Father
- 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.
As an exotemperament, there are a variety of acceptable tunings for father, ranging from roughly 720¢ to 800¢. However, since the main interest in an exotemperament is usually its mos scales, 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; this means that the most common tunings of father are between 720 and 750 cents. A potential reason to choose father as a temperament is to equate suspended chords and more conventional tertian chords (though options like trienstonic (4/3~9/7), blackwood (4/3~81/64), and fendo (4/3~13/10) are more accurate).
See Father family #Father and Trienstonic clan #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