51edo: Difference between revisions

Line 5:

51 = 3 × 17, and 51edo shares its [[3/2|fifth]] with [[17edo]].

Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an [[6L 1s~~|archeotonic~~]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.

Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an archeotonic [[6L 1s]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.

Alternatively, using the 51c val {{val| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. The 51cd val {{val| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]].

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! Degrees

! [[Cent]]s

! colspan="3" | [[Ups and ~~Downs Notation~~]]

! colspan="3" | [[Ups and downs notation]]

|-

| 0

Line 405:

| 1029/1024, {{monzo| 17 -16 3 }}

| {{Mapping| 51 81 143 }}

| -0.339

| −0.339

| 1.63

| 6.92

Line 412:

| 128/125, {{monzo| -13 17 -6 }}

| {{Mapping| 51 81 119 }} (51c)

| -2.789

| −2.789

| 2.41

| 10.3

@@ Line 5: / Line 5: @@
 = 3 × 17, and 51edo shares its [[3/2|fifth]] with [[17edo]].
-Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an [[6L 1s|archeotonic]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.
+Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an archeotonic [[6L&nbsp;1s]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.
 Alternatively, using the 51c val {{val| 51 81 '''119''' 143 }}, the [[5/4]] is mapped to 1\3 (400 cents), [[support]]ing [[augmented]]. In the 7-limit it tempers out [[245/243]] and supports [[hemiaug]] and [[rodan]]. The 51cd val {{val| 51 81 '''119''' '''144''' }} takes the same [[7/4]] from 17edo, and supports [[augene]].
@@ Line 22: / Line 22: @@
 ! Degrees
 ! [[Cent]]s
-! colspan="3" | [[Ups and Downs Notation]]
+! colspan="3" | [[Ups and downs notation]]
 |-
 | 0
@@ Line 405: / Line 405: @@
 | 1029/1024, {{monzo| 17 -16 3 }}
 | {{Mapping| 51 81 143 }}
-| -0.339
+| −0.339
 | 1.63
 | 6.92
@@ Line 412: / Line 412: @@
 | 128/125, {{monzo| -13 17 -6 }}
 | {{Mapping| 51 81 119 }} (51c)
-| -2.789
+| −2.789
 | 2.41
 | 10.3