Spoob

Interval information

Ratio	27682574402/27680640625
Factorization	2 × 5-6 × 712 × 11-6
Monzo	[1 0 -6 12 -6⟩
Size in cents	0.1209403¢
Name	spoob
Color name	1u6z12g68, tribiluzozogu octave
FJS name	[math]\displaystyle{ \text{6d8}^{7,7,7,7,7,7,7,7,7,7,7,7}_{5,5,5,5,5,5,11,11,11,11,11,11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	69.3764
Weil norm (log2 max(n, d))	69.3765
Wilson norm (sopfr(nd))	182
Comma size	unnoticeable
Open this interval in xen-calc

The spoob (monzo: [1 0 -6 12 -6⟩, ratio: 27 682 574 402 / 27 680 640 625), is an unnoticeable 11-limit comma measuring about 0.121 cents. It separates a stack of six 55/49's from the octave. It was named after an emoji on Xenharmonic Discord.

Temperaments

Tempering out this comma in the 11-limit defines the rank-4 spoob temperament, or in the 2.5.7.11 subgroup an unnamed rank-3 retraction thereof.

Spoob

Subgroup: 2.3.5.7.11

Comma list: 27682574402/27680640625

Mapping: [⟨6 0 0 0 1], ⟨0 1 0 0 0], ⟨0 0 1 0 -1], ⟨0 0 0 1 2]]

mapping generators: ~55/49, ~3, ~5, ~7

Optimal ET sequence: 72, 198, 270, 342, 612, 954, 1236, 1506, 1578, 1848, 3426, 4038, 5616, 6390, 6660, 7002, 7626, 7896, 8238, 8850, 9744, 9816, 10086, 10428, 11664, 11934, 12276, 36216, 48492, 60768, 84978, 97254, 98832d

Badness (Sintel): 3.91

Spoob retraction

Subgroup: 2.5.7.11

Comma list: 27682574402/27680640625

Subgroup-val mapping: [⟨6 0 0 1], ⟨0 1 0 -1], ⟨0 0 1 2]]

mapping generators: ~55/49, ~5, ~7

Optimal ET sequence: 72, 150, 186, 192, 198, 264, 270, 342, 348, 612, 618, 960, 1578, 7542, 8160, 9120, 10698, 12276, 13854, 23592, 25170, 26748, 28326, 40602, 42180, 67350, 68928

Badness (Sintel): 0.165