Fendo 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 parent comma of the fendo family is 40/39, which is tempered out in the rank-2 fendo (2.3.13/5) and rank-3 unintendo temperaments.

This article shows rank-2 extensions of fendo.

Fendo

Subgroup: 2.3.13/5

Comma list: 40/39

Edo join: 5 & 7

Mapping: [⟨1 1 2], ⟨0 1 -1]]

CWE tuning: ~2 = 1200 cents, ~3/2 = 710.153 cents

Badness: 0.111

Main extensions:

The concept of "fendo" tuning is well-represented by EDOs 8, 13, and 18. Each pair of these produces a rank-2 temperament in 2.3.5.13 separating 13/8 and 5/4 by 3/2 (octave-reduced), or equivalently tempering together 13/8 and 5/3. They differ from unintendo in that 5 is found somewhere along the chain of fifths rather than being its own generator.

Fendo-18

Subgroup: 2.3.5.13

Comma list: 40/39, 832/729

Edo join: 8 & 13

Mapping: [⟨1 1 -2 0], ⟨0 1 7 6]]

CWE tuning: ~2 = 1200 cents, ~3/2 = 742.362 cents

Badness: 2.330

To reach 5/4 you stack 7 generators and to reach 13/8 you stack six. 5/4 is tuned sharp; 13/8 is also sharp.

In terms of circle of fifths notation, 5 is the chromatic semitone and 13 is the augmented fourth.

Fendo-13

Subgroup: 2.3.5.13

Comma list: 40/39, 260/243

Edo join: 8 & 18

Mapping: [⟨2 2 1 5], ⟨0 1 3 2]]

CWE tuning: ~27/20 = 600 cents, ~3/2 = 726.538 cents

Badness: 1.064

To reach 5/4, you stack 3 generators; but note that the period is 600 cents. To reach 13/8, you stack 2 generators. 5/4 is flat; 13/8 is sharp.

Fendo-8

Subgroup: 2.3.5.13

Comma list: 40/39, 6656/6075

Edo join: 13 & 18

Mapping: [⟨1 1 6 8], ⟨0 1 -6 -7]]

CWE tuning: ~2 = 1200 cents, ~3/2 = 732.153 cents

Badness: 2.103

To reach 5/4, you go down 6 generators. To reach 13/8, you go down 7 generators. Both 5 and 13 are sharp.

In terms of circle of fifths notation, 5 is the diminished fifth and 13 is the diminished octave.