Editing Brass instrument (section)

===Tuning===
Since valves ''lower'' the pitch, a valve that makes a pitch too low (flat) creates an interval wider than desired, while a valve that plays sharp creates an interval narrower than desired. [[Intonation (music)|Intonation]] deficiencies of brass instruments that are independent of the tuning or temperament system are inherent in the physics of the most popular valve design, which uses a small number of valves in combination to avoid redundant and heavy lengths of tubing<ref>[https://web.archive.org/web/20090727085204/http://music.ou.edu/applied/horn/intonation.html Understanding Brass Instrument Intonation], University of Oklahoma Horn Studio</ref> (this is entirely separate from the slight deficiencies between [[Classical music|Western music's]] dominant [[Equal temperament|equal (even) temperament system]] and the [[Just intonation|just (not equal) temperament]] of the harmonic series itself). Since each lengthening of the tubing has an inversely proportional effect on pitch ([[Pitch of brass instruments]]), while pitch perception is logarithmic, there is no way for a simple, uncompensated addition of length to be correct in every combination when compared with the pitches of the open tubing and the other valves.<ref>{{Cite web|url=http://www.phys.unsw.edu.au/jw/brassacoustics.html#valves|title=Brass instrument (lip reed) acoustics: an introduction|website=www.phys.unsw.edu.au|access-date=2017-12-10|archive-url=https://web.archive.org/web/20140814070408/http://www.phys.unsw.edu.au/jw/brassacoustics.html#valves|archive-date=2014-08-14|url-status=dead}}</ref>

====Absolute tube length====
For example, given a length of tubing equaling 100 units of length when open, one may obtain the following tuning discrepancies:

{| class="wikitable"
|+ Valve combination and creation of pitch discrepancies
!Valve(s) !!Desired pitch !!Necessary valve length !!Component tubing length !!Difference !!Slide positions
|-
|Open tubing ||A{{music|#}}/B{{music|b}} ||0 || – || – ||1
|-
|2 ||A ||5.9 || – || – ||2
|-
|1 ||G{{music|#}}/A{{music|b}} ||12.2 || – || – ||3
|-
|1+2 or 3 ||G ||18.9 ||18.1 ||0.8 ||4
|-
|2+3 ||F{{music|#}}/G{{music|b}} ||25.9 ||24.8 ||1.1 ||5
|-
|1+3 or 4 ||F ||33.5 ||31.1 ||2.4 ||6 or T
|-
|1+2+3 or 2+4 ||E ||41.4 ||37 ||4.4 ||7 or T+2
|-
|1+4 ||D{{music|#}}/E{{music|b}} || – ||45.7 || – ||T+3
|-
|1+2+4 or 3+4 ||D || – ||52.4 || – ||T+4
|-
|2+3+4 ||C{{music|#}}/D{{music|b}} || – ||58.3 || – ||T+5
|-
|1+3+4 ||C || – ||64.6 || – ||T+6
|-
|1+2+3+4 ||B || – ||70.5 || – ||T+7
|}

Playing notes using valves (notably 1st + 3rd and 1st + 2nd + 3rd) requires [[#Tuning compensation|compensation]] to adjust the tuning appropriately, either by the player's lip-and-breath control, via mechanical assistance of some sort, or, in the case of horns, by the position of the stopping hand in the bell. 'T' stands for trigger on a trombone.

====Relative tube length====

Traditionally<ref>Christopher W. Monk, "The Older Brass Instruments: Cornet, Trombone, Trumpet", in ''Musical Instruments Through the Ages'', revised edition, edited by Anthony Baines, {{Page needed|date=October 2015}}<!--Inclusive pages needed.--> (London: Faber and Faber, 1966): {{Page needed|date=October 2015}}<!--Specific page reference for the word "traditionally" needed.--></ref> the valves lower the pitch of the instrument by adding extra lengths of tubing based on a [[just tuning]]:
* 1st valve: {{frac|1|8}} of main tube, making an interval of 9:8, a [[pythagorean major second]] 
* 2nd valve: {{frac|1|15}} of main tube, making an interval of 16:15, a [[just minor second]] 
* 3rd valve: {{frac|1|5}} of main tube, making an interval of 6:5, a [[just minor third]]

Combining the valves and the harmonics of the instrument leads to the following ratios and comparisons to 12-tone equal tuning and to a common [[five-limit tuning]] in C:
{| class="wikitable" style="text-align: center"
|- valign="top"
! Valves || Har-<br />monic || Note || Ratio || Cents || Cents from<br />12ET || Just<br />tuning || Cents from<br />just
|-
|○○○||2||C||1:1||0||0||1:1||0
|-
|●●●||3||C{{music|#}}/D{{music|b}}||180:167||130||30||16:15||18
|-
|●○●||3||D||60:53||215||15||9:8||11
|-
|○●●||3||D{{music|#}}/E{{music|b}}||45:38||293||−7||6:5||−23
|-
|●●○||3||E||180:143||398||−2||5:4||12
|-
|●○○||3||F||4:3||498||−2||4:3||0
|-
|○●○||3||F{{music|#}}/G{{music|b}}||45:32||590||−10||45:32||0
|-
|○○○||3||G||3:2||702||2||3:2||0
|-
|○●●||4||G{{music|#}}/A{{music|b}}||30:19||791||−9||8:5||−23
|-
|●●○||4||A||240:143||896||−4||5:3||12
|-
|●○○||4||A{{music|#}}/B{{music|b}}||16:9||996||−4||9:5||−22
|-
|○●○||4||B||15:8||1088||−12||15:8||0
|-
|○○○||4||C||2:1||1200||0||2:1||0
|-
|●●○||5||C{{music|#}}/D{{music|b}}||300:143||1283||−17||32:15||−29
|-
|●○○||5||D||20:9||1382||−18||9:4||−22
|-
|○●○||5||D{{music|#}}/E{{music|b}}||75:32||1475||−25||12:5||−41
|-
|○○○||5||E||5:2||1586||−14||5:2||0
|}