Heartland - Revision history

Xenllium at 10:26, 18 January 2026

2026-01-18T10:26:05Z

← Older revision		Revision as of 10:26, 18 January 2026
Line 15:		Line 15:

	[[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 ====
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	[[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 ===
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	[[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 ====
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	[[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 ====
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	[[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 ===
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	[[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

FloraC: Fix linking

2025-08-27T13:57:13Z

Fix linking

← Older revision		Revision as of 13:57, 27 August 2025
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	== See also ==		== See also ==
	* [[Rastmic clan]]		* [[Rastmic clan]]
	* [[Rastmic rank ~~three~~ clan]]		* [[Rastmic rank-3 clan]]

	[[Category:Regular temperament theory]]		[[Category:Regular temperament theory]]

Xenllium at 00:08, 29 April 2024

2024-04-29T00:08:15Z

← Older revision		Revision as of 00:08, 29 April 2024
Line 21:		Line 21:
	[[Comma list]]: 243/242, 1083/1078		[[Comma list]]: 243/242, 1083/1078

	[[Mapping]]: ~~{{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}}		[[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		[[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

Xenllium at 03:12, 2 December 2023

2023-12-02T03:12:05Z

← Older revision		Revision as of 03:12, 2 December 2023
Line 1:		Line 1:
	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."		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."

	~~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 [[Breed family\|jove temperament]].		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 [[Breed family\|jove temperament]]. For extending to the 2.3.5.7.11.13.19 subgroup, tempering out 364/363 gives an excellent tuning.

	== Temperament data ==		== Temperament data ==

Xenllium at 03:59, 29 November 2023

2023-11-29T03:59:42Z

← Older revision		Revision as of 03:59, 29 November 2023
Line 1:		Line 1:
	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."		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."

			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 [[Breed family\|jove temperament]].

	== Temperament data ==		== Temperament data ==

Xenllium: Created page with "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 temperamen..."

2023-11-24T00:57:57Z

Created page with "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 temperamen..."

New page

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."

== Temperament data ==
=== Parent temperaments ===
==== Heartland ====
[[Subgroup]]: 2.3.7.11.19

[[Comma list]]: 243/242, 1083/1078

[[Mapping]]: {{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]]: {{Optimal ET sequence|7, 14, 27e, 34dh, 41, 89, 130}}

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

[[Comma list]]: 243/242, 1083/1078

[[Mapping]]: {{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

=== 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]]: {{mapping|1 1 5 2 6|0 4 -15 10 -12}}

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

[[Optimal ET sequence]]: {{Optimal ET sequence|7, 27deh, 34, 41, 89, 130, 219}}

[[Badness]]: 0.010707

==== Heartful ====
[[Subgroup]]: 2.3.7.11.19

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

[[Mapping]]: {{mapping|1 1 -1 2 0|0 4 26 10 29}}

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

[[Optimal ET sequence]]: {{Optimal ET sequence|34dh, 41, 116e, 157e}}

[[Badness]]: 0.019908

==== Doublehearted ====
[[Subgroup]]: 2.3.7.11.19

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

[[Mapping]]: {{mapping|1 1 2 2 3|0 8 11 20 17}}

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

[[Optimal ET sequence]]: {{Optimal ET sequence|14, 27e, 41}}

[[Badness]]: 0.011318

==== Byhearted ====
[[Subgroup]]: 2.3.7.11.19

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

[[Mapping]]: {{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]]: {{Optimal ET sequence|14, 34dh, 48, 110e, 158e}}

[[Badness]]: 0.018062

=== 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]]: {{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]]: {{Optimal ET sequence|14cf, 27effg, 41, 89, 130g}}

==== 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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{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]]: {{Optimal ET sequence|14c, 27eg, 41, 68egg, 109efgg}}

[[Badness]]: 0.016652

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

[[Subgroup]]: Full 19-limit

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

[[Mapping]]: {{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]]: {{Optimal ET sequence|14cf, 34dh, 48f, 82dh}}

[[Badness]]: 0.021029

== Interval lattice ==
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">'''Interval lattice of heartland'''</div>
<div class="mw-collapsible-content">
{| class="wikitable center-all"
|-
|
| colspan="2" | 740.3¢
| colspan="2" | 915.6¢
| colspan="2" | 1090.9¢
| colspan="2" | 66.1¢
| colspan="2" | 241.4¢
| colspan="2" | 14/11 416.7¢
| colspan="2" | 591.9¢
| colspan="2" | 14/9 767.2¢
| colspan="2" | 19/11 942.5¢
| colspan="2" | 21/11 1117.8¢
| colspan="2" | 19/18 93.0¢
| colspan="2" | 7/6 268.3¢
| colspan="2" | 443.6¢
| colspan="2" | 618.8¢
| colspan="2" | 19/12 794.1¢
| colspan="2" | 7/4 969.4¢
| colspan="2" | 1144.6¢
| colspan="2" | 119.9¢
| colspan="2" | 19/16 295.2¢
| colspan="2" | 21/16 470.5¢
|
|-
| colspan="2" | 16/11 647.3¢
| colspan="2" | 822.6¢
| colspan="2" | 16/9 997.8¢
| colspan="2" | 1173.1¢
| colspan="2" | 12/11 148.4¢
| colspan="2" | 323.6¢
| colspan="2" | 4/3 498.9¢
| colspan="2" | 28/19 674.2¢
| colspan="2" | 18/11 849.5¢
| colspan="2" | 38/21 1024.7¢
| colspan="2" | 1/1 0.0¢
| colspan="2" | 21/19 175.3¢
| colspan="2" | 11/9 350.5¢
| colspan="2" | 19/14 525.8¢
| colspan="2" | 3/2 701.1¢
| colspan="2" | 876.4¢
| colspan="2" | 11/6 1051.6¢
| colspan="2" | 26.9¢
| colspan="2" | 9/8 202.2¢
| colspan="2" | 377.4¢
| colspan="2" | 11/8 552.7¢
|-
|
| colspan="2" | 32/21 729.5¢
| colspan="2" | 32/19 904.8¢
| colspan="2" | 1080.1¢
| colspan="2" | 55.4¢
| colspan="2" | 8/7 230.6¢
| colspan="2" | 24/19 405.9¢
| colspan="2" | 581.2¢
| colspan="2" | 756.4¢
| colspan="2" | 12/7 931.7¢
| colspan="2" | 36/19 1107.0¢
| colspan="2" | 22/21 82.2¢
| colspan="2" | 22/19 257.5¢
| colspan="2" | 9/7 432.8¢
| colspan="2" | 608.1¢
| colspan="2" | 11/7 783.3¢
| colspan="2" | 958.6¢
| colspan="2" | 1133.9¢
| colspan="2" | 109.1¢
| colspan="2" | 284.4¢
| colspan="2" | 459.7¢
|
|}
</div></div>

== Scales ==
[[File:Heartland scales.png]]

Heartland has 13, 27 and 41-tone MV3 scales, with 1L6m6s, 7L7m13s and 7L7m27s respectively.
* [[Heartland13]]
* [[Heartland27]]
* [[Heartland41]]

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

=== Triads ===
{| class="wikitable center-1"
|-
! #
! 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 ===
{| class="wikitable center-1"
|-
! #
! 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 ===
{| class="wikitable center-1"
|-
! #
! 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 ===
{| class="wikitable center-1"
|-
! #
! 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 ==
* [[Rastmic clan]]
* [[Rastmic rank three clan]]

[[Category:Regular temperament theory]]
[[Category:Heartland]]
[[Category:Rastmic]]
[[Category:Bihendrixmic]]
[[Category:Heartlandismic]]