5L 3s/Temperaments: Difference between revisions

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 Vulture/[[Hemifamity_temperaments|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.
 == Petrtri ==
+=== Petrtri proper ===
+Subgroup: 2.9/5.11/5.13/5
+Period: 1\1
+Optimal ([[POTE]]) generator:
+EDO generators: [[13edo|5\13]], [[21edo|8\21]], [[34edo|13\34]]
+[[Comma]] list: 100/99, 144/143
+[[Mapping]] (for 2, 9/5, 11/5, 13/5):
+Mapping generators: ~2, ~13/10
+{{Vals|legend=1| 13, 21, 34 }}
+==== Intervals ====
+Sortable table of intervals in the Dylathian mode and their Petrtri interpretations:
+{| class="wikitable right-2 right-3 right-4 right-5 sortable"
+|-
+! Degree
+! Size in 13edo
+! Size in 21edo
+! Size in 34edo
+! Size in POTE tuning
+! Note name on Q
+! class="unsortable"| Approximate ratios
+! #Gens up
+|-
+| 1
+| 0\13, 0.00
+| 0\21, 0.00
+| 0\34, 0.00
+| 0.00
+| Q
+| 1/1
+| 0
+|-
+| 2
+| 2\13, 184.62
+| 3\21, 171.43
+| 5\34, 176.47
+| 177.45
+| J
+| 10/9, 11/10
+| +3
+|-
+| 3
+| 4\13, 369.23
+| 6\21, 342.86
+| 10\34, 352.94
+| 354.90
+| K
+| 11/9
+| +6
+|-
+| 4
+| 5\13, 461.54
+| 8\21, 457.14
+| 13\34, 458.82
+| 459.15
+| L
+| 13/10
+| +1
+|-
+| 5
+| 7\13, 646.15
+| 11\21, 628.57
+| 18\34, 635.294
+| 636.60
+| M
+| 13/9
+| +4
+|-
+| 6
+| 9\13, 830.77
+| 14\21, 800.00
+| 23\34, 811.77
+| 814.05
+| N
+|
+| +7
+|-
+| 7
+| 10\13, 923.08
+| 16\21, 914.29
+| 26\34, 917.65
+| 918.30
+| O
+| 22/13
+| +2
+|-
+| 8
+| 12\13, 1107.69
+| 19\21, 1085.71
+| 31\34, 1094.12
+| 1095.75
+| P
+|
+| +5
+|}
 === Tridec ===
 Subgroup: 2.3.7/5.11/5.13/5