Ben Johnston's notation: Difference between revisions
ArrowHead294 (talk | contribs) No edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 3: | Line 3: | ||
'''Ben Johnston's notation''' is a staff notation system for [[just intonation]] developed by composer [[Ben Johnston]], which supports prime harmonics up to and including 31. It is employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered only occasionally in his music. | '''Ben Johnston's notation''' is a staff notation system for [[just intonation]] developed by composer [[Ben Johnston]], which supports prime harmonics up to and including 31. It is employed in his String Quartet No. 9, although intervals exceeding the [[13-limit]] are encountered only occasionally in his music. | ||
The base notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D| | The base notes (white keys on the piano) are selected so that the chord {{dash|F, A, C, E, G, B, D|med}} consists of three stacked 4:5:6 chords, i.e. {{dash|F, A, C|med}}, {{dash|C, E, G|med}}, and {{dash|G, B, D|med}} are just major triads. This in turn makes {{dash|C, D, E, F, G, A, B, C|med}} a justly-intonated [[Zarlino|Ptolemy–Zarlino "intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals: | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|+ Accidentals in Johnston's notation | |+ style="font-size: 105%;" | Accidentals in Johnston's notation | ||
|- | |- | ||
! Symbol !! Ratio !! Symbol !! Ratio | ! Symbol !! Ratio !! Symbol !! Ratio | ||
| Line 35: | Line 35: | ||
A chain of just fifths is given by: | A chain of just fifths is given by: | ||
... {{dash|F♭<sup>−−</sup>, C♭<sup>−−</sup>, G♭<sup>−−</sup>, D♭<sup>−−</sup>, A♭<sup>−</sup>, E♭<sup>−</sup>, B♭<sup>−</sup>, F, C, G, D, A<sup>+</sup>, E<sup>+</sup>, B<sup>+</sup>, F♯<sup>++</sup>, C♯<sup>++</sup>, G♯<sup>++</sup>, D♯<sup>++</sup>, A♯<sup>+++</sup>, E♯<sup>+++</sup>, B♯<sup>+++</sup>| | ... {{dash|F♭<sup>−−</sup>, C♭<sup>−−</sup>, G♭<sup>−−</sup>, D♭<sup>−−</sup>, A♭<sup>−</sup>, E♭<sup>−</sup>, B♭<sup>−</sup>, F, C, G, D, A<sup>+</sup>, E<sup>+</sup>, B<sup>+</sup>, F♯<sup>++</sup>, C♯<sup>++</sup>, G♯<sup>++</sup>, D♯<sup>++</sup>, A♯<sup>+++</sup>, E♯<sup>+++</sup>, B♯<sup>+++</sup>|hair|long}} ... | ||
with a plus or minus added for every loop around the ends of the core {{dash|F, A, C, E, G, B, D| | with a plus or minus added for every loop around the ends of the core {{dash|F, A, C, E, G, B, D|med}} sequence. | ||
The odd harmonic series up to 31 starting on C is given by: | The odd harmonic series up to 31 starting on C is given by: | ||
{{dash|C, G, E, B♭<sup>7</sup>, D, F↑, A♭<sup>13</sup>, B, C♯<sup>17</sup>, E♭<sup>19</sup>, F<sup>7+</sup>, F♯<sup>23+</sup>, G♯, A<sup>+</sup>, B♭<sup>29</sup>, B<sup>31</sup>| | {{dash|C, G, E, B♭<sup>7</sup>, D, F↑, A♭<sup>13</sup>, B, C♯<sup>17</sup>, E♭<sup>19</sup>, F<sup>7+</sup>, F♯<sup>23+</sup>, G♯, A<sup>+</sup>, B♭<sup>29</sup>, B<sup>31</sup>|hair|long}}. | ||
Johnston's notation sacrifices some mathematical intuition compared to [[Helmholtz–Ellis notation]], as it bases the natural notes on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer accidentals needed for music that emphasizes the 5-limit. | Johnston's notation sacrifices some mathematical intuition compared to [[Helmholtz–Ellis notation]], as it bases the natural notes on 4:5:6 chords rather than [[Pythagorean tuning]]. This comes at the possible advantage of fewer accidentals needed for music that emphasizes the 5-limit. | ||
== See also == | == See also == | ||
* [[ | * [[Helmholtz–Ellis notation]] | ||
* [[Functional Just System]] | * [[Functional Just System]] | ||