Ben Johnston's notation: Difference between revisions

Line 10:

! Symbol !! Ratio !! Symbol !! Ratio

|-

| + || [[81/80]] || - || 80/81

| + || [[81/80]] || − || 80/81

|-

| ♯ || [[25/24]] || ♭ || 24/25

|-

| 7 || 35/36 || 7 || [[36/35]]

| 7 || 35/36 || 7 || [[36/35]]

|-

| ↑ || [[33/32]] || ↓ || 32/33

|-

| 13 || [[65/64]] || 13 || 64/65

| 13 || [[65/64]] || 13 || 64/65

|-

| 17 || [[51/50]] || 17 || 50/51

| 17 || [[51/50]] || 17 || 50/51

|-

| 19 || 95/96 || 19 || [[96/95]]

| 19 || 95/96 || 19 || [[96/95]]

|-

| 23 || [[46/45]] || 23 || 45/46

| 23 || [[46/45]] || 23 || 45/46

|-

| 29 || [[145/144]] || 29 || 144/145

| 29 || [[145/144]] || 29 || 144/145

|-

| 31 || [[31/30]] || 31 || 30/31

| 31 || [[31/30]] || 31 || 30/31

|}

Johnston combines the symbols 7 7 ↑ ↓ with ♯ ♭ if symbols from both categories are present.

Johnston combines the symbols 7 7 ↑ ↓ with ♯ ♭ if symbols from both categories are present.

A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.

A circle of just fifths is given by ... D♭−− A♭− E♭− B♭− F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.

Johnston's notation sacrifices some mathematical purity compared to [[Helmholtz-Ellis notation]], as it is based on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer inflection markers needed for music that emphasizes the 5-limit.

@@ Line 10: / Line 10: @@
 ! Symbol !! Ratio !! Symbol !! Ratio
 |-
-| + || [[81/80]] || - || 80/81
+| + || [[81/80]] || &#x2212; || 80/81
 |-
 | ♯ || [[25/24]] || ♭ || 24/25
 |-
-| 7 || 35/36 || <span style="display: inline-block; transform: rotate(180deg)">7</span> || [[36/35]]
+| 7 || 35/36 || <span style="display: inline-block; transform: rotate(180deg);">7</span> || [[36/35]]
 |-
 | ↑ || [[33/32]] || ↓ || 32/33
 |-
-| 13 || [[65/64]] || <span style="display: inline-block; transform: rotate(180deg)">13</span> || 64/65
+| 13 || [[65/64]] || <span style="display: inline-block; transform: rotate(180deg);">13</span> || 64/65
 |-
-| 17 || [[51/50]] || <span style="display: inline-block; transform: rotate(180deg)">17</span> || 50/51
+| 17 || [[51/50]] || <span style="display: inline-block; transform: rotate(180deg);">17</span> || 50/51
 |-
-| 19 || 95/96 || <span style="display: inline-block; transform: rotate(180deg)">19</span> || [[96/95]]
+| 19 || 95/96 || <span style="display: inline-block; transform: rotate(180deg);">19</span> || [[96/95]]
 |-
-| 23 || [[46/45]] || <span style="display: inline-block; transform: rotate(180deg)">23</span> || 45/46
+| 23 || [[46/45]] || <span style="display: inline-block; transform: rotate(180deg);">23</span> || 45/46
 |-
-| 29 || [[145/144]] || <span style="display: inline-block; transform: rotate(180deg)">29</span> || 144/145
+| 29 || [[145/144]] || <span style="display: inline-block; transform: rotate(180deg);">29</span> || 144/145
 |-
-| 31 || [[31/30]] || <span style="display: inline-block; transform: rotate(180deg)">31</span> || 30/31
+| 31 || [[31/30]] || <span style="display: inline-block; transform: rotate(180deg);">31</span> || 30/31
 |}
-Johnston combines the symbols 7 <span style="display: inline-block; transform: rotate(180deg)">7</span> ↑ ↓ with ♯ ♭ if symbols from both categories are present.
+Johnston combines the symbols 7 <span style="display: inline-block; transform: rotate(180deg);">7</span> ↑ ↓ with ♯ ♭ if symbols from both categories are present.
-A circle of just fifths is given by ... D♭-- A♭- E♭- B♭- F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.
+A circle of just fifths is given by ... D♭&#x2212;&#x2212; A♭&#x2212; E♭&#x2212; B♭&#x2212; F C G D A+ E+ B+ F♯++ ..., with a plus or minus added for every loop around the ends of the core F A C E G B D sequence. The odd harmonic series up to 31 starting on C is given by C G E B♭7 D F↑ A♭13 B C♯17 E♭19 F+7 F♯+23 G♯ A+ B♭29 B31.
 Johnston's notation sacrifices some mathematical purity compared to [[Helmholtz-Ellis notation]], as it is based on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer inflection markers needed for music that emphasizes the 5-limit.