CAREFUL INTONATION

Whe singing, or playing a pitch-based musical iinstrument where the pitch is adjustable, you need to be able to hear whether or not the notes you produce are in tune with other notes you played or are playing and/or with other notes another instrument played or is playing.  You do this by comparing one note with another, either simultaneously or in sequence.

Generally speaking, simultaneous notes are easier than sequential notes to compare   Also, the simpler the relationship between the frequency of two notes, the easier they are to compare.  Also, if the notes are in a part of the pitch range that you are used to, this helps a lot.

This chart comes from our web pages dealing with musical accoustics.

How Easy	Interval	Ratio	Example
very	unison	1:1	C:C
very	octave	2:1	C:C
fairly easy	perfect 5th	3:2	C:G
fairly easy	perfect 4th	4:3	C:F
moderate	major 3rd	5:4	C:E
a bit hard	minor 3rd	6:5	E:G
a bit hard	major 6th	5:3	G:E
a bit hard	major 6nd	8:5	E:C
harder	minor 2th	9:8	C:D

Admittedly this chart is built from a  true octave and a perfect fifth interval of 3:2.  And in actuality the modern piano has intervals slightly different than that.  But, I still theorize that people rely somewhat on the interaction between the harmonics in the notes they are comparing, and when those clash, it  indicates that something is out of tune.  The simpler these ratios are, the  more obvious any clash will be, because the harmonics involved are greater in amplitude.

Anyway, let's look at an example.  Two notes that should be on the same pitch are very easy to compare.  Two notes that  should be an octave apart are almost as easy to compare because the second harmonic of the lower note should be the same pitch as the upper note.  Two notes a perfect fifth apart are fairly easy to compare because the third harmonic of the lower note should be the same pitch as the second harmonic of the upper note.  And so on it goes.

So, on an unfretted bowed string instrument where you can sustain notes long enough to compare them to each other and to other notes, you have the time to adjust your finger placement to bring the notes in tune.  My old violin teacher said that a player is always adjusting pitches while playing.  The better the player, the smaller those adjustments are, but they still do occur.  He said it's a feedback loop between your ear and your brain and your left hand fingers that must stay active to keep you in tune.

Besides harmonics clashing, another thing to listen for on a bowed string instrument is the response of  open strings to the one you are currently playing.  If you play a G on a D string and it is exactly in tune, the open G will resonate to give a pleasant ringing effect.  If you are slightly low or high in pitch,  that G will not resonate.  While playing the fingered G on the D string, you can tap the open G with another finger and see if that alters the sound of the instrument.  If it does, then the open G is resonating.

Instrument Tuning and Note Location