Ben Johnston's notation: Difference between revisions
ArrowHead294 (talk | contribs) No edit summary |
ArrowHead294 (talk | contribs) No edit summary |
||
| Line 3: | Line 3: | ||
'''Ben Johnston's notation''' is a staff notation system for [[just intonation]]. [[Ben Johnston]] developed it up to the [[31-limit]], employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered mostly incidentally in his music. | '''Ben Johnston's notation''' is a staff notation system for [[just intonation]]. [[Ben Johnston]] developed it up to the [[31-limit]], employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered mostly incidentally in his music. | ||
The base notes (white keys on the piano) are selected so that the chord | The base notes (white keys on the piano) are selected so that the chord F–A–C–E–G–B–D consists of three stacked 4:5:6 chords, i.e. F–A–C, C–E–G, and G–B–D are just major triads. Then the following accidentals are used for inflections, all of which denote [[superparticular]] ratios or their reciprocals: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Johnston notation | |+ Accidentals in Ben Johnston's notation | ||
|- | |- | ||
! Symbol !! Ratio !! Symbol !! Ratio | ! Symbol !! Ratio !! Symbol !! Ratio | ||
| Line 14: | Line 14: | ||
| ♯ || [[25/24]] || ♭ || 24/25 | | ♯ || [[25/24]] || ♭ || 24/25 | ||
|- | |- | ||
| 7 || 35/36 || | | 7 || 35/36 || {{invert|7}} || [[36/35]] | ||
|- | |- | ||
| ↑ || [[33/32]] || ↓ || 32/33 | | ↑ || [[33/32]] || ↓ || 32/33 | ||
|- | |- | ||
| 13 || [[65/64]] || | | 13 || [[65/64]] || {{invert|13}} || 64/65 | ||
|- | |- | ||
| 17 || [[51/50]] || | | 17 || [[51/50]] || {{invert|17}} || 50/51 | ||
|- | |- | ||
| 19 || 95/96 || | | 19 || 95/96 || {{invert|19}} || [[96/95]] | ||
|- | |- | ||
| 23 || [[46/45]] || | | 23 || [[46/45]] || {{invert|23}} || 45/46 | ||
|- | |- | ||
| 29 || [[145/144]] || | | 29 || [[145/144]] || {{invert|29}} || 144/145 | ||
|- | |- | ||
| 31 || [[31/30]] || | | 31 || [[31/30]] || {{invert|31}} || 30/31 | ||
|} | |} | ||
Johnston combines the symbols 7 | Johnston combines the symbols 7 {{invert|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. | ||
Revision as of 15:16, 9 May 2024
Ben Johnston's notation is a staff notation system for just intonation. Ben Johnston developed it up to the 31-limit, employed in his String Quartet No. 9, although intervals exceeding the 13-limit are encountered mostly incidentally in his music.
The base notes (white keys on the piano) are selected so that the chord F–A–C–E–G–B–D consists of three stacked 4:5:6 chords, i.e. F–A–C, C–E–G, and G–B–D are just major triads. Then the following accidentals are used for inflections, all of which denote superparticular ratios or their reciprocals:
| Symbol | Ratio | Symbol | Ratio |
|---|---|---|---|
| + | 81/80 | − | 80/81 |
| ♯ | 25/24 | ♭ | 24/25 |
| 7 | 35/36 | 7 | 36/35 |
| ↑ | 33/32 | ↓ | 32/33 |
| 13 | 65/64 | 13 | 64/65 |
| 17 | 51/50 | 17 | 50/51 |
| 19 | 95/96 | 19 | 96/95 |
| 23 | 46/45 | 23 | 45/46 |
| 29 | 145/144 | 29 | 144/145 |
| 31 | 31/30 | 31 | 30/31 |
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.
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.