So here’s a further investigation into trumpets playing in rock bands. This time it’s really tedious and quite in depth. Double win.
PHYSICS BIT:
So the concept of tuning in istruments is based on consonance and dissonance in sound waves. Two notes sound in tune if their nodes fall in the same place and the waves reinforce each other – such as multiples of a wave (harmonics), and out of tune if the nodes fall in different places, forming deconstructive waves. With deconstruction you can hear audible ‘beats’ where the volume repeatedly drops at the deconstructive summations. I don’t think anyone’s ever proved anything, but I suppose this is the source of the notion of ‘out-of-tune’, the compared irritation of pulsing volume versus the purity of a constant tone.
Multiplying the frequency of a wave means that whenever the displacement of the first wave is 0, so is the displacement of the higher tone, so they sound in tune. Other low ratios naturally sound in tune, e.g. 3:2 (perfect fifth) as after every two fundamental waves the displacement is both 0. Obviously certain low ratios all sound nice together, but as soon as you start fiddling with higher numbers like 9/8s things start to sound a bit off, and the deconstruction is more evident to the human ear. Twelve separate tones seems to be the limit of acceptability in this, any more and it sounds out-of-tune.
HISTORY BIT
There are two archaic systems which calculate all notes from a set interval and the octaves around each resulting new frequency.
Pythagorean:
A ratio of 3:2 takes a frequency up a perfect fifth. After 12 perfect fifths we should circle round to a unison note again (e.g. C G D A E B F# C# G# D# A# E# B#=C) however based on this notation it is obvious that B# does not = C in this case, as, based on the idea that octaves are some 2n multiple of the base frequency, this would imply that
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where x should be some whole number; in this case 129.2463 is not quite 128 where x = 7.
Hence the notion of a perfect fifth is not something that can be used to tune an instrument.
Compared to equal temperament, major intervals here are larger, and minor intervals are smaller. Bizarrely, before anyone thought of changing this system, people’s first port of call was redesigning instruments – harpsichords were often built with two tone keys for D#/Eb and G#/Ab, depending on what key you played in. Which I suppose is along the same lines as building a new piano everytime your old one went out of tune.
Meantone:
The next system was the mean tone system, built on major thirds – although this obviously had a problem of the same nature. This was slightly overcome by calculating whole tones as the mean half of a major third and semi-tones the half of the tone. The main problems with this tuning is that perfect fifths are far from perfect.
CONTEMPORARY BIT
Just intonation is based on harmonics of fifths and thirds, and makes adjustments in some of the smaller intervals in the scale, leading to the idea of major and minor whole tones. Interestingly the whole tone in the mean tone system is not only the mean of the major third, but also of the major and minor whole tones. This system is perfect for western music in instruments that can slightly alter tuning at will, because fifths and thirds are all perfectly in tune, the most dominant intervals in Western harmonic music.
Obviously some keys will sound better than others, as not all intervals are equal up and down the scale. If you are an instrument tuned to just intonation, you sound great in C, and shite in Db major.
Equal Temperament. At some point someone had the bright idea of tuning all intervals to be equal, i.e. taking an octave and dividing it into 12 equal parts. Thus every interval is the same at every point on the piano. This is brilliant because every key is equally in tune, however it does have the drawback of most intervals being approximations of just intonation, so major chords will not sound as good as just intonation.
If you are an untuned instrument (i.e. a voice) you’re great on your own, but shite if you’re with an equal temperament instrument like a piano. Naturally when one sings, one sings in just intonation. You just do, without thinking about it, because all the important intervals are percectly in tune. You adjust when you sing along to an equally tempered instrument such as a piano, which is fine if you can, but not necessarily so fine if you’re not playing an instrument that can quickly adjust tuning and intervals. This leads to the idea of bright and dull keys – for example, one has a tendency to sing flat in F or Bb major if accompanied by a piano.
So what does this mean in terms of the trumpet?
One:
If the same valve combinations are used to take each open harmonic up by a certain interval, since, in just intonation the intervals can differ slightly depending on what note you are playing in the key (a perfect fourth from unison is not the same as a perfect fourth from the major third), certain valve combinations will be out of tune with the desired interval. This can normally be altered with valve slides or skilful mouth-shape changes. Noteably, since the intervals between harmonics decreases in higher registers whilst there are still 6 valve combinations, certain valve combinations overlap with those in a different register. These will always be out of tune with each other.
Two:
Even with skillful adaptation of wolf notes, playing with an ensemble of musicians tuned in equal temperament will undoubtedly sound out of tune, especially in certain keys. Simply because the whole of certain registers will be slightly out, on top of the wolf notes which trumpets experience within their own tuning.
What can you do?
Fuck knows.
To be continued...
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