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{{Redirect|Terrain|the scale|Terrain (scale)}}
{{Redirect|Terrain|the scale|Terrain (scale)}}


Subgroup: 2.9/5.9/7
Terrain, the 6 & 21 temperament in the 2.9/5.9/7 subgroup, is related to [[domain (temperament)|domain]]. It is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1–7/5–9/5 and 1–9/7–9/5 chords are characteristic.


Commas: 250047/250000
[[Subgroup]]: 2.9/5.9/7


Sval name: 6&21
[[Comma list]]: 250047/250000


Related temperament: [[Minortonic_family#Domain|domain]]
{{Mapping|legend=2| 3 0 -4 | 0 1 2 }}


[[Tp_tuning|POT2 generator]]: ~10/9 = 182.461
{{Mapping|legend=3| 3 10/9 -7/9 2/9 | 0 -2/3 -1/3 2/3 }}


[[Gencom|Gencom]]: [63/50 10/9; 250047/250000]
: [[gencom]]: [63/50 10/9; 250047/250000]


Gencom mapping: [<3 10/9 -7/9 2/9|, <0 -2/3 -1/3 2/3|]
[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.461


Mapping: [<3 0 -4|, <0 1 2|]
{{Optimal ET sequence|legend=1| 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558 }}


EDOs: {{EDOs|6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558}}
[[Tp tuning #T2 tuning|RMS error]]: 0.00844 cents
 
[[Tp_tuning#T2 tuning|RMS error]]: 0.00844 cents
 
Terrain is a remarkable temperament, in that while its complexity is low, it has no discernible error. The 1-7/5-9/5 and 1-9/7-9/5 chords are characteristic.


[[File:terrain_3558edo.png|alt=terrain_3558edo.png|terrain_3558edo.png]]
[[File:terrain_3558edo.png|alt=terrain_3558edo.png|terrain_3558edo.png]]


[[terrain9|Nine note albitonic scale]]
Scales:
 
* [[terrain9]] – 9-tone albitonic scale
[[terrain15|Fifteen note chromatic scale]]
* [[terrain15]] – 15-tone chromatic scale


[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ 5 5 1 mode of 33 equal (with video)] [http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play] by [[Chris_Vaisvil|Chris Vaisvil]]
; Music
[http://chrisvaisvil.com/5-5-1-mode-of-33-equal-with-video/ 5 5 1 mode of 33 equal (with video)] [http://micro.soonlabel.com/33edo/20130827_551of33.mp3 play] by [[Chris Vaisvil]]


== Petrtri ==
== Petrtri ==
Subgroup: 2.11/5.13/5
Petrtri can be described as 3 & 5 temperament in the 2.11/5.13/5 subgroup.


Comma: 2200/2197
[[Subgroup]]: 2.11/5.13/5


Svalname: 3&5
[[Comma list]]: 2200/2197


[[Tp_tuning|POT2 generator]]: ~13/10 = 455.012
{{Mapping|legend=2| 1 0 1| 0 3 1 }}


[[Gencom|Gencom]]: [2 13/10; 2200/2197]
{{Mapping|legend=3| 1 0 -1/3 0 -1/3 2/3 | 0 0 -4/3 0 5/3 -1/3 }}


Gencom mapping: [<1 0 -1/3 0 -1/3 2/3|, <0 0 -4/3 0 5/3 -1/3|]
: [[gencom]]: [2 13/10; 2200/2197]


Mapping: [<1 0 1|, <0 3 1|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 455.012


EDOs: {{EDOs|21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c}}
{{Optimal ET sequence|legend=1| 21, 29, 153, 182, 211, 240, 269, 298, 327, 356, 385, 509, 741c, 1126c }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.0749 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.0749 cents


[[File:petrtri_385edo.png|alt=petrtri_385edo.png|petrtri_385edo.png]]
[[File:petrtri_385edo.png|alt=petrtri_385edo.png|petrtri_385edo.png]]


[[petrtri5|Five note haplotonic scale]]
* [[petrtri5]] – 5-tone haplotonic scale
 
* [[petrtri8]] – 8-tone albitonic scale
[[petrtri8|Eight note albitonic scale]]
* [[petrtri13]] – 13-tone chromatic scale
 
[[petrtri13|Thirteen note chromatic scale]]


== Barton ==
== Barton ==
Barton may be described as the 11 &amp; 13 temperament. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.  
Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.  


[[Subgroup]]: 2.5.11.13
[[Subgroup]]: 2.5.11.13
Line 90: Line 85:


== Voltage ==
== Voltage ==
Subgroup: 2.7.13
Voltage is the 3 &amp; 7 temperament in the 2.7.13 subgroup.
 
Comma: 28672/28561


Sval name: 3&amp;7
[[Subgroup]]: 2.7.13


[[Tp_tuning|POT2 generator]]: ~16/13 = 357.677
[[Comma list]]: 28672/28561


[[TOP_tuning|POTT generator]]: ~16/13 = 1200 - 300 log₂(7) (357.794)
{{Mapping|legend=2| 1 4 4 | 0 -4 -1 }}


Gencom: [2, 16/13; 28672/28561]
{{Mapping|legend=3| 1 0 0 4 0 4 | 0 0 0 -4 0 -1 }}


Gencom mapping: [&lt;1 0 0 4 0 4|, &lt;0 0 0 -4 0 -1|]
: [[gencom]]: [2, 16/13; 28672/28561]


Mapping: [&lt;1 4 4|, &lt;0 -4 -1|]
[[Optimal tuning]]:  
* [[POTE]]: ~2 = 1\1, ~16/13 = 357.677
* [[TOP tuning|POTT]]: ~2 = 1\1, ~16/13 = 357.794 (1200 - 300 log<sub>2</sub>(7))


EDOS: {{EDOs|3, 7, 10, 27, 37, 47, 57, 104}}
{{Optimal ET sequence|legend=1| 3, 7, 10, 27, 37, 47, 57, 104 }}


RMS error: 0.1423
RMS error: 0.1423


== Tridec ==
== Tridec ==
Subgroup: 2.7/5.11/5.13/5
Tridec, the 5 &amp; 8 temperament in the 2.7/5.11/5.13/5 subgroup, extends [[petrtri]].


Commas: 847/845, 1001/1000
[[Subgroup]]: 2.7/5.11/5.13/5


Sval name: 5&amp;8
[[Comma list]]: 847/845, 1001/1000


[[Tp_tuning|POT2 generator]]: ~13/10 = 454.556
{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}


[[Gencom|Gencom]]: [2 13/10; 847/845 1001/1000]
{{Mapping|legend=3| 1 0 -3/4 5/4 -3/4 1/4 | 0 0 0 -4 3 1 }}


Gencom mapping: [&lt;1 0 -3/4 5/4 -3/4 1/4|, &lt;0 0 0 -4 3 1|]
: [[gencom]]: [2 13/10; 847/845 1001/1000]


Mapping: [&lt;1 2 0 1|, &lt;0 -4 3 1|]
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/10 = 454.556


EDOs: {{EDOs|5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc}}
{{Optimal ET sequence|legend=1| 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c, 953bc }}


[[Tp_tuning#T2 tuning|RMS error]]: 0.1613 cents
[[Tp tuning #T2 tuning|RMS error]]: 0.1613 cents


[[File:tridec_235edo.png|alt=tridec_235edo.png|tridec_235edo.png]]
[[File:tridec_235edo.png|alt=tridec_235edo.png|tridec_235edo.png]]


[[Tridec8|Eight note albitonic scale]]
* [[Tridec8]] – 8-tone albitonic scale
 
* [[Tridec13]] – 13-tone chromatic scale
[[Tridec13|Thirteen note chromatic scale]]


== Nestoria ==
== Nestoria ==
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