Trumpet: Difference between revisions

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While the trumpet is generally designed for 12edo, there are several ways to play in other tuning systems – by custom trumpets (generally quartertone trumpets), non-standard fingerings, adjusting tuning slides, or by pitch bending via embouchure.

== Intonation ==

This section is largely supported by 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.

From Joseph Monzo:<blockquote>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. I don't intend to repeat his work beat for beat, so consider reading that article. Regardless, the combinations themselves:

{| class="wikitable"

|+Intonation of trumpet valve combinations

!Valves

!Ratio

!Cents

|-

|12

|143:120

| -304

|-

|23

|19:15

| -409

|-

|13

|53:40

| -487

|-

|123

|167:120

| -572

|}

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).

== Custom trumpets and quartertone trumpets ==

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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.

For instance, [[10edo]]'s semitone is 120 cents; to retune a standard trumpet from 12edo to 10edo, you could adjust the first valve (two semitones) from 200 cents to 240, the second valve (one semitone) from 100 cents to 120, and the third valve (three semitones) from 300 cents to 360.

For instance, [[10edo]]'s semitone is 120 cents; to retune a standard trumpet from 12edo to 10edo, you could adjust the first valve (two semitones) from 200 cents to 240, the second valve (one semitone) from 100 cents to 120, and the third valve (three semitones) from 300 cents to 360. (Note that this description of valve intonation is limited; see the Intonation section for a more detailed description).

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.

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* [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://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet], by Joseph L. Monzo (2003)

[[Category:Instruments]]

@@ Line 4: / Line 4: @@
 While the trumpet is generally designed for 12edo, there are several ways to play in other tuning systems – by custom trumpets (generally quartertone trumpets), non-standard fingerings, adjusting tuning slides, or by pitch bending via embouchure.
+== Intonation ==
+This section is largely supported by 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.
+From Joseph Monzo:<blockquote>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. I don't intend to repeat his work beat for beat, so consider reading that article. Regardless, the combinations themselves:
+{| class="wikitable"
+|+Intonation of trumpet valve combinations
+!Valves
+!Ratio
+!Cents
+|-
+|12
+|143:120
+| -304
+|-
+|23
+|19:15
+| -409
+|-
+|13
+|53:40
+| -487
+|-
+|123
+|167:120
+| -572
+|}
+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).
 == Custom trumpets and quartertone trumpets ==
@@ Line 110: / Line 144: @@
 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.
-For instance, [[10edo]]'s semitone is 120 cents; to retune a standard trumpet from 12edo to 10edo, you could adjust the first valve (two semitones) from 200 cents to 240, the second valve (one semitone) from 100 cents to 120, and the third valve (three semitones) from 300 cents to 360.
+For instance, [[10edo]]'s semitone is 120 cents; to retune a standard trumpet from 12edo to 10edo, you could adjust the first valve (two semitones) from 200 cents to 240, the second valve (one semitone) from 100 cents to 120, and the third valve (three semitones) from 300 cents to 360. (Note that this description of valve intonation is limited; see the Intonation section for a more detailed description).
 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.
@@ Line 169: / Line 203: @@
 * [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://www.tonalsoft.com/monzo/trumpet/trumpet-intonation.aspx Intonation of the valve trumpet], by Joseph L. Monzo (2003)
 [[Category:Instruments]]