Xenharmonic Wiki

User:FloraC/Sandbox: Difference between revisions

← Older editNewer edit →
VisualWikitext
Update
Line 1: Line 1:
== Temperament pages ==
== Temperament pages ==
Comment: the example below looks great to me by the very formatting.
'''Reverting all the databoxes''', but the cleanup will continue


Note:  
Note:  
Line 48: Line 48:
{{see also| Wikipedia: Septimal meantone temperament }}
{{see also| Wikipedia: Septimal meantone temperament }}


The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the tritone, and [[21/16]], C-E#, the augmented third. Septimal meantone also tempers out the common 7-limit comma [[225/224]] and is in fact can be defined as the 7-limit temperament that tempers out 81/80 and 225/224.
The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the tritone, and [[21/16]], C-E#, the augmented third. Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.
 
Period: 1\1
 
Optimal ([[POTE]]) generator: ~3/2 = 696.495
 
EDO generators: [[12edo|7\12]], [[19edo|11\19]], [[31edo|18\31]], [[43edo|25\43]], [[50edo|29\50]]
 
Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
<div class="mw-collapsible-content">
 
{| class="wikitable right-1 right-2 sortable"
|+
|-
! #
! Cents<ref>octave-reduced</ref>
! class="unsortable"| Approximate ratios<ref>2.3.5.7, odd limit ≤ 27</ref>
|-
| 0
| 0.0
| 1/1
|-
| 1
| 696.5
| 3/2
|-
| 2
| 193.0
| 9/8, 10/9
|-
| 3
| 889.5
| 5/3
|-
| 4
| 386.0
| 5/4
|-
| 5
| 1082.5
| 15/8, 28/15
|-
| 6
| 579.0
| 7/5
|-
| 7
| 75.5
| 21/20, 25/24, 28/27
|-
| 8
| 772.0
| 14/9, 25/16
|-
| 9
| 268.5
| 7/6
|-
| 10
| 965.0
| 7/4
|-
| 11
| 461.4
| 21/16
|}
<references/></div></div>
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
Subgroup: 2.3.5.7
Line 132: Line 59:


{{Multival|legend=1| 1 4 10 4 13 12 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}
[[POTE generator]]: ~3/2 = 696.495


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 139: Line 68:


[[Tuning ranges]]:  
[[Tuning ranges]]:  
* valid range: [694.737, 700.000] (19 to 12)
* valid range: [694.737, 700.000] (11\19 to 7\12)
* nice range: [694.786, 701.955]
* nice range: [694.786, 701.955]
* strict range: [694.786, 700.000]
* strict range: [694.786, 700.000]


Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.


{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
Line 149: Line 78:
[[Badness]]: 0.0137
[[Badness]]: 0.0137


</div></div>
Scales: [[meantone5]], [[meantone7]], [[meantone12]]


== Archytas ==
== Archytas ==
{{main| Archytas }}


Period: 1\1
Subgroup: 2.3.5.7
 
Optimal ([[POTE]]) generators: ~3/2 = 709.3213, ~5/4 = 393.3747
 
EDO generators: [[15edo|(9, 5)\15]], [[22edo|(13, 7)\22]], [[27edo|(16, 9)\27]]
 
Scales: [[archytas12]], [[archytas12synch]]
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


[[Comma list]]: 64/63
[[Comma list]]: 64/63


Mapping: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]


Mapping [[generator]]s: ~2, ~3, ~5
Mapping generators: ~2, ~3, ~5


Map to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
Map to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
Line 177: Line 97:
: Angle (3/2, 5/4) = 90 degrees
: Angle (3/2, 5/4) = 90 degrees


Minimax tuning:  
[[POTE generator]]s: ~3/2 = 709.3213, ~5/4 = 393.3747
 
[[Minimax tuning]]:  
* [[7-odd-limit]]
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
Line 187: Line 109:
{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 49 }}
{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 49 }}


</div></div>
Scales: [[archytas12]], [[archytas12synch]]


== Commas ==
== Commas ==
Retrieved from "https://en.xen.wiki/w/User:FloraC/Sandbox"