43rd-octave temperaments

Fractional-octave temperaments

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← 42nd-octave • 43rd-octave • 44th-octave →

43edo was first noticed by the French Baroque acoustician Joseph Sauveur, and one step of 43edo has been called a meride. A temperament that augments 43edo's properties is hence named the meridic temperament. Likewise, the tuning is notable for having an extremely accurate approximation of 16/15. Thus, 43rd-octave temperaments may be used to preserve that mapping.

Meridic

See also: Mitonismic temperaments § Meridic

Subgroup: 2.3.5.7

Comma list: 5250987/5242880, 2202927104/2197265625

Mapping: [⟨43 0 168 257], ⟨0 1 -1 -2]]

Mapping generators: ~64/63, ~3

POTE generator: ~3/2 = 701.8376

Optimal ET sequence: 43, 172d, 215d, 258, 301, 559, 860, 2021d, 2881cd

Badness: 0.230038

11-limit

Subgroup: 2.3.5.7.11

Comma list: 41503/41472, 172032/171875, 1240029/1239040

Mapping: [⟨43 0 168 257 -192], ⟨0 1 -1 -2 5]]

POTE generator: ~3/2 = 701.8572

Optimal ET sequence: 258, 301, 559, 860

Badness: 0.111149

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2200/2197, 4096/4095, 21168/21125, 39366/39325

Mapping: [⟨43 0 168 257 -192 91], ⟨0 1 -1 -2 5 1]]

POTE generator: ~3/2 = 701.8510

Optimal ET sequence: 258, 301, 559, 860f

Badness: 0.071435

17-limit

Subgroup: 2.3.5.7.11.13.17

Comma list: 833/832, 1701/1700, 2200/2197, 4096/4095, 11016/11011

Mapping: [⟨43 0 168 257 -192 91 -165], ⟨0 1 -1 -2 5 1 5]]

POTE generator: ~3/2 = 701.8718

Optimal ET sequence: 258, 301, 559, 860f

Badness: 0.047292