Archytas clan

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 archytas clan (or archy family) tempers out the Archytas' comma, 64/63. This means a stack of two 3/2 fifths octave-reduced equals a whole tone of 8/7~9/8 tempered together; two of these tones or equivalently four stacked fifths octave-reduced equal a 9/7 major third. Note the similarity in function to 81/80 in meantone, where four stacked fifths octave-reduced equal a 5/4 major third. This leads to tunings with 3's and 7's quite sharp, such as those of 22edo.

This article focuses on rank-2 temperaments. See Archytas family for the rank-3 temperament resulting from tempering out 64/63 alone in the full 7-limit.

Archy

Main article: Superpyth

Subgroup: 2.3.7

Comma list: 64/63

Sval mapping: [⟨1 0 6], ⟨0 1 -2]]

sval mapping generators: ~2, ~3

Gencom mapping: [⟨1 0 0 6], ⟨0 1 0 -2]]

gencom: [2 3; 64/63]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.595

error map: ⟨0.000 +7.640 +11.984]

• POTE: ~2 = 1200.000, ~3/2 = 709.321

error map: ⟨0.000 +7.366 +12.532]

Optimal ET sequence: 2, 3, 5, 12, 17, 22, 137bdd, 159bddd, 181bbddd

Badness (Sintel): 0.159

Scales: archy5, archy7, archy12

Overview to extensions

7-limit extensions

The second comma in the comma list defines which 7-limit family member we are looking at:

• Schism adds 360/343, for an exotemperament well tuned around 12edo;
• Dominant adds 36/35, for a tuning flat of 17c-edo;
• Quasisuper adds 2430/2401, for a tuning between 17c-edo and 22edo;
• Superpyth adds 245/243, for a tuning between 22edo and 27edo;
• Quasiultra adds 33614/32805, for a tuning between 27edo and 32edo;
• Ultrapyth adds 6860/6561, for a tuning sharp of 32edo;
• Mother adds 16/15, for an exotemperament well tuned around 5edo.

These all use the same generators as archy.

686/675 gives beatles, splitting the fifth in two. 8748/8575 gives immunized, splitting the twelfth in two. 50/49 gives pajara with a semioctave period. 392/375 gives progress, splitting the twelfth in three. 250/243 gives porcupine, splitting the fourth in three. 126/125 gives augene with a 1/3-octave period. 4375/4374 gives modus, splitting the fifth in four. 3125/3024 gives brightstone. 9604/9375 gives fervor. 3125/2916 gives sixix. 3125/3087 gives passion. Those split the generator in five in various ways. 28/27 gives blacksmith with a 1/5-octave period. Finally, 15625/15552 gives catalan, splitting the twelfth in six.

Temperaments discussed elsewhere are:

• Mother (+16/15) → Father family
• Dominant (+36/35) → Meantone family
• Medusa (+15/14) → Very low accuracy temperaments
• Suhajira (+243/242) → Neutral clan
• Immunized (+8748/8575) → Immunity family
• Pajara (+50/49) → Diaschismic family
• Augene (+126/125) → Augmented family
• Porcupine (+250/243) → Porcupine family
• Modus (+4375/4374) → Tetracot family
• Brightstone (+3125/3024) → Magic family
• Passion (+3125/3087) → Passion family
• Blacksmith (+28/27) → Limmic temperaments
• Catalan (+15625/15552) → Kleismic family

Considered below are superpyth, quasisuper, ultrapyth, quasiultra, schism, beatles, progress, fervor, and sixix.

Subgroup extensions

Omitting prime 5, archy can be extended to the 2.3.7.11 subgroup by identifying 11/8 as a diminished fourth (C–Gb). This is called supra, given right below.

Supra

Subgroup: 2.3.7.11

Comma list: 64/63, 99/98

Sval mapping: [⟨1 0 6 13], ⟨0 1 -2 -6]]

Gencom mapping: [⟨1 0 0 6 13], ⟨0 1 0 -2 -6]]

gencom: [2 3; 64/63 99/98]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 708.456
• POTE: ~2 = 1200.000, ~3/2 = 707.192

Optimal ET sequence: 5, 12, 17, 39d, 56d

Badness (Sintel): 0.352

Scales: supra7, supra12

Supraphon

Subgroup: 2.3.7.11.13

Comma list: 64/63, 78/77, 99/98

Sval mapping: [⟨1 0 6 13 18], ⟨0 1 -2 -6 -9]]

Gencom mapping: [⟨1 0 0 6 13 18], ⟨0 1 0 -2 -6 -9]]

gencom: [2 3; 64/63 78/77 99/98]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 707.344
• POTE: ~2 = 1200.000, ~3/2 = 706.137

Optimal ET sequence: 12f, 17

Badness (Sintel): 0.498

Scales: supra7, supra12

Superpyth

Main article: Superpyth

For the 5-limit version, see Syntonic–diatonic equivalence continuum #Superpyth (5-limit).

Superpyth adds 245/243 and 1728/1715 to the comma list and can be described as 22 & 27. ~5/4 is found at +9 generator steps, as an augmented second (C–D#).

Subgroup: 2.3.5.7

Comma list: 64/63, 245/243

Mapping: [⟨1 0 -12 6], ⟨0 1 9 -2]]

Wedgie: ⟨⟨ 1 9 -2 12 -6 -30 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.591

error map: ⟨0.000 +7.636 +0.002 +11.993]

• POTE: ~2 = 1200.000, ~3/2 = 710.291

error map: ⟨0.000 +8.336 +6.305 +10.592]

Optimal ET sequence: 5, 17, 22, 27, 49, 174bbcddd

Badness (Sintel): 0.818

11-limit

The canonical extension to the 13-limit finds the ~11/8 at +16 generator steps, as a double-augmented second (C–Dx) and finds the ~13/8 at +13 generator steps, as a double-augmented fourth (C–Fx).

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 245/243

Mapping: [⟨1 0 -12 6 -22], ⟨0 1 9 -2 16]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.514
• POTE: ~2 = 1200.000, ~3/2 = 710.175

Optimal ET sequence: 22, 27e, 49

Badness (Sintel): 0.826

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 78/77, 91/90, 100/99

Mapping: [⟨1 0 -12 6 -22 -17], ⟨0 1 9 -2 16 13]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.836
• POTE: ~2 = 1200.000, ~3/2 = 710.479

Optimal ET sequence: 22, 27e, 49, 76bcde

Badness (Sintel): 1.02

Thomas

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 100/99, 169/168, 245/243

Mapping: [⟨1 1 -3 4 -6 4], ⟨0 2 18 -4 32 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~16/13 = 354.759
• POTE: ~2 = 1200.000, ~16/13 = 355.036

Optimal ET sequence: 27e, 44, 71d, 98bde

Badness (Sintel): 2.03

Suprapyth

Suprapyth finds the ~11/8 at the diminished fifth (C–Gb), and finds the ~13/8 at the diminished seventh (C–Bbb).

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 99/98

Mapping: [⟨1 0 -12 6 13], ⟨0 1 9 -2 -6]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.356
• POTE: ~2 = 1200.000, ~3/2 = 709.495

Optimal ET sequence: 5, 17, 22

Badness (Sintel): 1.08

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 65/63, 99/98

Mapping: [⟨1 0 -12 6 13 18], ⟨0 1 9 -2 -6 -9]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 708.702
• POTE: ~2 = 1200.000, ~3/2 = 708.703

Optimal ET sequence: 5f, 17, 22

Badness (Sintel): 1.50

Quasisuper

Quasisuper can be described as 17c & 22, with the ~5/4 mapped to -13 generator steps, as a double-diminished fifth (C–Gbb).

Subgroup: 2.3.5.7

Comma list: 64/63, 2430/2401

Mapping: [⟨1 0 23 6], ⟨0 1 -13 -2]]

Wedgie: ⟨⟨ 1 -13 -2 -23 -6 32 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 708.769

error map: ⟨0.000 +6.814 -0.310 +13.636]

• POTE: ~2 = 1200.000, ~3/2 = 708.238

error map: ⟨0.000 +6.283 +6.586 +14.697]

Optimal ET sequence: 17c, 22, 61d

Badness (Sintel): 1.61

Quasisupra

Quasisupra can be viewed as an extension of the excellent 2.3.7.11 temperament supra, with the quasisuper mapping of 5 thrown in, rather than the superpyth mapping of 5 (which results in suprapyth).

Subgroup: 2.3.5.7.11

Comma list: 64/63, 99/98, 121/120

Mapping: [⟨1 0 23 6 13], ⟨0 1 -13 -2 -6]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 708.713
• POTE: ~2 = 1200.000, ~3/2 = 708.205

Optimal ET sequence: 17c, 22, 39d, 61d

Badness (Sintel): 1.06

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 78/77, 91/90, 121/120

Mapping: [⟨1 0 23 6 13 18], ⟨0 1 -13 -2 -6 -9]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 708.411
• POTE: ~2 = 1200.000, ~3/2 = 708.004

Optimal ET sequence: 17c, 22, 39d

Badness (Sintel): 1.25

Quasisoup

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 2430/2401

Mapping: [⟨1 0 23 6 -22], ⟨0 1 -13 -2 16]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 709.043
• POTE: ~2 = 1200.000, ~3/2 = 709.021

Optimal ET sequence: 22

Badness (Sintel): 2.76

Ultrapyth

Ultrapyth can be viewed as an extension of the excellent 2.3.7.13/5 oceanfront temperament, mapping the ~5/4 to +14 fifths as a double-augmented unison (C–Cx).

Subgroup: 2.3.5.7

Comma list: 64/63, 6860/6561

Mapping: [⟨1 0 -20 6], ⟨0 1 14 -2]]

Wedgie: ⟨⟨ 1 14 -2 20 -6 -44 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 713.218

error map: ⟨0.000 +11.263 -1.264 +4.738]

• POTE: ~2 = 1200.000, ~3/2 = 713.651

error map: ⟨0.000 +11.696 +4.800 +3.872]

Optimal ET sequence: 5, 27c, 32, 37

Badness (Sintel): 2.74

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 2401/2376

Mapping: [⟨1 0 -20 6 21], ⟨0 1 14 -2 -11]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 713.282
• POTE: ~2 = 1200.000, ~3/2 = 713.395

Optimal ET sequence: 5, 32, 37

Badness (Sintel): 2.26

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 91/90, 1573/1568

Mapping: [⟨1 0 -20 6 21 -25], ⟨0 1 14 -2 -11 18]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 713.309
• POTE: ~2 = 1200.000, ~3/2 = 713.500

Optimal ET sequence: 5, 32, 37

Badness (Sintel): 2.03

Ultramarine

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 3773/3645

Mapping: [⟨1 0 -20 6 -38], ⟨0 1 14 -2 26]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 713.395
• POTE: ~2 = 1200.000, ~3/2 = 713.791

Optimal ET sequence: 5e, 32e, 37, 79bce

Badness (Sintel): 2.58

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 91/90, 100/99, 847/845

Mapping: [⟨1 0 -20 6 -38 -25], ⟨0 1 14 -2 26 18]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 713.708
• POTE: ~2 = 1200.000, ~3/2 = 713.811

Optimal ET sequence: 5e, 32e, 37, 79bcef

Badness (Sintel): 1.89

Quasiultra

Quasiultra is to ultrapyth what quasisuper is to superpyth. It is the 27 & 32 temperament, mapping the ~5/4 to -18 fifths as a double diminished sixth (C–Abbb).

Subgroup: 2.3.5.7

Comma list: 64/63, 33614/32805

Mapping: [⟨1 0 31 6], ⟨0 1 -18 -2]]

Wedgie: ⟨⟨ 1 -18 -2 -31 -6 46 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 711.838

error map: ⟨0.000 +9.883 +0.608 +7.499]

• CWE: ~2 = 1200.000, ~3/2 = 711.543

error map: ⟨0.000 +9.588 +5.914 +8.088]

Optimal ET sequence: 27, 86bd, 113bcd, 140bbcd

Badness (Sintel): 3.34

Schism

See also: Schismatic family § Schism

Schism tempers out the schisma, mapping the ~5/4 to -8 fifths as a diminished fourth (C–Fb) as does any schismic temperament. 12edo is recommendable tuning, though 29edo (29d val), 41edo (41d val), and 53edo (53dd val) can be used.

Subgroup: 2.3.5.7

Comma list: 64/63, 360/343

Mapping: [⟨1 0 15 6], ⟨0 1 -8 -2]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 702.270

error map: ⟨0.000 +0.315 -4.471 +26.635]

• POTE: ~2 = 1200.000, ~3/2 = 701.556

error map: ⟨0.000 -0.399 +1.237 +28.062]

Wedgie: ⟨⟨ 1 -8 -2 -15 -6 18 ]]

Optimal ET sequence: 5c, 7c, 12

Badness (Sintel): 1.43

11-limit

Subgroup: 2.3.5.7.11

Comma list: 45/44, 64/63, 99/98

Mapping: [⟨1 0 15 6 13], ⟨0 1 -8 -2 -6]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~3/2 = 703.383
• POTE: ~2 = 1200.000, ~3/2 = 702.136

Optimal ET sequence: 5c, 7ce, 12, 29de

Badness (Sintel): 1.24

Beatles

For the 5-limit version, see Miscellaneous 5-limit temperaments #Beatles.

Subgroup: 2.3.5.7

Comma list: 64/63, 686/675

Mapping: [⟨1 1 5 4], ⟨0 2 -9 -4]]

Wedgie: ⟨⟨ 2 -9 -4 -19 -12 16 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~49/40 = 356.634

error map: ⟨0.000 +11.312 +3.984 +4.640]

• POTE: ~2 = 1200.000, ~49/40 = 355.904

error map: ⟨0.000 +9.853 +10.549 +7.558]

Optimal ET sequence: 10, 17c, 27, 64b, 91bcd, 118bccd

Badness (Sintel): 1.16

Music

• Beatles Improv by Herman Miller

11-limit

Subgroup: 2.3.5.7.11

Comma list: 64/63, 100/99, 686/675

Mapping: [⟨1 1 5 4 10], ⟨0 2 -9 -4 -22]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~49/40 = 356.719
• POTE: ~2 = 1200.000, ~49/40 = 356.140

Optimal ET sequence: 10e, 17cee, 27e, 64be, 91bcdee

Badness (Sintel): 1.51

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 64/63, 91/90, 100/99, 169/168

Mapping: [⟨1 1 5 4 10 4], ⟨0 2 -9 -4 -22 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~16/13 = 356.722
• POTE: ~2 = 1200.000, ~16/13 = 356.229

Optimal ET sequence: 10e, 27e, 37, 64be

Badness (Sintel): 1.25

Ringo

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 540/539

Mapping: [⟨1 1 5 4 2], ⟨0 2 -9 -4 5]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/9 = 355.992
• POTE: ~2 = 1200.000, ~11/9 = 355.419

Optimal ET sequence: 10, 17c, 27e

Badness (Sintel): 1.09

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 78/77, 91/90

Mapping: [⟨1 1 5 4 2 4], ⟨0 2 -9 -4 5 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~11/9 = 356.004
• POTE: ~2 = 1200.000, ~11/9 = 355.456

Optimal ET sequence: 10, 17c, 27e

Badness (Sintel): 0.935

Beetle

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 686/675

Mapping: [⟨1 1 5 4 -1], ⟨0 2 -9 -4 15]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~49/40 = 356.694
• POTE: ~2 = 1200.000, ~49/40 = 356.710

Optimal ET sequence: 10, 27, 37

Badness (Sintel): 1.92

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 55/54, 64/63, 91/90, 169/168

Mapping: [⟨1 1 5 4 -1 4], ⟨0 2 -9 -4 15 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~16/13 = 356.700
• POTE: ~2 = 1200.000, ~16/13 = 356.701

Optimal ET sequence: 10, 27, 37

Badness (Sintel): 1.40

Progress

For the 5-limit version, see Miscellaneous 5-limit temperaments #Progress.

Subgroup: 2.3.5.7

Comma list: 64/63, 392/375

Mapping: [⟨1 0 5 6], ⟨0 3 -5 -6]]

mapping generators: ~2, ~10/7

Wedgie: ⟨⟨ 3 -5 -6 -15 -18 0 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/7 = 638.782

error map: ⟨0.000 +14.391 +19.777 -1.518]

• POTE: ~2 = 1200.000, ~10/7 = 637.878

error map: ⟨0.000 +11.679 +24.297 +3.907]

Optimal ET sequence: 2, 13, 15, 32c

Badness (Sintel): 1.68

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 77/75

Mapping: [⟨1 0 5 6 4], ⟨0 3 -5 -6 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/7 = 638.846
• POTE: ~2 = 1200.000, ~10/7 = 637.915

Optimal ET sequence: 2, 13, 15, 32c, 47bc

Badness (Sintel): 1.03

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 66/65, 77/75

Mapping: [⟨1 0 5 6 4 0], ⟨0 3 -5 -6 -1 7]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/7 = 637.871
• POTE: ~2 = 1200.000, ~10/7 = 637.635

Optimal ET sequence: 15, 17c, 32cf

Badness (Sintel): 1.08

Progressive

Subgroup: 2.3.5.7.11.13

Comma list: 26/25, 56/55, 64/63, 77/75

Mapping: [⟨1 0 5 6 4 9], ⟨0 3 -5 -6 -1 -10]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~10/7 = 637.797
• POTE: ~2 = 1200.000, ~10/7 = 636.761

Optimal ET sequence: 2f, 15f, 17c

Badness (Sintel): 1.35

Fervor

For the 5-limit version, see Miscellaneous 5-limit temperaments #Fervor.

Subgroup: 2.3.5.7

Comma list: 64/63, 9604/9375

Mapping: [⟨1 4 -2 -2], ⟨0 -5 9 10]]

mapping generators: ~2, ~7/5

Wedgie: ⟨⟨ 5 -9 -10 -26 -30 2 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~7/5 = 577.353

error map: ⟨0.000 +11.278 +9.867 +4.709]

• POTE: ~2 = 1200.000, ~7/5 = 577.776

error map: ⟨0.000 +9.163 +13.673 +8.937]

Optimal ET sequence: 2, 25, 27

Badness (Sintel): 2.74

11-limit

Subgroup: 2.3.5.7.11

Comma list: 56/55, 64/63, 1350/1331

Mapping: [⟨1 4 -2 -2 3], ⟨0 -5 9 10 1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~7/5 = 577.296
• POTE: ~2 = 1200.000, ~7/5 = 577.850

Optimal ET sequence: 2, 25e, 27e

Badness (Sintel): 1.72

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 56/55, 64/63, 78/77, 507/500

Mapping: [⟨1 4 -2 -2 3 -4], ⟨0 -5 9 10 1 16]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~7/5 = 577.374
• POTE: ~2 = 1200.000, ~7/5 = 578.060

Optimal ET sequence: 2f, 27e

Badness (Sintel): 1.64

Sixix

For the 5-limit version, see Syntonic–chromatic equivalence continuum #Sixix (5-limit).

See also: Dual-fifth temperaments § Dual-3 Sixix

Sixix is related to the kleismic family in a way similar to the one between meantone and mavila. In both cases the generator is nominally a 6/5 and the complexity to generate major and minor chords is the same, but in sixix it is tuned extremely sharply, to the point where the 3rd and 5th harmonics are reached by going down instead of up, inverting the logic of chord construction.

Subgroup: 2.3.5.7

Comma list: 64/63, 3125/2916

Mapping: [⟨1 3 4 0], ⟨0 -5 -6 10]]

Wedgie: ⟨⟨ 5 6 -10 -2 -30 -40 ]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~6/5 = 337.519

error map: ⟨0.000 +10.449 -11.429 +6.366]

• POTE: ~2 = 1200.000, ~6/5 = 337.442

error map: ⟨0.000 +10.835 -10.965 +5.594]

Optimal ET sequence: 7, 18d, 25, 32

Badness (Sintel): 4.02

11-limit

Subgroup: 2.3.5.7.11

Comma list: 55/54, 64/63, 125/121

Mapping: [⟨1 3 4 0 6], ⟨0 -5 -6 10 -9]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~6/5 = 337.749
• POTE: ~2 = 1200.000, ~6/5 = 337.564

Optimal ET sequence: 7, 25e, 32

Badness (Sintel): 2.34

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 40/39, 55/54, 64/63, 125/121

Mapping: [⟨1 3 4 0 6 4], ⟨0 -5 -6 10 -9 -1]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~6/5 = 337.793
• POTE: ~2 = 1200.000, ~6/5 = 337.483

Optimal ET sequence: 7, 25e, 32f

Badness (Sintel): 1.91

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 40/39, 55/54, 64/63, 85/84, 125/121

Mapping: [⟨1 3 4 0 6 4 1], ⟨0 -5 -6 10 -9 -1 11]]

Optimal tunings:

• CTE: ~2 = 1200.000, ~6/5 = 337.629
• POTE: ~2 = 1200.000, ~6/5 = 337.513

Optimal ET sequence: 7, 25e, 32f

Badness (Sintel): 2.00