As many of you know, I am a bit of a tuning enthusiast. Here are some fairly basic guidelines that will help performers who use pitch-adjustable instruments get in tune more quickly. Now, look at the major scale and these cent deviations:
This is what results when the primary triads are perfectly tuned: the I, IV, and V chords. It turns out that iii and vi are also in tune here. But not ii, and vii(dim) is a bit more complex; in general, it will work as a diminished triad with this tuning. But, even given this basic information, performers really should always keep these tendencies in the back of their minds when they play music in any particular key. By the way, this works whether for the major key or the relative minor. Thus, whether in the key of C major or A minor, D is still 4 cents sharp.
This will, of course, vary depending on how complex the harmony gets. But common music uses the primary triads and those common minor triads often enough that these adjustments will be very useful as a starting point when playing through a piece of music and figuring out how to get everything in tune.
Also observe that in this major scale, with the basic primary and secondary triads, there are really not that many options for how each note functions. For example, in C major, these are the possible diatonic triads that each note can be acting in:
C: I, IV, vi
D: ii, V, vii(dim)
E: I, iii, vi
F: ii, IV, vii(dim)
G: I, iii, V
A: ii, IV, vi
B: iii, V, vii(dim)
Now, let’s look at the tuning consequences for each note:
C: Each possible chord that C occurs in is already in tune with our in-tune C major scale. No further adjustments necessary.
D: Although the ii chord is not in tune in C major, it is not because of this note(most of the time), for technical reasons I won’t go into here. Thus, no further adjustment is necessary.
E: Each possible chord that E occurs in is already in tune with our C major scale. No further adjustments necessary.
F: In the ii chord, this will need to be tuned 21 cents sharper. In the IV chord, no further adjustments are necessary. In the vii(dim) chord, it will be fine as is, but sometimes is tuned as if it is the seventh of the V7 chord (lowered 28 cents). One is a major chord, one is a diminished chord, and one is a minor chord, so with some basic ear training it should become easy to distinguish between these different chords and functions of this note. Note that the difference in tuning between usage in the ii chord and the V7 chord is approximately a quarter-tone, but I otherwise won’t go into too much detail about tuning dominant seventh chords; that’s a bit more advanced subject than what I want to cover right now.
G: Each possible chord that G occurs in is already in tune with our C major scale. No further adjustments necessary.
A: The IV and vi chords are already in tune, but the A in the ii chord will need to be tuned 21 cents sharper for the same reason why the F in the ii chord will need to be raised. This note probably requires the most discerning ear to nail correctly all the time, because it will require being able to tell the difference between the IV chord (easy, the only major chord possibility) and two minor chords (ii, vi) one of which will need to be raised and the other which will not.
B: Each possible chord that B occurs in is already in tune with our in-tune major scale. No further adjustments necessary.
So, only two notes should really present any amount of tuning difficulty: the fourth and sixth scale degree. These patterns will be quite reliable when playing diatonic music that has no accidentals. When accidentals do begin to happen, these patterns will begin to shift around a bit more. However, accidentals usually mean a key change. So, if you can figure out what the new key is, simply shift the pattern to the new key. Thus, if the key changes to G, instead of the C major scale tuning that I gave above, the new pattern would be:
Because G major is so closely related to C major, the tuning tendencies are quite similar. In fact, there are only two significant changes: the F is now an F# with it’s own tuning, and the A is now raised by 4 cents instead of being lowered. Note that the A is now about where we would have tuned the A in the ii chord of C major. In fact, in a very real tuning sense, most ii chords can be thought of as a very temporary foray into the key of the V chord, especially if it immediately precedes a V chord of some kind.
Despite this information, every performing group will also have it’s own tuning idiosyncrasies, so it is always important to keep open ears and to further make any adjustments necessary to match the other players no matter what they’re doing. But if everyone tried to follow these guidelines that I describe above, this whole process of getting the group in tune will be a lot easier.