Father

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This page is about the regular temperament. For the scale structure sometimes associated with it, see 5L 3s.

Father is a very coarse, simplistic, and inaccurate exotemperament. It tempers out 16/15, the classical diatonic semitone. This means the classical major third (5/4) is conflated with the perfect fourth (4/3), making it one that challenges the very notion of JI approximation, and playing harmony in it, it sounds only remotely reminiscent of the 5-limit no matter how it is tuned. If one could get their head around this way of hearing intervals, they may as well take a look at the 7-limit interpretation, where it tempers out 28/27 and 36/35.

The main interest in this temperament is its mos scales, as antipentic (3L 2s) and oneirotonic (5L 3s) are often chosen first, and only later is each step associated with a ratio consistent with this temperament. Another potential reason to choose this temperament is to equate suspended chords and more conventional tertian chords (though options like trienstonian (4/3~9/7), blackwood (4/3~81/64), and fendo (4/3~13/10) are more accurate).

As an exotemperament, it has a large range of acceptable tunings, from roughly 3\5 (720 ¢) to 2\3 (800 ¢). However, only tunings between 3\5 and 5\8 (750 ¢) generate oneirotonic scales.

See Father family #Father for technical details.

Interval chain

In the following table, odd harmonics 1–9 are labeled in bold.

# Cents* Approximate ratios
0 0.0 1/1
1 727.9 3/2, 8/5, 14/9
2 255.7 6/5, 7/6, 9/8
3 983.6 7/4, 9/5
4 511.4 7/5

* In 7-limit CTE tuning

Tunings

Tuning spectrum

Edo
Generator
Eigenmonzo
(Unchanged-interval)*
Generator (¢) Comments
1\2 600.0 Lower bound of 5-odd-limit diamond monotone
3/2 702.0 Pythagorean tuning
3\5 720.0 Lower bound of 7-odd-limit diamond monotone
9-odd-limit diamond monotone (singleton)
7/4 722.9
7/6 733.4
8\13 738.5
9/5 739.2 1/3-comma
7/5 745.6 7-odd-limit minimax
5\8 750.0 Upper bound of 7-odd-limit diamond monotone
5/3 757.8 1/2-comma, 5-odd-limit minimax
9/7 764.9 9-odd-limit minimax
2\3 800.0 Upper bound of 5-odd-limit diamond monotone
5/4 813.7 Full-comma

* Besides the octave

Music