1-21/19-11/9 21/19-21/19-18/11 heartlandismic 21-odd-limit
14 1-19/18-21/19 19/18-22/21-38/21 heartlandismic 21-odd-limit
15 1-22/21-21/19 22/21-19/18-38/21 heartlandismic 21-odd-limit

Tetrads

# Transversal Steps Type Odd limit
1 1-11/9-3/2-11/6 11/9-11/9-11/9-12/11 rastmic 11-odd-limit
2 1-9/8-3/2-11/6 9/8-4/3-11/9-12/11 rastmic 11-odd-limit
3 1-9/8-11/9-11/6 9/8-12/11-3/2-12/11 rastmic 11-odd-limit
4 1-9/8-11/9-3/2 9/8-12/11-11/9-4/3 rastmic 11-odd-limit
5 1-11/9-11/8-3/2 11/9-9/8-12/11-4/3 rastmic 11-odd-limit
6 1-12/11-11/9-3/2 12/11-9/8-11/9-4/3 rastmic 11-odd-limit
7 1-9/8-11/9-11/8 9/8-12/11-9/8-16/11 rastmic 11-odd-limit
8 1-19/14-19/12-11/6 19/14-7/6-22/19-12/11 bihendrix 19-odd-limit
9 1-22/19-19/14-11/6 22/19-7/6-19/14-12/11 bihendrix 19-odd-limit
10 1-19/14-11/7-11/6 19/14-22/19-7/6-12/11 bihendrix 19-odd-limit
11 1-7/6-19/14-11/6 7/6-22/19-19/14-12/11 bihendrix 19-odd-limit
12 1-7/6-19/14-19/12 7/6-22/19-7/6-24/19 bihendrix 19-odd-limit
13 1-22/19-19/14-11/7 22/19-7/6-22/19-14/11 bihendrix 19-odd-limit
14 1-11/9-3/2-11/7 11/9-11/9-22/21-14/11 rastmic 21-odd-limit
15 1-11/9-9/7-11/7 11/9-22/21-11/9-14/11 rastmic 21-odd-limit
16 1-22/21-9/7-11/7 22/21-11/9-11/9-14/11 rastmic 21-odd-limit
17 1-11/9-9/7-3/2 11/9-22/21-7/6-4/3 rastmic 21-odd-limit
18 1-7/6-11/9-3/2 7/6-22/21-11/9-4/3 rastmic 21-odd-limit
19 1-9/8-11/9-9/7 9/8-12/11-22/21-14/9 rastmic 21-odd-limit
20 1-22/21-11/9-9/7 22/21-7/6-22/21-14/9 rastmic 21-odd-limit
21 1-22/21-8/7-9/7 22/21-12/11-9/8-14/9 rastmic 21-odd-limit
22 1-19/14-3/2-11/6 19/14-21/19-11/9-12/11 bihendrix 21-odd-limit
23 1-11/9-19/14-11/6 11/9-21/19-19/14-12/11 bihendrix 21-odd-limit
24 1-11/9-19/14-11/7 11/9-21/19-22/19-14/11 bihendrix 21-odd-limit
25 1-22/19-9/7-11/7 22/19-21/19-11/9-14/11 bihendrix 21-odd-limit
26 1-7/6-19/14-3/2 7/6-22/19-21/19-4/3 bihendrix 21-odd-limit
27 1-21/19-19/14-3/2 21/19-11/9-21/19-4/3 bihendrix 21-odd-limit
28 1-21/19-9/7-3/2 21/19-22/19-7/6-4/3 bihendrix 21-odd-limit
29 1-22/19-9/7-19/14 22/19-21/19-19/18-28/19 bihendrix 21-odd-limit
30 1-21/19-9/7-19/14 21/19-22/19-19/18-28/19 bihendrix 21-odd-limit
31 1-7/6-11/9-19/14 7/6-22/21-21/19-28/19 bihendrix 21-odd-limit
32 1-22/19-11/9-19/14 22/19-19/18-21/19-28/19 bihendrix 21-odd-limit
33 1-19/18-11/9-19/14 19/18-22/19-21/19-28/19 bihendrix 21-odd-limit
34 1-19/18-7/6-19/14 19/18-21/19-22/19-28/19 bihendrix 21-odd-limit
35 1-21/19-7/6-19/14 21/19-19/18-22/19-28/19 bihendrix 21-odd-limit
36 1-21/19-22/19-19/14 21/19-22/21-7/6-28/19 bihendrix 21-odd-limit
37 1-21/19-22/19-9/7 21/19-22/21-21/19-14/9 bihendrix 21-odd-limit
38 1-21/19-7/6-11/9 21/19-19/18-22/21-18/11 heartlandismic 21-odd-limit
39 1-21/19-22/19-11/9 21/19-22/21-19/18-18/11 heartlandismic 21-odd-limit
40 1-19/18-21/19-11/9 19/18-22/21-21/19-18/11 heartlandismic 21-odd-limit
41 1-22/21-21/19-11/9 22/21-19/18-21/19-18/11 heartlandismic 21-odd-limit
42 1-19/18-21/19-7/6 19/18-22/21-19/18-12/7 heartlandismic 21-odd-limit
43 1-22/21-21/19-22/19 22/21-19/18-22/21-19/11 heartlandismic 21-odd-limit
44 1-11/9-19/14-3/2 11/9-21/19-21/19-4/3 heartland 21-odd-limit
45 1-21/19-11/9-3/2 21/19-21/19-11/9-4/3 heartland 21-odd-limit
46 1-11/9-9/7-19/14 11/9-22/21-19/18-28/19 heartland 21-odd-limit
47 1-21/19-11/9-19/14 21/19-21/19-21/19-28/19 heartland 21-odd-limit
48 1-19/18-21/19-19/14 19/18-22/21-11/9-28/19 heartland 21-odd-limit
49 1-22/19-11/9-9/7 22/19-19/18-22/21-14/9 heartland 21-odd-limit
50 1-21/19-11/9-9/7 21/19-21/19-22/21-14/9 heartland 21-odd-limit
51 1-22/21-22/19-9/7 22/21-21/19-21/19-14/9 heartland 21-odd-limit
52 1-22/21-21/19-9/7 22/21-19/18-22/19-14/9 heartland 21-odd-limit

Pentads

# Transversal Steps Type Odd limit
1 1-11/9-11/8-3/2-11/6 11/9-9/8-12/11-11/9-12/11 rastmic 11-odd-limit
2 1-9/8-11/8-3/2-11/6 9/8-11/9-12/11-11/9-12/11 rastmic 11-odd-limit
3 1-9/8-11/9-3/2-11/6 9/8-12/11-11/9-11/9-12/11 rastmic 11-odd-limit
4 1-9/8-11/9-11/8-11/6 9/8-12/11-9/8-4/3-12/11 rastmic 11-odd-limit
5 1-9/8-11/9-11/8-3/2 9/8-12/11-9/8-12/11-4/3 rastmic 11-odd-limit
6 1-7/6-19/14-19/12-11/6 7/6-22/19-7/6-22/19-12/11 bihendrix 19-odd-limit
7 1-22/19-19/14-11/7-11/6 22/19-7/6-22/19-7/6-12/11 bihendrix 19-odd-limit
8 1-11/9-3/2-11/7-11/6 11/9-11/9-22/21-7/6-12/11 rastmic 21-odd-limit
9 1-7/6-11/9-3/2-11/6 7/6-22/21-11/9-11/9-12/11 rastmic 21-odd-limit
10 1-11/9-11/8-3/2-11/7 1/1-1/1-1/1-1/1-14/11 rastmic 21-odd-limit
11 1-22/19-9/7-19/14-11/7 22/19-21/19-19/18-22/19-14/11 rastmic 21-odd-limit
12 1-22/19-11/9-19/14-11/7 22/19-19/18-21/19-22/19-14/11 rastmic 21-odd-limit
13 1-22/21-8/7-9/7-11/7 1/1-1/1-1/1-1/1-14/11 rastmic 21-odd-limit
14 1-7/6-11/9-4/3-3/2 7/6-22/21-12/11-9/8-4/3 rastmic 21-odd-limit
15 1-9/8-11/9-9/7-3/2 9/8-12/11-22/21-7/6-4/3 rastmic 21-odd-limit
16 1-19/14-3/2-19/12-11/6 19/14-21/19-19/18-22/19-12/11 bihendrix 21-odd-limit
17 1-19/14-3/2-11/7-11/6 19/14-21/19-22/21-7/6-12/11 bihendrix 21-odd-limit
18 1-11/9-19/14-11/7-11/6 11/9-21/19-22/19-7/6-12/11 bihendrix 21-odd-limit
19 1-7/6-19/14-3/2-11/6 7/6-22/19-21/19-11/9-12/11 bihendrix 21-odd-limit
20 1-7/6-11/9-19/14-11/6 7/6-22/21-21/19-19/14-12/11 bihendrix 21-odd-limit
21 1-22/19-11/9-19/14-11/6 22/19-19/18-21/19-19/14-12/11 bihendrix 21-odd-limit
22 1-7/6-19/14-3/2-19/12 7/6-22/19-21/19-19/18-24/19 bihendrix 21-odd-limit
23 1-19/18-7/6-19/14-19/12 19/18-21/19-22/19-7/6-24/19 bihendrix 21-odd-limit
24 1-22/19-9/7-19/14-11/7 22/19-21/19-19/18-22/19-14/11 bihendrix 21-odd-limit
25 1-22/19-11/9-19/14-11/7 22/19-19/18-21/19-22/19-14/11 bihendrix 21-odd-limit
26 1-21/19-9/7-19/14-3/2 21/19-22/19-19/18-21/19-4/3 bihendrix 21-odd-limit
27 1-21/19-7/6-19/14-3/2 21/19-19/18-22/19-21/19-4/3 bihendrix 21-odd-limit
28 1-21/19-22/19-9/7-19/14 21/19-22/21-21/19-19/18-28/19 bihendrix 21-odd-limit
29 1-19/18-7/6-11/9-19/14 19/18-21/19-22/21-21/19-28/19 bihendrix 21-odd-limit
30 1-19/18-21/19-7/6-11/9 19/18-22/21-19/18-22/21-18/11 heartlandismic 21-odd-limit
31 1-22/21-21/19-22/19-11/9 22/21-19/18-22/21-19/18-18/11 heartlandismic 21-odd-limit
32 1-11/9-19/14-3/2-11/6 11/9-21/19-21/19-11/9-12/11 heartland 21-odd-limit
33 1-11/9-19/14-3/2-11/7 11/9-21/19-21/19-22/21-14/11 heartland 21-odd-limit
34 1-11/9-9/7-19/14-11/7 11/9-22/21-19/18-22/19-14/11 heartland 21-odd-limit
35 1-22/19-11/9-9/7-11/7 22/19-19/18-22/21-11/9-14/11 heartland 21-odd-limit
36 1-22/21-22/19-9/7-11/7 22/21-21/19-21/19-11/9-14/11 heartland 21-odd-limit
37 1-11/9-9/7-19/14-3/2 11/9-22/21-19/18-21/19-4/3 heartland 21-odd-limit
38 1-7/6-11/9-19/14-3/2 7/6-22/21-21/19-21/19-4/3 heartland 21-odd-limit
39 1-21/19-11/9-19/14-3/2 21/19-21/19-21/19-21/19-4/3 heartland 21-odd-limit
40 1-21/19-11/9-9/7-3/2 21/19-21/19-22/21-7/6-4/3 heartland 21-odd-limit
41 1-21/19-7/6-11/9-3/2 21/19-19/18-22/21-11/9-4/3 heartland 21-odd-limit
42 1-22/19-11/9-9/7-19/14 22/19-19/18-22/21-19/18-28/19 heartland 21-odd-limit
43 1-21/19-11/9-9/7-19/14 21/19-21/19-22/21-19/18-28/19 heartland 21-odd-limit
44 1-21/19-7/6-11/9-19/14 21/19-19/18-22/21-21/19-28/19 heartland 21-odd-limit
45 1-21/19-22/19-11/9-19/14 21/19-22/21-19/18-21/19-28/19 heartland 21-odd-limit
46 1-19/18-21/19-11/9-19/14 19/18-22/21-21/19-21/19-28/19 heartland 21-odd-limit
47 1-19/18-21/19-7/6-19/14 19/18-22/21-19/18-22/19-28/19 heartland 21-odd-limit
48 1-21/19-22/19-11/9-9/7 21/19-22/21-19/18-22/21-14/9 heartland 21-odd-limit
49 1-22/21-22/19-11/9-9/7 22/21-21/19-19/18-22/21-14/9 heartland 21-odd-limit
50 1-22/21-21/19-11/9-9/7 22/21-19/18-21/19-22/21-14/9 heartland 21-odd-limit
51 1-22/21-21/19-22/19-9/7 22/21-19/18-22/21-21/19-14/9 heartland 21-odd-limit

Hexads

# Transversal Steps Type Odd limit
1 1-9/8-11/9-11/8-3/2-11/6 9/8-12/11-9/8-12/11-11/9-12/11 rastmic 11-odd-limit
2 1-11/9-11/8-3/2-11/7-11/6 11/9-9/8-12/11-22/21-7/6-12/11 rastmic 21-odd-limit
3 1-9/8-11/8-3/2-7/4-11/6 9/8-11/9-12/11-7/6-22/21-12/11 rastmic 21-odd-limit
4 1-7/6-19/14-3/2-19/12-11/6 7/6-22/19-21/19-19/18-22/21-12/11 bihendrix 21-odd-limit
5 1-22/19-11/9-19/14-11/7-11/6 22/19-19/18-21/19-22/19-7/6-12/11 bihendrix 21-odd-limit
6 1-11/9-19/14-3/2-11/7-11/6 11/9-21/19-21/19-22/21-7/6-12/11 heartland 21-odd-limit
7 1-7/6-11/9-19/14-3/2-11/6 7/6-22/21-21/19-21/19-11/9-12/11 heartland 21-odd-limit
8 1-11/9-9/7-19/14-3/2-11/7 11/9-22/21-19/18-21/19-22/21-14/11 heartland 21-odd-limit
9 1-22/19-11/9-9/7-19/14-11/7 22/19-19/18-22/21-19/18-22/19-14/11 heartland 21-odd-limit
10 1-22/21-22/19-11/9-9/7-11/7 22/21-21/19-19/18-22/21-11/9-14/11 heartland 21-odd-limit
11 1-21/19-11/9-9/7-19/14-3/2 21/19-21/19-22/21-19/18-21/19-4/3 heartland 21-odd-limit
12 1-21/19-7/6-11/9-19/14-3/2 21/19-19/18-22/21-21/19-21/19-4/3 heartland 21-odd-limit
13 1-21/19-22/19-11/9-9/7-19/14 21/19-22/21-19/18-22/21-19/18-28/19 heartland 21-odd-limit
14 1-19/18-21/19-7/6-11/9-19/14 19/18-22/21-19/18-22/21-21/19-28/19 heartland 21-odd-limit
15 1-22/21-21/19-22/19-11/9-9/7 22/21-19/18-22/21-19/18-22/21-14/9 heartland 21-odd-limit

See also

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