Orwellismic family
- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
The orwellismic family of rank-3 temperaments tempers out the orwellisma, 1728/1715.
Orwellismic
Orwellismic uses three ~7/6 generators to reach 8/5 while preserving the lattice structure of the 2.3.7 subgroup. Ideally, 7/6 and 5/4 are both tuned slightly sharp.
Subgroup: 2.3.5.7
Comma list: 1728/1715
Mapping: [⟨1 0 0 2], ⟨0 1 0 1], ⟨0 0 3 -1]]
- mapping generators: ~2, ~3, ~12/7
Mapping to lattice: [⟨0 0 -3 1], ⟨0 1 0 1]]
Lattice basis:
- 7/6 length = 0.7526, 3/2 length = 1.3931
- Angle (7/6, 3/2) = 97.5081
- WE: ~2 = 1199.4176 ¢, ~3/2 = 701.8055 ¢, ~12/7 = 928.9445 ¢
- error map: ⟨-0.582 -0.732 +0.520 +2.288]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.6429 ¢, ~12/7 = 929.2316 ¢
- error map: ⟨0.000 -0.312 +1.381 +3.585]
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [3/2 3/4 3/4 -3/4⟩, [3/2 3/4 -1/4 1/4⟩]
- unchanged-interval (eigenmonzo) basis: 2.3.7/5
Optimal ET sequence: 4, 5, 9, 17, 18, 22, 27, 31, 53, 80, 84, 111, 164d, 195d, 275d, 306d
Badness (Sintel): 0.826
Projection pair: ~5 = 1728/343 to 2.3.7
Scales: orwellismic9, orwellismic diatonic
Guanyin
Guanyin is the most natural 11-limit extension of orwellismic, where two ~7/6 generators make 15/11, tempering out 540/539, and two sharpened ~5/4's make 11/7, tempering out 176/175.
Subgroup: 2.3.5.7.11
Comma list: 176/175, 540/539
Mapping: [⟨1 0 0 2 -2], ⟨0 1 0 1 1], ⟨0 0 3 -1 5]]
Mapping to lattice: [⟨0 0 -3 1 -5], ⟨0 1 0 1 1]]
Lattice basis:
- 7/6 length = 0.5167, 3/2 length = 1.3055
- Angle (7/6, 3/2) = 79.0940
- WE: ~2 = 1199.2336 ¢, ~3/2 = 702.4159 ¢, ~12/7 = 929.3128 ¢
- error map: ⟨-0.7664 -0.3055 +1.6247 +1.9781 -1.5717]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.2876 ¢, ~12/7 = 929.7608 ¢
- error map: ⟨0.0000 +0.3326 +2.9688 +3.7009 -0.2261]
- [[1 0 0 0 0⟩, [-2/9 0 -5/9 5/9 4/9⟩, [4/3 0 1/3 -1/3 1/3⟩, [4/3 0 -2/3 2/3 1/3⟩, [0 0 0 0 1⟩]
- unchanged-interval (eigenmonzo) basis: 2.11.7/5
Optimal ET sequence: 22, 27e, 31, 53, 58, 80, 111, 280cd
Badness (Sintel): 0.494
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807 to 2.3.7
Scales: guanyin22
- Music
- Trio for SoftSaturn, NebulaSing and TromBonehead (archived 2010) by Gene Ward Smith – SoundCloud | details | play – in Guanyin[22], 111edo tuning
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 176/175, 351/350, 540/539
Mapping: [⟨1 0 0 2 -2 3], ⟨0 1 0 1 1 -2], ⟨0 0 3 -1 5 5]]
Optimal tunings:
- WE: ~2 = 1199.2015 ¢, ~3/2 = 702.4954 ¢, ~12/7 = 929.2881 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.6821 ¢, ~12/7 = 929.7296 ¢
Optimal ET sequence: 22, 27e, 31, 53, 58, 80, 111, 280cdf
Badness (Sintel): 0.708
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 221184/16897 to 2.3.7
Avalokita
This extension used to be known as georgian.
Subgroup: 2.3.5.7.11.13
Comma list: 144/143, 176/175, 196/195
Mapping: [⟨1 0 0 2 -2 6], ⟨0 1 0 1 1 1], ⟨0 0 3 -1 5 -5]]
Optimal tunings:
- WE: ~2 = 1198.4320 ¢, ~3/2 = 702.7802 ¢, ~12/7 = 929.4834 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.5889 ¢, ~12/7 = 930.5977 ¢
Optimal ET sequence: 22f, 27e, 31, 49f, 58, 138cdeff, 196cdefff, 254ccdeeffff
Badness (Sintel): 0.845
Projection pairs: ~5 = 1728/343, ~11 = 186624/16807, ~13 = 16807/1296 to 2.3.7
Orwellian
Orwellian is another 11-limit extension of orwellismic that tempers out 99/98, which is supported by 11-limit orwell.
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384
Mapping: [⟨1 0 0 2 5], ⟨0 1 0 1 0], ⟨0 0 3 -1 -2]]
- WE: ~2 = 1200.7839 ¢, ~3/2 = 699.6996 ¢, ~12/7 = 928.6481 ¢
- error map: ⟨+0.784 -1.471 -0.369 +4.577 -4.695]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 699.6270 ¢, ~12/7 = 928.0978 ¢
- error map: ⟨0.000 -2.328 -2.020 +2.703 -7.514]
Optimal ET sequence: 4, 5, 9, 17, 22, 31, 53, 84e
Badness (Sintel): 0.859
Scales: orwellian chromatic