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== Theory ==
== Theory ==
As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val| 61 97 142 '''171''' }} [[support]]s [[valentine]] (15 & 46), and is the [[optimal patent val]] for [[freivald]] (24 & 37) in the 7-, 11- and 13-limit. The 61d [[val]] {{val| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. [[Peter Kosmorsky]] has an interesting poem about its tuning profile, as follows.  
As an equal temperament, 61et is characterized by [[tempering out]] 20000/19683 ([[tetracot comma]]) and 262144/253125 ([[passion comma]]) in the 5-limit. In the 7-limit, the [[patent val]] {{val| 61 97 142 '''171''' }} [[support]]s [[valentine]] (15 & 46), and is the [[optimal patent val]] for [[freivald]] (24 & 37) in the 7-, 11- and 13-limit. The 61d [[val]] {{val| 61 97 142 '''172''' }} is a great tuning for [[modus]] and [[quasisuper]], and is a simple but out-of-tune edo tuning for [[parakleismic]]. [[Peter Kosmorsky]] has an interesting poem about its tuning profile, as follows.  


=== Introductory poem ===
=== Introductory poem ===
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== Notation ==
== Notation ==
=== Sagittal notation ===
This notation uses the same sagittal sequence as [[54edo #Sagittal notation|54edo]].


===Sagittal notation===
==== Evo flavor ====
This notation uses the same sagittal sequence as [[54edo#Sagittal notation|54-EDO]].
====Evo flavor====
 
<imagemap>
<imagemap>
File:61-EDO_Evo_Sagittal.svg
File:61-EDO_Evo_Sagittal.svg
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</imagemap>
</imagemap>


====Revo flavor====
==== Revo flavor ====
 
<imagemap>
<imagemap>
File:61-EDO_Revo_Sagittal.svg
File:61-EDO_Revo_Sagittal.svg
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</imagemap>
</imagemap>


====Evo-SZ flavor====
==== Evo-SZ flavor ====
 
<imagemap>
<imagemap>
File:61-EDO_Evo-SZ_Sagittal.svg
File:61-EDO_Evo-SZ_Sagittal.svg
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</imagemap>
</imagemap>


In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{Monzo| 97 -61 }}
| {{Mapping| 61 97 }}
| -1.97
| 1.97
| 10.0
|-
| 2.3.5
| 20000/19683, 262144/253125
| {{Mapping| 61 97 142 }}
| -2.33
| 1.69
| 8.59
|- style="border-top: double;"
| 2.3.5.7
| 64/63, 2430/2401, 3125/3087
| {{mapping| 61 97 142 172 }} (61d)
| -3.06
| 1.93
| 9.84
|- style="border-top: double;"
| 2.3.5.7
| 126/125, 1029/1024, 2240/2187
| {{Mapping| 61 97 142 171 }} (61)
| -1.32
| 2.29
| 11.7
|}


[[Category:Todo:add rank 2 temperaments table]]
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperament
|-
| 1
| 3\61
| 59.0
| 28/27
| [[Dodecacot]] (61de…)
|-
| 1
| 4\61
| 78.7
| 22/21
| [[Valentine]] (61)
|-
| 1
| 5\61
| 98.4
| 16/15
| [[Passion]] (61de…) / [[passionate]] (61)
|-
| 1
| 7\61
| 137.7
| 13/12
| [[Quartemka]] (61)
|-
| 1
| 9\61
| 177.0
| 10/9
| [[Modus]] (61de) / [[wollemia]] (61e)
|-
| 1
| 11\61
| 236.1
| 8/7
| [[Rodan]] (61, 7-limit, out of tune)
|-
| 1
| 16\61
| 314.8
| 6/5
| [[Parakleismic]] (61d)
|-
| 1
| 23\61
| 452.5
| 13/10
| [[Maja]] (61d)
|-
| 1
| 25\61
| 491.8
| 4/3
| [[Quasisuper]] (61d)
|-
| 1
| 28\61
| 550.8
| 11/8
| [[Freivald]] (61)
|}
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave
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