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{{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}} | |||
{{ | '''Father''' is a very coarse, simplistic [[exotemperament]]. It [[Tempering out|tempers out]] [[16/15]], the classical diatonic semitone. This means the [[5/4|classical major third (5/4)]] is conflated with the [[4/3|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 scale]]s, featuring [[3L 2s|antipentic (3L 2s)]] and [[5L 3s|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, prime harmonics are labeled in '''bold'''. | |||
{| class="wikitable center-1 right-2" | |||
|- | |||
! # !! 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 | |||
|} | |||
<nowiki>*</nowiki> in 7-limit CTE tuning | |||
== Tunings == | |||
=== Tuning spectrum === | |||
{| class="wikitable center-all left-4" | |||
|- | |||
! Edo<br>Generator !! Eigenmonzo<br>(Unchanged-interval) !! Generator (¢) !! Comments | |||
|- | |||
| 1\2 || || 600.0 || Lower bound of 5-odd-limit diamond monotone | |||
|- | |||
| || 4/3 || 702.0 || Untempered | |||
|- | |||
| 3\5 || || 720.0 || Lower bound of 7-odd-limit diamond monotone<br>9-odd-limit diamond monotone (singleton) | |||
|- | |||
| || 8/7 || 722.9 || | |||
|- | |||
| || 7/6 || 733.4 || | |||
|- | |||
| 8\13 || || 738.5 || | |||
|- | |||
| || 10/9 || 739.2 || | |||
|- | |||
| || 7/5 || 745.6 || 7-odd-limit minimax | |||
|- | |||
| 5\8 || || 750.0 || Upper bound of 7-odd-limit diamond monotone | |||
|- | |||
| || 6/5 || 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 | |||
|} | |||
[[Category:Temperaments]] | |||
[[Category:Father| ]] <!-- main article --> | |||
[[Category:Father family]] | |||
[[Category:Trienstonic clan]] | |||
[[Category:Mint temperaments]] | |||
Revision as of 08:17, 22 September 2023
- This page is about the regular temperament. For the scale structure sometimes associated with it, see 5L 3s.
Father is a very coarse, simplistic 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, prime harmonics 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 |
* 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 | |
| 4/3 | 702.0 | Untempered | |
| 3\5 | 720.0 | Lower bound of 7-odd-limit diamond monotone 9-odd-limit diamond monotone (singleton) | |
| 8/7 | 722.9 | ||
| 7/6 | 733.4 | ||
| 8\13 | 738.5 | ||
| 10/9 | 739.2 | ||
| 7/5 | 745.6 | 7-odd-limit minimax | |
| 5\8 | 750.0 | Upper bound of 7-odd-limit diamond monotone | |
| 6/5 | 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 |