205edo: Difference between revisions

Line 19:

The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[Wikipedia: Nicola Vicentino|Nicola Vicentino]]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx adaptive-JI scheme of 1555]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.

=== ~~Divisors~~ ===

=== Subsets and supersets ===

205 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also [[2460edo|2460/12]], so that a single step is precisely 12 [[mina]]s.

=== ~~Notation~~ ===

== Notation ==

=== Ups and downs ===

205edo can be notated with [[Ups and downs notation|ups and downs]] representing 5\205 = 1\41, and lifts and drops (written as / and \) representing 1\205. This has the advantage of building on a familiarity with 41edo, and is especially useful for [[Kite guitar|Kite guitarists]] who want to notate microbends more precisely.

{| class="wikitable"

|+

!0

! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! …

!1

!2

!3

!4

!5

!6

!7

!8

!9

!10

!11

!12

!13

!14

!15

!16

!~~...~~

|-

|P1

| P1 || /1 || //1 || ^\\1 || ^\1 || ^1 || ^/1 || ^//1 || v\\m2 || v\m2 || vm2 || v/m2 || v//m2 || \\m2 || \m2 || m2 || /m2 || …

|/1

|//1

|^\\1

|^\1

|^1

|^/1

|^//1

|v\\m2

|v\m2

|vm2

|v/m2

|v//m2

|\\m2

|\m2

|m2

|/m2

|~~...~~

|}

Line 128:

Line 95:

| 63\205<br>(19\205)

| 368.780<br>(111.220)

| ~~10125~~/~~8192~~<br>(16/15)

| 1024/891<br>(16/15)

| [[~~Qintosec~~]]

| [[Quintosec]]

|-

| 41

@@ Line 19: / Line 19: @@
 The 119\205 meantone fifth is extremely close to the 1/4-comma fifth, being only 0.007 cents sharp of it. Moreover the steps are half a cent flat of 1/4 of a syntonic comma. This makes the Tonal Plexus keyboard potentially of use in implementing [[Wikipedia: Nicola Vicentino|Nicola Vicentino]]'s [http://www.tonalsoft.com/monzo/vicentino/vicentino.aspx adaptive-JI scheme of 1555]. It also means that authentic 1/4-comma meantone tuning is, for practical purposes, available in 205 and allows for historically authentic performances of 1/4-comma music on the historically newfangled Tonal Plexus.
-=== Divisors ===
+=== Subsets and supersets ===
 factors into primes as 5 × 41, a fact some advocates of the division make use of; it is also [[2460edo|2460/12]], so that a single step is precisely 12 [[mina]]s.
-=== Notation ===
+== Notation ==
+=== Ups and downs ===
 edo can be notated with [[Ups and downs notation|ups and downs]] representing 5\205 = 1\41, and lifts and drops (written as / and \) representing 1\205. This has the advantage of building on a familiarity with 41edo, and is especially useful for [[Kite guitar|Kite guitarists]] who want to notate microbends more precisely.
 {| class="wikitable"
 |+
-!0
+! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9 !! 10 !! 11 !! 12 !! 13 !! 14 !! 15 !! 16 !! …
-!1
-!2
-!3
-!4
-!5
-!6
-!7
-!8
-!9
-!10
-!11
-!12
-!13
-!14
-!15
-!16
-!...
 |-
-|P1
+| P1 || /1 || //1 || ^\\1 || ^\1 || ^1 || ^/1 || ^//1 || v\\m2 || v\m2 || vm2 || v/m2 || v//m2 || \\m2 || \m2 || m2 || /m2 || …
-|/1
-|//1
-|^\\1
-|^\1
-|^1
-|^/1
-|^//1
-|v\\m2
-|v\m2
-|vm2
-|v/m2
-|v//m2
-|\\m2
-|\m2
-|m2
-|/m2
-|...
 |}
@@ Line 128: / Line 95: @@
 | 63\205<br>(19\205)
 | 368.780<br>(111.220)
-| 10125/8192<br>(16/15)
+| 1024/891<br>(16/15)
-| [[Qintosec]]
+| [[Quintosec]]
 |-
 | 41