Negri extensions: Difference between revisions

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* '''Negric''' (10e & 19e) – tempering out 33/32, 49/48, and 77/75

* '''Negroni''' (10 & 19e) – tempering out 49/48, 55/54, and 225/224

The most important of these is undecimal negri, in which the generator, representing 13/12, 14/13, 15/14, and 16/15, goes one step further to stand in for ~12/11. The poor accuracy comes with a not overly complex mapping, as you can find ~16/11 just five generator steps away. Its evil cousin, negric, finds ~11/8 where negri will find ~15/11, which is of course conflated with [[4/3]].

The other pair of extensions are of higher complexity, but are well rewarded with better intonation. Negril finds ~11/8 where negroni will find ~15/11 and vice versa. They unite in [[29edo]], which can be recommended as a tuning for both.

Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to [[wilsec]]. This has the effect of slicing the generator in two, and is supported by [[20edo|20]], [[29edo|29]], and [[38edo|38df]].

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| 1

| 125.4

| 16/15, 15/14, 14/~~13, 13/12~~

| 13/12, 14/13, 15/14, 16/15

| 12/11

|

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| 2

| 250.7

| '''8/7'''~~, 7/6~~, 15/13

| 7/6, '''8/7''', 15/13

| 13/11

|

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| 6

| 752.1

| 14/9, 32/21~~, 20/13~~

| 14/9, 20/13, 32/21

|

@@ Line 4: / Line 4: @@
 * '''Negric''' (10e & 19e) – tempering out 33/32, 49/48, and 77/75
 * '''Negroni''' (10 & 19e) – tempering out 49/48, 55/54, and 225/224
+The most important of these is undecimal negri, in which the generator, representing 13/12, 14/13, 15/14, and 16/15, goes one step further to stand in for ~12/11. The poor accuracy comes with a not overly complex mapping, as you can find ~16/11 just five generator steps away. Its evil cousin, negric, finds ~11/8 where negri will find ~15/11, which is of course conflated with [[4/3]].
+The other pair of extensions are of higher complexity, but are well rewarded with better intonation. Negril finds ~11/8 where negroni will find ~15/11 and vice versa. They unite in [[29edo]], which can be recommended as a tuning for both.
 Another possible path which relates a sense of compromise is to temper out [[121/120]], leading to [[wilsec]]. This has the effect of slicing the generator in two, and is supported by [[20edo|20]], [[29edo|29]], and [[38edo|38df]].
@@ Line 33: / Line 37: @@
 | 1
 | 125.4
-| 16/15, 15/14, 14/13, 13/12
+| 13/12, 14/13, 15/14, 16/15
 | 12/11
 |
@@ Line 41: / Line 45: @@
 | 2
 | 250.7
-| '''8/7''', 7/6, 15/13
+| 7/6, '''8/7''', 15/13
 | 13/11
 |
@@ Line 73: / Line 77: @@
 | 6
 | 752.1
-| 14/9, 32/21, 20/13
+| 14/9, 20/13, 32/21
 |
 |