Father: Difference between revisions

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{{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}}

'''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]].

'''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 ==

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"

|-

! # !! Cents* !! Approximate ~~Ratios~~

! # !! Cents* !! Approximate ratios

|-

| 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 ==

{| 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 ~~Generator~~ !! Eigenmonzo (Unchanged-interval) !! Generator (¢) !! Comments

! Edo generator !! Eigenmonzo (Unchanged-interval)* !! Generator (¢) !! Comments

|-

| 1\2 || || 600.0 || Lower bound of 5-odd-limit diamond monotone

|-

| || 4/3 || 702.0 || ~~Untempered~~

| || 3/2 || 702.0 || Pythagorean tuning

|-

| 3\5 || || 720.0 || Lower bound of 7-odd-limit diamond monotone 9-odd-limit diamond monotone (singleton)

|-

| || 8/7 || 722.9 ||

| || 7/4 || 722.9 ||

|-

| || 7/6 || 733.4 ||

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Line 80:

| 8\13 || || 738.5 ||

|-

| || 10/9 || 739.2 ||

| || 9/5 || 739.2 || 1/3-comma

|-

| || 7/5 || 745.6 || 7-odd-limit minimax

Line 48:

Line 86:

| 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

Line 56:

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| || 5/4 || 813.7 || Full-comma

|}

<nowiki />* Besides the octave

== Music ==

* ''[[Noodles adorno foucault]]''

~~[[Category:Temperaments]]~~

[[Category:Father| ]]

[[Category:Father| ]]

[[Category:Rank-2 temperaments]]

[[Category:Exotemperaments]]

[[Category:Father family]]

[[Category:Trienstonic clan]]

[[Category:Mint temperaments]]

@@ Line 1: / Line 1: @@
 {{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}}
-'''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]].
+'''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 ==
-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"
 |-
-! # !! Cents* !! Approximate Ratios
+! # !! Cents* !! Approximate ratios
 |-
 | 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 ==
+{| 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
+! 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
+| || 3/2 || 702.0 || Pythagorean tuning
 |-
 | 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 ||
@@ Line 42: / Line 80: @@
 | 8\13 ||  || 738.5 ||
 |-
-|  || 10/9 || 739.2 ||
+|  || 9/5 || 739.2 || 1/3-comma
 |-
 |  || 7/5 || 745.6 || 7-odd-limit minimax
@@ Line 48: / Line 86: @@
 | 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
@@ Line 56: / Line 94: @@
 | || 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:Trienstonic clan]]
 [[Category:Mint temperaments]]