Ben Johnston's notation - Revision history

TallKite: /* See also */ added color notation link

2025-07-16T05:20:17Z

ArrowHead294 at 18:29, 13 December 2024

2024-12-13T18:29:16Z

← Older revision		Revision as of 18:29, 13 December 2024
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	* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]		* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]

	{{~~Notation navbox~~}}		{{Navbox notation}}

	[[Category:Just intonation]]		[[Category:Just intonation]]

ArrowHead294 at 15:16, 10 December 2024

2024-12-10T15:16:29Z

← Older revision		Revision as of 15:16, 10 December 2024
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	== See also ==		== See also ==
	* [[~~Johnston-Copper~~ notation]]		* [[Johnston–Copper notation]]
	* [[~~Helmholtz–Ellis~~ notation]]		* [[Helmholtz–Ellis notation]]
	* [[Functional Just System]]		* [[Functional Just System]]

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	* [http://tonalsoft.com/enc/j/johnston.aspx Johnston notation] on the [[Tonalsoft encyclopedia]]		* [http://tonalsoft.com/enc/j/johnston.aspx Johnston notation] on the [[Tonalsoft encyclopedia]]
	* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]		* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]


	{{Notation navbox}}		{{Notation navbox}}

BudjarnLambeth: /* See also */ add link

2024-12-03T00:05:12Z

BudjarnLambeth: {{Notation navbox}}

2024-12-02T23:18:34Z

← Older revision		Revision as of 23:18, 2 December 2024
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	* [http://tonalsoft.com/enc/j/johnston.aspx Johnston notation] on the [[Tonalsoft encyclopedia]]		* [http://tonalsoft.com/enc/j/johnston.aspx Johnston notation] on the [[Tonalsoft encyclopedia]]
	* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]		* [http://www.marcsabat.com/pdfs/EJItext.pdf Marc Sabat - On Ben Johnston’s Notation and the Performance Practice of Extended Just Intonation]


			{{Notation navbox}}

	[[Category:Just intonation]]		[[Category:Just intonation]]

ArrowHead294 at 15:41, 15 November 2024

2024-11-15T15:41:12Z

← Older revision		Revision as of 15:41, 15 November 2024
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	'''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\|~~s=hair\|d=~~med}} consists of three stacked 4:5:6 chords, i.e. {{dash\|F, A, C\|~~s=hair\|d=~~med}}, {{dash\|C, E, G\|~~s=hair\|d=~~med}}, and {{dash\|G, B, D\|~~s=hair\|d=~~med}} are just major triads. This in turn makes {{dash\|C, D, E, F, G, A, B, C\|~~s=hair\|d=~~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:		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
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	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>\|s=hair\|d=long}} ...		... {{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\|~~s=hair\|d=~~med}} sequence.		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>\|s=hair\|d=long}}.		{{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]]		* [[Helmholtz–Ellis notation]]
	* [[Functional Just System]]		* [[Functional Just System]]

ArrowHead294 at 18:04, 21 May 2024

2024-05-21T18:04:25Z

← Older revision		Revision as of 18:04, 21 May 2024
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	{{Wikipedia\| Ben Johnston (composer) #Staff notation}}		{{Wikipedia\| Ben Johnston (composer) #Staff notation}}

	'''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]] 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\|s=hair\|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash\|F, A, C\|s=hair\|d=med}}, {{dash\|C, E, G\|s=hair\|d=med}}, and {{dash\|G, B, D\|s=hair\|d=med}} are just major triads. This in turn makes {{dash\|C, D, E, F, G, A, B, C\|s=hair\|d=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:		The base notes (white keys on the piano) are selected so that the chord {{dash\|F, A, C, E, G, B, D\|s=hair\|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash\|F, A, C\|s=hair\|d=med}}, {{dash\|C, E, G\|s=hair\|d=med}}, and {{dash\|G, B, D\|s=hair\|d=med}} are just major triads. This in turn makes {{dash\|C, D, E, F, G, A, B, C\|s=hair\|d=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:

ArrowHead294 at 19:29, 20 May 2024

2024-05-20T19:29:55Z

ArrowHead294 at 19:25, 20 May 2024

2024-05-20T19:25:40Z

← Older revision		Revision as of 19:25, 20 May 2024
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	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 ==
			* [[Helmholtz–Ellis notation]]
			* [[Functional Just System]]

	== External links ==		== External links ==

ArrowHead294 at 19:15, 20 May 2024

2024-05-20T19:15:38Z

← Older revision		Revision as of 19:15, 20 May 2024
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	{{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>\|s=hair\|d=long}}.		{{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>\|s=hair\|d=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.

	== External links ==		== External links ==

← Older revision		Revision as of 05:20, 16 July 2025
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	* [[Helmholtz–Ellis notation]]		* [[Helmholtz–Ellis notation]]
	* [[Functional Just System]]		* [[Functional Just System]]
			* [[Color notation]]

	== External links ==		== External links ==

← Older revision		Revision as of 00:05, 3 December 2024
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	== See also ==		== See also ==
			* [[Johnston-Copper notation]]
	* [[Helmholtz–Ellis notation]]		* [[Helmholtz–Ellis notation]]
	* [[Functional Just System]]		* [[Functional Just System]]

← Older revision		Revision as of 19:29, 20 May 2024
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 ~~natural~~ notes (white keys on the piano) are selected so that the chord {{dash\|F, A, C, E, G, B, D\|s=hair\|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash\|F, A, C\|s=hair\|d=med}}, {{dash\|C, E, G\|s=hair\|d=med}}, and {{dash\|G, B, D\|s=hair\|d=med}} are just major triads~~, which~~ makes {{dash\|C, D, E, F, G, A, B, C\|s=hair\|d=med}} a justly-intonated Ptolemy–Zarlino ~~[[Zarlino\|~~"intense" diatonic scale]]. Then the following accidentals are used for inflections, all of which denote [[superparticular ratio]]s or their reciprocals:		The base notes (white keys on the piano) are selected so that the chord {{dash\|F, A, C, E, G, B, D\|s=hair\|d=med}} consists of three stacked 4:5:6 chords, i.e. {{dash\|F, A, C\|s=hair\|d=med}}, {{dash\|C, E, G\|s=hair\|d=med}}, and {{dash\|G, B, D\|s=hair\|d=med}} are just major triads. This in turn makes {{dash\|C, D, E, F, G, A, B, C\|s=hair\|d=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"
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	\| + \|\| [[81/80]] \|\| − \|\| 80/81		\| + \|\| [[81/80]] \|\| − \|\| 80/81
	\|-		\|-
	\| ♯ \|\| [[25/24]] \|\| ♭ \|\| 24/25		\| ♯ \|\| [[25/24]] \|\| ♭ \|\| 24/25
	\|-		\|-
	\| 7 \|\| 35/36 \|\| {{invert\|7}} \|\| [[36/35]]		\| 7 \|\| 35/36 \|\| {{invert\|7}} \|\| [[36/35]]
	\|-		\|-
	\| ↑ \|\| [[33/32]] \|\| ↓ \|\| 32/33		\| ↑ \|\| [[33/32]] \|\| ↓ \|\| 32/33
	\|-		\|-
	\| 13 \|\| [[65/64]] \|\| {{invert\|13}} \|\| 64/65		\| 13 \|\| [[65/64]] \|\| {{invert\|13}} \|\| 64/65
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	\|}		\|}

	Johnston combines ~~the symbols~~ 7 {{invert\|7}} ~~↑ ↓~~ with sharps (♯) and flats (♭) if symbols from both categories are present.		Johnston combines numeric accidentals (7, {{invert\|7}}, ↑, ↓, 13, {{invert\|13}}, etc.) with sharps (♯) and flats (♭) if symbols from both categories are present.

	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> \|s=hair\|d=long}} ...		... {{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>\|s=hair\|d=long}} ...

	with a plus or minus added for every loop around the ends of the core {{dash\|F, A, C, E, G, B, D\|s=hair\|d=med}} sequence.		with a plus or minus added for every loop around the ends of the core {{dash\|F, A, C, E, G, B, D\|s=hair\|d=med}} sequence.
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	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>\|s=hair\|d=long}}.		{{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>\|s=hair\|d=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.