Father: Difference between revisions

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-'''Father''' may refer to:
+{{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}}
-* a low-accuracy 2.3.5 temperament that generates a 5L 3s scale; see [[Trienstonic clan #Father]]
-* (a misnomer for) [[5L 3s]] aka oneirotonic, a [[MOS]] scale and its associated musical framework
-{{Disambiguation}}
+'''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 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).
+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 ==
+In the following table, odd harmonics 1–9 are labeled in '''bold'''.
+{| class="wikitable center-1 right-2"
+|-
+! # !! Cents* !! Approximate ratios
+|-
+| 0 || 0.0 || '''1/1'''
+|-
+| 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
+|-
+| 4 || 553.8 || 7/5
+|-
+| 5 || 92.2 || 21/20
+|}
+<nowiki />* In 7-limit CWE tuning
+== 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 ===
+{| 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
+|-
+| || 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)
+|-
+|  || 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, 5-limit CEE & CSEE
+|-
+| || 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
+|}
+<nowiki />* Besides the octave
+== Music ==
+* ''[[Noodles adorno foucault]]''
+[[Category:Father| ]] <!-- Main article -->
+[[Category:Rank-2 temperaments]]
+[[Category:Exotemperaments]]
+[[Category:Father family]]
+[[Category:Trienstonic clan]]
+[[Category:Mint temperaments]]