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Father: Difference between revisions

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**Imported revision 252490896 - Original comment: **
 
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m Separate the comma groups with ";" as elsewhere; link 16/15 in the 7-limit group like every other ratio on the page
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{About|the regular temperament|the scale structure sometimes associated with it|5L 3s}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
{{Infobox regtemp
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-09-09 18:09:51 UTC</tt>.<br>
| Title = Father
: The original revision id was <tt>252490896</tt>.<br>
| Subgroups = 2.3.5, 2.3.5.7
: The revision comment was: <tt></tt><br>
| Comma basis = [[16/15]] (5-limit); <br>[[16/15]], [[28/27]] (7-limit)
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Edo join 1 = 2(d) | Edo join 2 = 3(d)
<h4>Original Wikitext content:</h4>
| Mapping = 1; 1 -1 3
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">See [[Trienstonic clan]].</pre></div>
| Generators = 3/2 | Generators tuning = 738.443 | Optimization method = CWE
<h4>Original HTML content:</h4>
| MOS scales = [[1L 1s]], [[2L 1s]], [[3L 2s]]
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Father&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Trienstonic%20clan"&gt;Trienstonic clan&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
| Pergen = (P8, P5)
| Odd limit 1 = 5 | Mistuning 1 = 55.9 | Complexity 1 = 3
| Odd limit 2 = 7 | Mistuning 2 = 68.1 | Complexity 2 = 5
}}
'''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, which are the primary structure it represents as an exotemperament.
 
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 norm-based 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 norm-based 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]]
Retrieved from "https://en.xen.wiki/w/Father"