Father: Difference between revisions
CompactStar (talk | contribs) No edit summary |
+one more step in the interval chain table. Cleanup |
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== Interval chain == | == Interval chain == | ||
In the following table, | In the following table, odd harmonics 1–9 are labeled in '''bold'''. | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
| Line 18: | Line 18: | ||
| 1 || 727.9 || '''3/2''', '''8/5''', 14/9 | | 1 || 727.9 || '''3/2''', '''8/5''', 14/9 | ||
|- | |- | ||
| 2 || 255.7 || 6/5, 7/6, 9/8 | | 2 || 255.7 || 6/5, 7/6, '''9/8''' | ||
|- | |- | ||
| 3 || 983.6 || '''7/4''', 9/5 | | 3 || 983.6 || '''7/4''', 9/5 | ||
|- | |||
| 4 || 511.4 || 7/5 | |||
|} | |} | ||
<nowiki>*</nowiki> in 7-limit CTE tuning | <nowiki>*</nowiki> in 7-limit CTE tuning | ||
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| 1\2 || || 600.0 || Lower bound of 5-odd-limit diamond monotone | | 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<br>9-odd-limit diamond monotone (singleton) | | 3\5 || || 720.0 || Lower bound of 7-odd-limit diamond monotone<br>9-odd-limit diamond monotone (singleton) | ||
|- | |- | ||
| || | | || 7/4 || 722.9 || | ||
|- | |- | ||
| || 7/6 || 733.4 || | | || 7/6 || 733.4 || | ||
| Line 42: | Line 44: | ||
| 8\13 || || 738.5 || | | 8\13 || || 738.5 || | ||
|- | |- | ||
| || | | || 9/5 || 739.2 || 1/3-comma | ||
|- | |- | ||
| || 7/5 || 745.6 || 7-odd-limit minimax | | || 7/5 || 745.6 || 7-odd-limit minimax | ||
| Line 48: | Line 50: | ||
| 5\8 || || 750.0 || Upper bound of 7-odd-limit diamond monotone | | 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 | | || 9/7 || 764.9 || 9-odd-limit minimax | ||
Revision as of 09:25, 4 May 2024
- 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 in its mos scales, featuring antipentic (3L 2s) and oneirotonic (5L 3s) when properly tuned. It is likely the case that those scales are often chosen first, and only later is each step associated with a ratio consistent with this temperament.
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 |