Piano - Revision history

FloraC: Percussion -> percussive keyboard; style

2026-09-02T16:33:27Z

Percussion -> percussive keyboard; style

← Older revision		Revision as of 16:33, 2 September 2026
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	The '''piano''' is a ~~percussion~~ instrument, in which an action of felt-covered hammers strike strings stretched on a metal frame attached to a resonant soundboard.		The '''piano''' is a percussive [[keyboard]] instrument, in which an action of felt-covered hammers strike strings stretched on a metal frame attached to a resonant soundboard.

	The history of the piano is closely intertwined with the standardization of [[~~12-EDO~~]] in the West. The development of steel frames with precision machining gave them the necessary capacity to hold the high level of tension (~~18-30~~ tons) to remain in tune reliably over time.		The history of the piano is closely intertwined with the standardization of [[12edo]] in the West. The development of steel frames with precision machining gave them the necessary capacity to hold the high level of tension (18–30 tons) to remain in tune reliably over time.

	The piano can be used to play microtonal music in a variety of ways. A single piano's strings can be retuned; due to the risk of breaking strings, this is generally subject to a maximum of +/- 50 cents on each pitch.		The piano can be used to play microtonal music in a variety of ways. A single piano's strings can be retuned; due to the risk of breaking strings, this is generally subject to a maximum of +/- 50 cents on each pitch.
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	== See also ==		== See also ==
	* [[Keyboard]]
	* [[Fluid piano]]		* [[Fluid piano]]

	[[Category:Instruments]]		[[Category:Instruments]]

Xenjacob: Fleshed out summary + more links to pieces

2026-09-02T14:57:51Z

Fleshed out summary + more links to pieces

← Older revision		Revision as of 14:57, 2 September 2026
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	The '''piano''' can be used to play microtonal music in a variety of ways.		The '''piano''' is a percussion instrument, in which an action of felt-covered hammers strike strings stretched on a metal frame attached to a resonant soundboard.

			The history of the piano is closely intertwined with the standardization of [[12-EDO]] in the West. The development of steel frames with precision machining gave them the necessary capacity to hold the high level of tension (18-30 tons) to remain in tune reliably over time.

			The piano can be used to play microtonal music in a variety of ways. A single piano's strings can be retuned; due to the risk of breaking strings, this is generally subject to a maximum of +/- 50 cents on each pitch.

			For tunings of more than 12 pitches per octave, the difference accumulates. If one tunes the lower keys normally and works their way up a bigger scale, the higher strings sound increasingly inharmonic, more bell-like. For microtonal music to avoid this timbral distortion, multiple pianos must be used: a solo player can play two keyboards at a right angle, or many players can play many pianos.

	== Retuned standard piano ==		== Retuned standard piano ==
	[[Ben Johnston]] used pianos ~~with~~ just ~~tunings~~ for his [https://www.youtube.com/watch?v=h8ugV5e1n4Q Sonata for Microtonal Piano] (1964)		[[Ben Johnston]] used pianos tuned in 12-tone just intonation scales for his [https://www.youtube.com/watch?v=h8ugV5e1n4Q Sonata for Microtonal Piano] (1964)
	and [https://www.youtube.com/watch?v=Nx27dfey6iM Suite for Microtonal Piano] (1978).		and [https://www.youtube.com/watch?v=Nx27dfey6iM Suite for Microtonal Piano] (1978).

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	\|}		\|}

	[[Kyle Gann]]'s [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018) ~~uses~~ three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica"/>		[[Kyle Gann]]'s [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018) was written for three Disklavier pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica"/>

	{\| class="wikitable"		{\| class="wikitable"
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	\| 15/8 \|\| 1088 \|\| 225/128 \|\| 977 \|\| 117/64 \|\| 1044		\| 15/8 \|\| 1088 \|\| 225/128 \|\| 977 \|\| 117/64 \|\| 1044
	\|}		\|}
			[[Arnold Dreyblatt]] employed a 40-key miniature pianoforte in his [https://www.dreyblatt.net/musical-instruments Orchestra of Excited Strings], tuned to the 11-limit [[Dreyblatt tuning system]].

			== Two standard pianos a quarter-tone apart ==
			Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]]. Examples include [[Charles Ives]]' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924), [[Ivan Wyschnegradsky]]'s [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934), and John Eaton's [https://www.youtube.com/watch?v=PhCyVFRBbj4 Microtonal Fantasy] (1965).

			== Retuning two pianos ==
			In 1992, [[Georg Hajdu]] published a report of the "17 Tones" project<ref>[https://www.georghajdu.de/gh/fileadmin/material/articles/17_tones.ICMC.pdf Georg Hajdu's 1992 ICMC paper on the 17-tone piano project]</ref>, in which five composers wrote music featuring two player pianos tuned to [[17edo]].

			In 2006-2008, [[Jacob Barton]] had two surplus grand pianos tuned to 17edo and produced the [[SeventeenTonePianoProject\|Seventeen Tone Piano Project]], a series of four calls for works and concerts at Rice University.

			In 2008, [[Aaron Krister Johnson]] produced an event featuring two upright pianos tuned to [[19edo]] as part of Midwest MicroFest (now [[UnTwelve]]).

	Philip Golub's [https://phillipgolub.bandcamp.com/album/loop-7 Loop 7] (2025) uses two pianos retuned to play in [[22edo]].		Philip Golub's [https://phillipgolub.bandcamp.com/album/loop-7 Loop 7] (2025) uses two pianos retuned to play in [[22edo]].

	== ~~Two standard~~ pianos ~~a quarter-tone apart~~ ==		== Microtonal music with more than two pianos ==
	~~Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]]. Examples include [[Charles Ives]]'~~ [https://www.youtube.com/watch?v=~~EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces]~~ (~~1924~~) and [[~~Ivan Wyschnegradsky~~]]'s [https://www.youtube.com/watch?v=~~eS6U0I43OF4 24 Préludes]~~ (~~1934~~).
			* [https://www.youtube.com/watch?v=1L2vLH2KgSU Georg Friedrich Haas: ''Limited Approximations'' (2010)] for orchestra and 6 pianos tuned to 1/12th tones ([[72edo]]
			* [https://www.youtube.com/watch?v=kpHSC8eWWL8 Taylor Brook: ''Virtutes Occultae'' (2017)] for "six physically modeled virtual pianos, each with a unique tuning in an extended 11-limit just intonation

	== Custom-built pianos ==		== Custom-built pianos ==
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	There are some videos of Steve Cohn playing a Förster three-manual quarter-tone piano [https://www.youtube.com/watch?v=W7AqXnHjxd0 available] on [https://www.youtube.com/watch?v=PdP4epQIUrU YouTube].		There are some videos of Steve Cohn playing a Förster three-manual quarter-tone piano [https://www.youtube.com/watch?v=W7AqXnHjxd0 available] on [https://www.youtube.com/watch?v=PdP4epQIUrU YouTube].

	[[Julián Carrillo]] had pianos constructed in a range of tunings from 1/3-tones to 1/16-tones.<ref name="grove-microtonal"/> These used conventional piano keyboards, so the range decreases as the divisions of the tuning get smaller.<ref name="huygens-carrillo"/>		[[Julián Carrillo]] had pianos constructed in a range of tunings from 1/3-tones to 1/16-tones.<ref name="grove-microtonal"/> These ''pianos metamorfoseadores'', also known as Carrillo pianos, used conventional piano keyboards, so the range decreases as the divisions of the tuning get smaller.<ref name="huygens-carrillo"/>

	[[Michael Harrison]]'s harmonic piano plays a 24-note just scale and can be heard on [https://www.youtube.com/watch?v=yG69xptl1Bc From Ancient Worlds] (1992).		[[Michael Harrison]]'s harmonic piano plays a 24-note just scale and can be heard on [https://www.youtube.com/watch?v=yG69xptl1Bc From Ancient Worlds] (1992).
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	Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning"/>		Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning"/>

			[[Ivor Darreg]]'s 1967 essay [http://www.tonalsoft.com/sonic-arts/darreg/piano.htm Shall We Improve The Piano?] addresses head-on a number of issues faced by music-makers wanting to use acoustic pianos.

	== References ==		== References ==
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	</ref>		</ref>
	<ref name="gann-hyperchromatica">		<ref name="gann-hyperchromatica">
	Kyle Gann, [https://www.kylegann.com/Hyperchromatica.html Hyperchromatica]		Kyle Gann, [https://www.kylegann.com/Hyperchromatica.html Hyperchromatica] Note: this recording is an electronic realization, and the piece remains unperformed on acoustic pianos.
	</ref>		</ref>
	<ref name="jarvi-performing">		<ref name="jarvi-performing">

FloraC: - redundant whitespaces. + see also

2026-09-02T06:20:11Z

- redundant whitespaces. + see also

← Older revision		Revision as of 06:20, 2 September 2026
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	== Retuned standard piano ==		== Retuned standard piano ==
			[[Ben Johnston]] used pianos with just tunings for his [https://www.youtube.com/watch?v=h8ugV5e1n4Q Sonata for Microtonal Piano] (1964)
	[[Ben Johnston]] used pianos with just tunings for his
	[https://www.youtube.com/watch?v=h8ugV5e1n4Q Sonata for Microtonal Piano] (1964)
	and [https://www.youtube.com/watch?v=Nx27dfey6iM Suite for Microtonal Piano] (1978).		and [https://www.youtube.com/watch?v=Nx27dfey6iM Suite for Microtonal Piano] (1978).

	The table below shows the tunings used in		The table below shows the tunings used in [[Terry Riley]]'s [https://www.youtube.com/watch?v=TmgWeioQoTU&list=OLAK5uy_lI5rJKDFOeqWn2Yr82DVik6DhsENUTWgY&index=1 The Harp of New Albion] (1986), [[La Monte Young]]'s [https://lamonteyoung.bandcamp.com/album/the-well-tuned-piano-in-the-magenta-lights-87-v-10-6-43-00-pm-87-v-11-1-07-45-am-nyc The Well-Tuned Piano] (1964-present), and [[Michael Harrison]]'s [https://michaelharrison.bandcamp.com/album/revelation Revelation] (2007).
	[[Terry Riley]]'s [https://www.youtube.com/watch?v=TmgWeioQoTU&list=OLAK5uy_lI5rJKDFOeqWn2Yr82DVik6DhsENUTWgY&index=1 The Harp of New Albion] (1986),		<ref name="grady-riley"/>
	[[La Monte Young]]'s [https://lamonteyoung.bandcamp.com/album/the-well-tuned-piano-in-the-magenta-lights-87-v-10-6-43-00-pm-87-v-11-1-07-45-am-nyc The Well-Tuned Piano] (1964-present),		<ref name="gann-young"/>
	and [[Michael Harrison]]'s [https://michaelharrison.bandcamp.com/album/revelation Revelation] (2007).		<ref name="harrison-revelation"/>
	<ref name="grady-riley" />
	<ref name="gann-young" />
	<ref name="harrison-revelation" />

	{\| class="wikitable"		{\| class="wikitable"
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	\|}		\|}

	[[Kyle Gann]]'s [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018)		[[Kyle Gann]]'s [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018) uses three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica"/>
	uses three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica" />

	{\| class="wikitable"		{\| class="wikitable"
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	== Two standard pianos a quarter-tone apart ==		== Two standard pianos a quarter-tone apart ==
			Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]]. Examples include [[Charles Ives]]' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924) and [[Ivan Wyschnegradsky]]'s [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934).
	Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]].
	Examples include
	[[Charles Ives]]' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924) and
	[[Ivan Wyschnegradsky]]'s [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934).

	== Custom-built pianos ==		== Custom-built pianos ==
			Some pianos with multiple manuals have been made for playing quarter-tone music.<ref name="jarvi-performing" /> The table below, adapted from the Grove Dictionary of Musical Instruments, shows some of them.<ref name="grove-microtonal" />
	Some pianos with multiple manuals have been made for playing quarter-tone music.<ref name="jarvi-performing" />
	The table below, adapted from the Grove Dictionary of Musical Instruments, shows some of them.<ref name="grove-microtonal" />

	{\| class="wikitable"		{\| class="wikitable"
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	\|}		\|}

	There are some videos of Steve Cohn playing a Förster three-manual quarter-tone piano		There are some videos of Steve Cohn playing a Förster three-manual quarter-tone piano [https://www.youtube.com/watch?v=W7AqXnHjxd0 available] on [https://www.youtube.com/watch?v=PdP4epQIUrU YouTube].
	[https://www.youtube.com/watch?v=W7AqXnHjxd0 available] on
	[https://www.youtube.com/watch?v=PdP4epQIUrU YouTube].

	[[Julián Carrillo]] had pianos constructed in a range of tunings from 1/3-tones to 1/16-tones.<ref name="grove-microtonal" />		[[Julián Carrillo]] had pianos constructed in a range of tunings from 1/3-tones to 1/16-tones.<ref name="grove-microtonal"/> These used conventional piano keyboards, so the range decreases as the divisions of the tuning get smaller.<ref name="huygens-carrillo"/>
	These used conventional piano keyboards, so the range decreases as the divisions of the tuning get smaller.<ref name="huygens-carrillo" />

	[[Michael Harrison]]'s harmonic piano plays a 24-note just scale and can be heard on [https://www.youtube.com/watch?v=yG69xptl1Bc From Ancient Worlds] (1992).		[[Michael Harrison]]'s harmonic piano plays a 24-note just scale and can be heard on [https://www.youtube.com/watch?v=yG69xptl1Bc From Ancient Worlds] (1992).

	== Exciters for strings ==		== Exciters for strings ==
			By using some device to excite harmonics of the piano strings, it can be used to play notes higher up the harmonic series. For example, the [https://instrumentslab.org/project/magnetic-resonator-piano-2 magnetic resonator piano] uses electromagnets to excite the strings. This can be heard on Xenia Pestova Bennett's [https://diatriberecords.bandcamp.com/album/atomic-legacies Atomic Legacies] (2020).
	By using some device to excite harmonics of the piano strings, it can be used to play notes higher up the harmonic series.
	For example, the [https://instrumentslab.org/project/magnetic-resonator-piano-2 magnetic resonator piano] uses electromagnets to excite the strings.
	This can be heard on Xenia Pestova Bennett's [https://diatriberecords.bandcamp.com/album/atomic-legacies Atomic Legacies] (2020).

	== Further reading ==		== Further reading ==
			[[Hermann von Helmholtz\|Helmholtz]] discusses the acoustics of pianos in ''On the Sensations of Tone''.<ref name="helmholtz1895sensations"/>

	~~[[Hermann von Helmholtz\|Helmholtz]] discusses the acoustics of pianos in ''On the Sensations of Tone''.<ref name="helmholtz1895sensations" />~~		Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning"/>

	Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning" />

	== References ==		== References ==
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	== See also ==		== See also ==
			* [[Keyboard]]
	* [[Fluid piano]]		* [[Fluid piano]]

	[[Category:Instruments]]		[[Category:Instruments]]

Naren: More internal links

2026-09-01T21:28:46Z

Naren: Create page

2026-09-01T21:25:03Z

Create page

New page

The '''piano''' can be used to play microtonal music in a variety of ways.

== Retuned standard piano ==

[[Ben Johnston]] used pianos with just tunings for his
[https://www.youtube.com/watch?v=h8ugV5e1n4Q Sonata for Microtonal Piano] (1964)
and [https://www.youtube.com/watch?v=Nx27dfey6iM Suite for Microtonal Piano] (1978).

The table below shows the tunings used in
[[Terry Riley]]'s [https://www.youtube.com/watch?v=TmgWeioQoTU&list=OLAK5uy_lI5rJKDFOeqWn2Yr82DVik6DhsENUTWgY&index=1 The Harp of New Albion] (1986),
[[La Monte Young]]'s [https://lamonteyoung.bandcamp.com/album/the-well-tuned-piano-in-the-magenta-lights-87-v-10-6-43-00-pm-87-v-11-1-07-45-am-nyc The Well-Tuned Piano] (1964-present),
and [[Michael Harrison]]'s [https://michaelharrison.bandcamp.com/album/revelation Revelation] (2007).
<ref name="grady-riley" />
<ref name="gann-young" />
<ref name="harrison-revelation" />

{| class="wikitable"
|-
! colspan="2" | Harp of New Albion
! colspan="2" | The Well-Tuned Piano
! colspan="2" | Revelation
|-
! Ratio !! Cents !! Ratio !! Cents !! Ratio !! Cents
|-
| 1/1 || 0 || 1/1 || 0 || 1/1 || 0
|-
| 16/15 || 112 || 567/512 || 177 || 567/512 || 177
|-
| 9/8 || 204 || 9/8 || 204 || 9/8 || 204
|-
| 6/5 || 316 || 147/128 || 240 || 81/64 || 408
|-
| 5/4 || 386 || 21/16 || 471 || 21/16 || 471
|-
| 4/3 || 498 || 1323/1024 || 444 || 729/512 || 612
|-
| 64/45 || 610 || 189/128 || 675 || 189/128 || 675
|-
| 3/2 || 702 || 3/2 || 702 || 3/2 || 702
|-
| 8/5 || 814 || 49/32 || 738 || 27/16 || 906
|-
| 5/3 || 884 || 7/4 || 969 || 7/4 || 969
|-
| 16/9 || 996 || 441/256 || 942 || 243/128 || 1110
|-
| 15/8 || 1088 || 63/32 || 1173 || 63/32 || 1173
|}

Kyle Gann's [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018)
uses three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica" />

{| class="wikitable"
|-
! colspan="2" | Piano 1
! colspan="2" | Piano 2
! colspan="2" | Piano 3
|-
! Ratio !! Cents !! Ratio !! Cents !! Ratio !! Cents
|-
| 1/1 || 0 || 121/64 || 1103 || 63/32 || 1173
|-
| 135/128 || 92 || 33/32 || 53 || 65/64 || 27
|-
| 35/32 || 155 || 143/128 || 192 || 143/128 || 192
|-
| 9/8 || 204 || 75/64 || 275 || 75/64 || 275
|-
| 5/4 || 386 || 77/64 || 320 || 39/32 || 342
|-
| 21/16 || 471 || 165/128 || 440 || 81/64 || 408
|-
| 11/8 || 551 || 11/8 || 551 || 169/128 || 481
|-
| 3/2 || 702 || 45/32 || 590 || 91/64 || 609
|-
| 49/32 || 738 || 99/64 || 755 || 195/128 || 729
|-
| 105/64 || 857 || 25/16 || 773 || 13/8 || 841
|-
| 7/4 || 969 || 55/32 || 938 || 27/16 || 906
|-
| 15/8 || 1088 || 225/128 || 977 || 117/64 || 1044
|}

Philip Golub's [https://phillipgolub.bandcamp.com/album/loop-7 Loop 7] (2025) uses two pianos retuned to play in [[22edo]].

== Two standard pianos a quarter-tone apart ==

Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]].
Examples include
Charles Ives' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924) and
Ivan Wyschnegradsky's [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934).

== Custom-built pianos ==

Some pianos with multiple manuals have been made for playing quarter-tone music.<ref name="jarvi-performing" />
The table below, adapted from the Grove Dictionary of Musical Instruments, shows some of them.<ref name="grove-microtonal" />

{| class="wikitable"
! Inventor/builder !! Date !! Manuals
|-
| G.A. Behrens-Senegalden (Berlin) || 1892 || 2
|-
| Ivan Wyschnegradsky (Paris), built by Pleyel || 1922 || 2
|-
| Alois Hába (Berlin), Ivan Wyschnegradsky, built by Grotrian Steinweg || 1923-4 || 3
|-
| Moritz Stoehr (New York) || 1924 || 2
|-
| Alois Hába (Prague), built by Förster || 1924 || 2
|-
| Ivan Wyschnegradsky, built by Otto Pappe || 1924 || 3?
|-
| Alois Hába, built by Förster || 1925-9 || 3
|-
| Hans Barth (New York), built by George L. Weitz of Baldwin || 1928 || 2
|-
| Ivan Wyschnegradsky, built by Förster || 1928-9|| 3
|}

There are some videos of Steve Cohn playing a Förster three-manual quarter-tone piano
[https://www.youtube.com/watch?v=W7AqXnHjxd0 available] on
[https://www.youtube.com/watch?v=PdP4epQIUrU YouTube].

[[Julián Carrillo]] had pianos constructed in a range of tunings from 1/3-tones to 1/16-tones.<ref name="grove-microtonal" />
These used conventional piano keyboards, so the range decreases as the divisions of the tuning get smaller.<ref name="huygens-carrillo" />

[[Michael Harrison]]'s harmonic piano plays a 24-note just scale and can be heard on [https://www.youtube.com/watch?v=yG69xptl1Bc From Ancient Worlds] (1992).

== Exciters for strings ==

By using some device to excite harmonics of the piano strings, it can be used to play notes higher up the harmonic series.
For example, the [https://instrumentslab.org/project/magnetic-resonator-piano-2 magnetic resonator piano] uses electromagnets to excite the strings.
This can be heard on Xenia Pestova Bennett's [https://diatriberecords.bandcamp.com/album/atomic-legacies Atomic Legacies] (2020).

== Further reading ==

Helmholtz discusses the acoustics of pianos in ''On the Sensations of Tone''.<ref name="helmholtz1895sensations" />

Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning" />

== References ==
<references>
<ref name="gann-young">
Kyle Gann, [https://www.kylegann.com/wtp.html La Monte Young's The Well-Tuned Piano]
</ref>
<ref name="harrison-revelation">
Michael Harrison, [https://www.michaelharrison.com/documents/lattices/revelation-tuning.pdf Revelation Tuning]
</ref>
<ref name="grady-riley">
Kraig Grady, [https://anaphoriasouth.blogspot.com/2016/02/rileys-5-limit-tuning-for-harp-of-new.html Riley's 5 limit tuning for "Harp of New Albion"]
</ref>
<ref name="gann-hyperchromatica">
Kyle Gann, [https://www.kylegann.com/Hyperchromatica.html Hyperchromatica]
</ref>
<ref name="jarvi-performing">
Elisa Järvi, [https://dipproceedings.lmta.lt/wp-content/uploads/files/jarvi.pdf Performing on the new quarter-tone piano – re-discovering repertoire]
</ref>
<ref name="grove-microtonal">
Hugh Davies/Alexander Bonus, [https://archive.org/details/grovedictionaryo0003unse_w4m2/page/461/ Microtonal instruments]. The Grove Dictionary of Musical Instruments, Second Edition, 2014, p.461.
</ref>
<ref name="huygens-carrillo">
[https://huygens-fokker.org/en/carrillopiano Carrillo piano], Huygens-Fokker Foundation
</ref>
<ref name="helmholtz1895sensations">
Helmholtz and Ellis, [https://archive.org/details/onsensationsofto00helmrich/ On the Sensations of Tone]. Longmans, Green, and Co, 1895.
</ref>
<ref name="jorgensen1991tuning">
Owen H. Jorgensen, [https://archive.org/details/tuningcontaining0000jorg Tuning]. Michigan State University Press, 1991.
</ref>
</references>

== See also ==
* [[Fluid piano]]

[[Category:Instruments]]

← Older revision		Revision as of 21:28, 1 September 2026
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	Kyle Gann's [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018)		[[Kyle Gann]]'s [https://othermindsrecords.bandcamp.com/album/hyperchromatica Hyperchromatica] (2018)
	uses three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica" />		uses three pianos with the just tunings shown in the table below.<ref name="gann-hyperchromatica" />

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	Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]].		Two standard pianos tuned a quarter-tone apart can be used to play music in [[24edo]].
	Examples include		Examples include
	Charles Ives' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924) and		[[Charles Ives]]' [https://www.youtube.com/watch?v=EXJPnUZhETg&list=PLB6BCC23A3D7CA817&index=1 Three Quarter-Tone Pieces] (1924) and
	Ivan Wyschnegradsky's [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934).		[[Ivan Wyschnegradsky]]'s [https://www.youtube.com/watch?v=eS6U0I43OF4 24 Préludes] (1934).

	== Custom-built pianos ==		== Custom-built pianos ==
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	== Further reading ==		== Further reading ==

	Helmholtz discusses the acoustics of pianos in ''On the Sensations of Tone''.<ref name="helmholtz1895sensations" />		[[Hermann von Helmholtz\|Helmholtz]] discusses the acoustics of pianos in ''On the Sensations of Tone''.<ref name="helmholtz1895sensations" />

	Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning" />		Owen H. Jorgensen's ''Tuning'' discusses historical temperaments used on the piano.<ref name="jorgensen1991tuning" />