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{{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}}
{{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]].  
'''Father''' is a very coarse, simplistic, and inaccurate [[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.  
The main interest in this temperament is its [[mos scale]]s, as [[3L 2s|antipentic (3L 2s)]] and [[5L 3s|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).  


See [[Father family #Father]] and [[Trienstonic clan #Father]] for technical details.  
As an exotemperament, it has a large range of acceptable tunings, from roughly [[5edo|3\5]] (720{{c}}) to [[3edo|2\3]] (800{{c}}). However, only tunings between 3\5 and [[8edo|5\8]] (750{{c}}) generate oneirotonic scales.
 
See [[Father family #Father]] for technical details.  


== Interval chain ==
== Interval chain ==
In the following table, prime harmonics are labeled in '''bold'''.  
In the following table, odd harmonics 1–9 are labeled in '''bold'''.  


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! # !! Cents* !! Approximate Ratios
! # !! Cents* !! Approximate ratios
|-
|-
| 0 || 0.0 || '''1/1'''
| 0 || 0.0 || '''1/1'''
|-
|-
| 1 || 727.9 || '''3/2''', '''8/5''', 14/9
| 1 || 738.4 || '''3/2''', '''8/5''', 14/9
|-
| 2 || 276.9 || 6/5, 7/6, '''9/8'''
|-
| 3 || 1015.3 || '''7/4''', 9/5
|-
|-
| 2 || 255.7 || 6/5, 7/6, 9/8
| 4 || 553.8 || 7/5
|-
|-
| 3 || 983.6 || '''7/4''', 9/5
| 5 || 92.2 || 21/20
|}
|}
<nowiki>*</nowiki> in 7-limit CTE tuning
<nowiki />* In 7-limit CWE tuning


== Tunings ==
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 5-limit prime-optimized tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~3/2 = 737.469{{c}}
| CWE: ~3/2 = 742.290{{c}}
| POTE: ~3/2 = 743.986{{c}}
|}
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~3/2 = 727.855{{c}}
| CWE: ~3/2 = 738.443{{c}}
| POTE: ~3/2 = 742.002{{c}}
|}
=== Tuning spectrum ===
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
! Edo<br>Generator !! Eigenmonzo<br>(Unchanged-interval) !! Generator (¢) !! Comments
! Edo<br>generator !! Eigenmonzo<br>(Unchanged-interval)* !! Generator (¢) !! Comments
|-
|-
| 1\2 ||  || 600.0 || Lower bound of 5-odd-limit diamond monotone
| 1\2 ||  || 600.0 || Lower bound of 5-odd-limit diamond monotone
|-
|-
| || 4/3 || 702.0 || Untempered
| || 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)
|-
|-
|  || 8/7 || 722.9 ||
|  || 7/4 || 722.9 ||
|-
|-
|  || 7/6 || 733.4 ||
|  || 7/6 || 733.4 ||
Line 42: Line 80:
| 8\13 ||  || 738.5 ||
| 8\13 ||  || 738.5 ||
|-
|-
|  || 10/9 || 739.2 ||  
|  || 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 86:
| 5\8 ||  || 750.0 || Upper bound of 7-odd-limit diamond monotone
| 5\8 ||  || 750.0 || Upper bound of 7-odd-limit diamond monotone
|-
|-
| || 6/5 || 757.8 || 1/2-comma, 5-odd-limit minimax
| || 5/3 || 757.8 || 1/2-comma, 5-odd-limit minimax, 5-limit CEE & CSEE
|-
|-
| || 9/7 || 764.9 || 9-odd-limit minimax
| || 9/7 || 764.9 || 9-odd-limit minimax
Line 56: Line 94:
| || 5/4 || 813.7 || Full-comma
| || 5/4 || 813.7 || Full-comma
|}
|}
<nowiki />* Besides the octave
== Music ==
* ''[[Noodles adorno foucault]]''


[[Category:Temperaments]]
[[Category:Father| ]] <!-- Main article -->
[[Category:Father| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Exotemperaments]]
[[Category:Father family]]
[[Category:Father family]]
[[Category:Trienstonic clan]]
[[Category:Trienstonic clan]]
[[Category:Mint temperaments]]
[[Category:Mint temperaments]]
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