61edo: Difference between revisions

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== 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]] ({{nowrap|15 & 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap|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 ===

Line 100:

| {{Monzo| 97 -61 }}

| {{Mapping| 61 97 }}

| -1.97

| −1.97

| 1.97

| 10.0

Line 107:

| 20000/19683, 262144/253125

| {{Mapping| 61 97 142 }}

| -2.33

| −2.33

| 1.69

| 8.59

Line 114:

| 64/63, 2430/2401, 3125/3087

| {{mapping| 61 97 142 172 }} (61d)

| -3.06

| −3.06

| 1.93

| 9.84

Line 121:

| 126/125, 1029/1024, 2240/2187

| {{Mapping| 61 97 142 171 }} (61)

| -1.32

| −1.32

| 2.29

| 11.7

@@ Line 3: / Line 3: @@
 == 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]] ({{nowrap|15 &amp; 46}}), and is the [[optimal patent val]] for [[freivald]] ({{nowrap|24 &amp; 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 ===
@@ Line 100: / Line 100: @@
 | {{Monzo| 97 -61 }}
 | {{Mapping| 61 97 }}
-| -1.97
+| −1.97
 | 1.97
 | 10.0
@@ Line 107: / Line 107: @@
 | 20000/19683, 262144/253125
 | {{Mapping| 61 97 142 }}
-| -2.33
+| −2.33
 | 1.69
 | 8.59
@@ Line 114: / Line 114: @@
 | 64/63, 2430/2401, 3125/3087
 | {{mapping| 61 97 142 172 }} (61d)
-| -3.06
+| −3.06
 | 1.93
 | 9.84
@@ Line 121: / Line 121: @@
 | 126/125, 1029/1024, 2240/2187
 | {{Mapping| 61 97 142 171 }} (61)
-| -1.32
+| −1.32
 | 2.29
 | 11.7