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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


[[Category:Disambiguation pages]]
'''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]]

Latest revision as of 15:18, 19 July 2025

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 its mos scales, as 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. 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 3\5 (720 ¢) to 2\3 (800 ¢). However, only tunings between 3\5 and 5\8 (750 ¢) generate oneirotonic scales.

See Father family #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
1 738.4 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

* In 7-limit CWE tuning

Tunings

5-limit prime-optimized tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~3/2 = 737.469 ¢ CWE: ~3/2 = 742.290 ¢ POTE: ~3/2 = 743.986 ¢
7-limit prime-optimized tunings
Euclidean
Constrained Constrained & skewed Destretched
Tenney CTE: ~3/2 = 727.855 ¢ CWE: ~3/2 = 738.443 ¢ POTE: ~3/2 = 742.002 ¢

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, 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

* Besides the octave

Music

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