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This section is largely taken from the article [http://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet] by [[Joseph Monzo]].  
This section is largely taken from the article [http://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet] by [[Joseph Monzo]].  


As noted in the opening section, trumpets are justly tuned. A trumpet is based on the [[harmonic series]], and each valve of the trumpet lowers the pitch. Later in this article, in the retuning section, valves are described to lower the pitch of the instrument in clean cent values (i.e. 100c, 200c, 300c). This works for a general basis of understanding retuning; however, valve tubing lengths are also tuned on a just intonation basis. In general, the first valve tubing is 1/8th the length of the main slide, the second 1/15th, the third 1/5th.  
As noted in the opening section, trumpets are justly tuned. A trumpet is based on the [[harmonic series]], and each valve of the trumpet lowers the pitch. Later in this article, in the retuning section, valves are described to lower the pitch of the instrument in clean cent values (i.e. 100c, 200c, 300c). This works for a general basis of understanding retuning; however, valve tubing lengths are also tuned on a just intonation basis. In general, the first valve tubing is 1/8th the length of the main slide, the second 1/15th, the third 1/5th. (For four-valve trumpets: if it is a quartertone trumpet, the fourth valve is usually 1/30th of the main slide; if it is an extended range trumpet, the fourth valve is usually 13/40th.)


From the article:
In the article, Monzo explains that combining valves will change these ratios to more complex values. In summary, the combinations themselves:
 
<blockquote sign="Joseph Monzo">
the 1st valve lowers the pitch by a 9:8 ratio (-~204 cents = "2 semitones"),
 
the 2nd by a 16:15 (-~112 cents = "1 semitone"), and
 
the 3rd by a 6:5 (-~316 cents = "3 semitones").
</blockquote>
 
Monzo continues, explaining that combining valves will change these ratios to more complex values. In summary, the combinations themselves:


<blockquote sign="Joseph Monzo (reformatted)">
{| class="wikitable center-all"
{| class="wikitable center-all"
|+Intonation of trumpet valve combinations
|+Intonation of standard trumpet valve combinations
! Valves
!Valves
! ΔLength
!ΔLength
! Frequency<br>Ratio
!Frequency<br>Ratio
! Cents
!Cents
|-
| 2
| +1/15
|15/16
| -112
|-
|-
| 12
|1
| +23/120
| +1/8
|8/9
| -204
|-
|12
| +23/120
| 120/143
| 120/143
| -304
| -304
|-
|-
| 23
|3
| +4/15
| +1/5
| 15/19
|5/6
| -316
|-
|23
| +4/15
|15/19
| -409
| -409
|-
|-
| 13
|13
| +13/40
| +13/40
| 40/53
| 40/53
| -487
| -487
|-
|-
| 123
|123
| +47/120
| +47/120
| 120/167
|120/167
| -572
| -572
|}
|}
</blockquote>


Observe that as valve combinations grow, the pitch sharpens from its target more and more (i.e. the valve combination 123 should target -600c but ends up 28 cents sharp). This is why, for large combinations like 13 and 123, it's advised in 12edo tuning to kick your third valve slide to accommodate this sharpening effect.
Observe that as valve combinations grow, the pitch sharpens from its target more and more (i.e. the valve combination 123 should target -600c but ends up 28 cents sharp). This is why, for large combinations like 13 and 123, it's advised in 12edo tuning to kick your third valve slide to accommodate this sharpening effect.


== Custom trumpets and quartertone trumpets ==
==Custom trumpets and quartertone trumpets==
There is a relatively short history of trumpets designed for the purpose of playing in extended tuning systems. The most popular microtonal trumpets are quartertone trumpets, which have a history of use in jazz and maqam.
There is a relatively short history of trumpets designed for the purpose of playing in extended tuning systems. The most popular microtonal trumpets are quartertone trumpets, which have a history of use in jazz and maqam.


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{{W|Ibrahim Maalouf}} is an active French-Lebanese jazz musician and trumpeter known for combining Middle Eastern folk with modern jazz music. His father, {{w|Nassim Maalouf}}, is credited with inventing a quartertone trumpet, which both he and Maalouf used. Ibrahim often uses his quartertone trumpet to play Arabic [[maqam]]s in his jazz music.
{{W|Ibrahim Maalouf}} is an active French-Lebanese jazz musician and trumpeter known for combining Middle Eastern folk with modern jazz music. His father, {{w|Nassim Maalouf}}, is credited with inventing a quartertone trumpet, which both he and Maalouf used. Ibrahim often uses his quartertone trumpet to play Arabic [[maqam]]s in his jazz music.


=== Commercial quartertone trumpets ===
===Commercial quartertone trumpets===
Professional trumpet technicians have historically created rotary valves which attach to the main tuning slide that lower the pitch of the trumpet by a quartertone.   
Professional trumpet technicians have historically created rotary valves which attach to the main tuning slide that lower the pitch of the trumpet by a quartertone.   


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In 2018, Monette shared a [https://www.monette.net/post/2018/04/20/our-first-ever-custom-quarter-tone-trumpet post] about their "first ever custom quarter-tone trumpet."
In 2018, Monette shared a [https://www.monette.net/post/2018/04/20/our-first-ever-custom-quarter-tone-trumpet post] about their "first ever custom quarter-tone trumpet."


=== Other ===
===Other ===
[https://www.youtube.com/watch?v=G4IRPPFnbEk Vasilis Nalbantis] created a xenharmonic trumpet, the "Nalbantis," designed to play maqams. Unlike other trumpets listed, the additional button is pressure-sensitive, allowing for more pitches, but less pitch accuracy, when playing the trumpet. The button changes the length of the tuning slide.
[https://www.youtube.com/watch?v=G4IRPPFnbEk Vasilis Nalbantis] created a xenharmonic trumpet, the "Nalbantis," designed to play maqams. Unlike other trumpets listed, the additional button is pressure-sensitive, allowing for more pitches, but less pitch accuracy, when playing the trumpet. The button changes the length of the tuning slide.


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A custom trumpet is the best and easiest way to play xenharmonic music; however, it certainly isn't always a practical option.  
A custom trumpet is the best and easiest way to play xenharmonic music; however, it certainly isn't always a practical option.  


=== Quartertones ===
===Quartertones===
==== Alternative fingerings ====
====Alternative fingerings ====
Quartertones for most notes can be approximated well with alternative fingerings and the use of the third valve slide.
Quartertones for most notes can be approximated well with alternative fingerings and the use of the third valve slide.


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|+Fingerings for quartertones on a standard trumpet
|+Fingerings for quartertones on a standard trumpet
! Note
! Note
| G
|G
| vG#
|vG#
| G#
|G#
| vA
| vA
| A
| A
| vA#
| vA#
| A#
| A#
| vB
|vB
| B
|B
| vC
|vC
| C
|C
| vC#
|vC#
| C#
|C#
| vD
|vD
| D
|D
| vD#
| vD#
| D#
|D#
| vE
|vE
| E
| E
| vF
|vF
| F
|F
| vF#
|vF#
| F#
|F#
| vG
|vG
| G
|G
|-
|-
! Fingering
!Fingering
| 0
|0
| 23 (S)
| 23 (S)
| 23
|23
| 3 (S)
|3 (S)
| 12
|12
| 123 (S)
|123 (S)
| 1
|1
| 13 (S)
|13 (S)
| 2
|2
| 23 (S)
| 23 (S)
| 0
| 0
| 3 (S)
|3 (S)
| 12
|12
| 13 (S)
|13 (S)
|1
|23 (S)
|2
|3 (S)
|0
|13 (S)
| 1
| 1
| 23 (S)
|123 (S)<br>or 23 (S)
| 2
|2
| 3 (S)
|13 (S)<br>or 3 (S)
| 0
|0
| 13 (S)
| 1
| 123 (S)<br>or 23 (S)
| 2
| 13 (S)<br>or 3 (S)
| 0
|}
|}
The (S) signifies that use of the third valve slide is necessary.
The (S) signifies that use of the third valve slide is necessary.


=== General xenharmonic music ===
===General xenharmonic music===
[[File:Adams A4 QT with adjusted third slide.jpg|alt=Adams A4 Quartertone with an adjusted third valve tubing for 19edo.|thumb|308x308px|Adams A4 Quartertone with an adjusted third valve tubing for 19edo.]]
[[File:Adams A4 QT with adjusted third slide.jpg|alt=Adams A4 Quartertone with an adjusted third valve tubing for 19edo.|thumb|308x308px|Adams A4 Quartertone with an adjusted third valve tubing for 19edo.]]


==== Retuning valves ====
====Retuning valves ====
On most trumpets, you can play [[edo]]s with fewer divisions than 12edo by retuning each valve slide individually. Because each valve's tubing is adjustable, you can lengthen them to lower the pitch by the number of cents corresponding to the semitones targeted by the valve. This method can be done similarly on quartertone trumpets; however, usually, the quartertone valve tubing (50 cents) cannot be adjusted.   
On most trumpets, you can play [[edo]]s with fewer divisions than 12edo by retuning each valve slide individually. Because each valve's tubing is adjustable, you can lengthen them to lower the pitch by the number of cents corresponding to the semitones targeted by the valve. This method can be done similarly on quartertone trumpets; however, usually, the quartertone valve tubing (50 cents) cannot be adjusted.   


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Keep in mind that this retuning method grows less accurate in the lower register, because trumpets are built on the [[harmonic series]]. Tuning systems with, for instance, a poor [[3/2]] (fifth), will now have a perfect 3/2 when played on the trumpet; similarly, notes between low C and middle G will be offsets of that perfect 3/2. This creates a sort of limited, quasi-[[just intonation]] sound (as brass instruments already are). You can fix this in real-time by adjusting your embouchure, "lipping" the notes.
Keep in mind that this retuning method grows less accurate in the lower register, because trumpets are built on the [[harmonic series]]. Tuning systems with, for instance, a poor [[3/2]] (fifth), will now have a perfect 3/2 when played on the trumpet; similarly, notes between low C and middle G will be offsets of that perfect 3/2. This creates a sort of limited, quasi-[[just intonation]] sound (as brass instruments already are). You can fix this in real-time by adjusting your embouchure, "lipping" the notes.


==== Alternative fingerings ====
====Alternative fingerings====
There are several fingering combinations for the trumpet that are not traditionally used simply because they do not approximate any pitch in 12edo. These notes can be used as a very limited set of additional pitches for xenharmonic music. These have limited functionality, but can be seen featured in small works, such as on Oli Parker's YouTube video, [https://www.youtube.com/watch?v=xQxHsx6JnJY ''The Xenharmonic Trumpet''].   
There are several fingering combinations for the trumpet that are not traditionally used simply because they do not approximate any pitch in 12edo. These notes can be used as a very limited set of additional pitches for xenharmonic music. These have limited functionality, but can be seen featured in small works, such as on Oli Parker's YouTube video, [https://www.youtube.com/watch?v=xQxHsx6JnJY ''The Xenharmonic Trumpet''].   


==== Lipping ====
==== Lipping====
A common way to bend pitches on trumpet is to "lip" the note - effectively moving your embouchure to crudely target a pitch other than the speed of air and tubing length would otherwise allow. This method can be used to play xenharmonic music and is often used in conjunction with other methods of playing xenharmonic music.
A common way to bend pitches on trumpet is to "lip" the note - effectively moving your embouchure to crudely target a pitch other than the speed of air and tubing length would otherwise allow. This method can be used to play xenharmonic music and is often used in conjunction with other methods of playing xenharmonic music.


== Notation ==
==Notation==
[[File:Quartertone Trumpet Fingerings.png|alt=A subset of a fingering chart for quartertone trumpet in Don Ellis notation.|thumb|259x259px|A subset of a fingering chart for quartertone trumpet in Don Ellis notation.]]
[[File:Quartertone Trumpet Fingerings.png|alt=A subset of a fingering chart for quartertone trumpet in Don Ellis notation.|thumb|259x259px|A subset of a fingering chart for quartertone trumpet in Don Ellis notation.]]
Like any other instrument, xenharmonic notation doesn't need to deviate far beyond the existing standards. However, with the trumpet in particular, there has been some discourse on specific types of notation which would allow for sight-reading quartertonal music, due to the implementation of a single button which "enables" quartertones.  
Like any other instrument, xenharmonic notation doesn't need to deviate far beyond the existing standards. However, with the trumpet in particular, there has been some discourse on specific types of notation which would allow for sight-reading quartertonal music, due to the implementation of a single button which "enables" quartertones.  
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For the Nalbantis trumpet, Vasilis created a simple notation system for 48 divisions, which can be seen in his piece, [https://www.youtube.com/watch?v=gPGdyt11O3w Χερουβικός Ύμνος].
For the Nalbantis trumpet, Vasilis created a simple notation system for 48 divisions, which can be seen in his piece, [https://www.youtube.com/watch?v=gPGdyt11O3w Χερουβικός Ύμνος].


== Music ==
==Music==
''Note: This is not a comprehensive list for many of the artists listed.''
''Note: This is not a comprehensive list for many of the artists listed.''


; Stephen Altoft
;Stephen Altoft
* [https://www.youtube.com/watch?v=fT4p57OdeeQ ''Time Dreaming''] (19edo)
*[https://www.youtube.com/watch?v=fT4p57OdeeQ ''Time Dreaming''] (19edo)
* [https://www.youtube.com/watch?v=ZvJB3wer5M8 ''Four Aspects'']
* [https://www.youtube.com/watch?v=ZvJB3wer5M8 ''Four Aspects'']
* [https://www.youtube.com/watch?v=YvxjifU3Qwk ''Gathering Meaning''] (19edo)
* [https://www.youtube.com/watch?v=YvxjifU3Qwk ''Gathering Meaning''] (19edo)


; Don Ellis
;Don Ellis
* [https://www.youtube.com/watch?v=DmPRS0rTOFQ ''Old Man's Tear''] (24edo)
* [https://www.youtube.com/watch?v=DmPRS0rTOFQ ''Old Man's Tear''] (24edo)
* [https://www.youtube.com/watch?v=pl0rrwYDmE8 ''Sladka Pitka''] (24edo)
*[https://www.youtube.com/watch?v=pl0rrwYDmE8 ''Sladka Pitka''] (24edo)
* [https://www.youtube.com/watch?v=7JkfNJWjqrg ''Indian Lady''] (24edo)
*[https://www.youtube.com/watch?v=7JkfNJWjqrg ''Indian Lady''] (24edo)


; [[luphoria]]
;[[luphoria]]
* [https://www.youtube.com/watch?v=Dcpkrci64Ms ''look''] (34edo with 17edo trumpet)
* [https://www.youtube.com/watch?v=Dcpkrci64Ms ''look''] (34edo with 17edo trumpet)


; Ibrahim Maalouf
;Ibrahim Maalouf
* [https://www.youtube.com/watch?v=9StA0PQXWzo ''Questions and Answers''] (24edo)
*[https://www.youtube.com/watch?v=9StA0PQXWzo ''Questions and Answers''] (24edo)
* [https://www.youtube.com/watch?v=wpg8jBFaj3c ''Beirut''] (24edo)
*[https://www.youtube.com/watch?v=wpg8jBFaj3c ''Beirut''] (24edo)
* [https://www.youtube.com/watch?v=y8ndu0CYwGU ''Feeling Good'' (feat. Dear Silas)] (24edo)
*[https://www.youtube.com/watch?v=y8ndu0CYwGU ''Feeling Good'' (feat. Dear Silas)] (24edo)


; Nassim Maalouf
;Nassim Maalouf
* [https://www.youtube.com/watch?v=jClH5PHiwZA ''Walid Gholmieh''] (24edo)
*[https://www.youtube.com/watch?v=jClH5PHiwZA ''Walid Gholmieh''] (24edo)


; Vasilis Nalbantis
;Vasilis Nalbantis
* [https://www.youtube.com/watch?v=gPGdyt11O3w ''Χερουβικός Ύμνος''] (48-tone unequal tuning)
*[https://www.youtube.com/watch?v=gPGdyt11O3w ''Χερουβικός Ύμνος''] (48-tone unequal tuning)
* [https://www.youtube.com/watch?v=WcWiUwBzwTU ''Βασίλης Ναλμπάντης''] (48-tone unequal tuning)
*[https://www.youtube.com/watch?v=WcWiUwBzwTU ''Βασίλης Ναλμπάντης''] (48-tone unequal tuning)
* [https://www.youtube.com/watch?v=Sdpgh2L-FAc ''Τεριρέμ''] (48-tone unequal tuning)
*[https://www.youtube.com/watch?v=Sdpgh2L-FAc ''Τεριρέμ''] (48-tone unequal tuning)


; Oli Parker
;Oli Parker
* [https://www.youtube.com/watch?v=xQxHsx6JnJY ''The Xenharmonic Trumpet'']
* [https://www.youtube.com/watch?v=xQxHsx6JnJY ''The Xenharmonic Trumpet'']


== External links ==
==External links==
* The Microtonal Trumpet, by Stephen Altoft, Donald Bousted — extended techniques, [[19edo]] trumpet
*The Microtonal Trumpet, by Stephen Altoft, Donald Bousted — extended techniques, [[19edo]] trumpet
** [http://web.archive.org/web/20161010053305/http://microtonaltrumpet.com/ The Microtonal Trumpet] (2007-2016, archived)
**[http://web.archive.org/web/20161010053305/http://microtonaltrumpet.com/ The Microtonal Trumpet] (2007-2016, archived)
** [http://web.archive.org/web/20220925135607/https://microtonalprojects.com/the-microtonal-trumpet/ The Microtonal Trumpet] on Microtonal Projects' BLOG (2017-2022, archived)
**[http://web.archive.org/web/20220925135607/https://microtonalprojects.com/the-microtonal-trumpet/ The Microtonal Trumpet] on Microtonal Projects' BLOG (2017-2022, archived)
* [http://web.archive.org/web/20140224083226/http://www.marcoblaauw.com:80/en/instruments Double Bell Trumpet] (2007-2014, archived), by Marco Blaauw — quartertone ([[24edo]]) trumpet
* [http://web.archive.org/web/20140224083226/http://www.marcoblaauw.com:80/en/instruments Double Bell Trumpet] (2007-2014, archived), by Marco Blaauw — quartertone ([[24edo]]) trumpet
* [http://themoderntrumpet.com/2020/12/01/microtones/ Microtones] on The Modern Trumpet, by Nathan Plante — extended techniques, quartertone (24edo) trumpet
*[http://themoderntrumpet.com/2020/12/01/microtones/ Microtones] on The Modern Trumpet, by Nathan Plante — extended techniques, quartertone (24edo) trumpet
* [http://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet], by Joseph L. Monzo (2003)
*[http://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet], by Joseph L. Monzo (2003)


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