Your tuner and your ear disagree about the third. The ear is right.
Tuners measure against equal temperament, and string players in an ensemble do not play it. On a major third the gap is 13.7 cents, more than most students set as their tolerance. This page gives the numbers, what they ask of you and where they stop being true.
A major third has three defensible places.
Play an F♯ over a D. A musician can defend three places for it.
- Equal 400.0
- Just 5:4 386.3
- Pythagorean 81:64 407.8
Twenty-two cents separate the outer two. That is wider than the six cents a careful student works to and wider than the four an advanced one works to. A tuner that measures against the middle value and calls the third fine may be describing a violinist who is about to spend a rehearsal wondering why the chord beats.
The pure third at 5:4 stops a chord beating. The Pythagorean third at 81:64 is where a melodic line leans, and string players lean there unprompted. Equal temperament is the compromise a keyboard makes to play in every key with twelve fixed pitches. A violin has no such obligation.
Just intonation is relative. A temperament is absolute.
People use these two words as if they named the same kind of thing. They do not, and the difference decides what the app asks of you.
Just intonation has no notes of its own. It has distances from a tonic, written as whole-number ratios, and a whole-number ratio is what stops two notes beating against each other. Without a tonic it says nothing, so the app asks for one.
A temperament bends the pure intervals so a fixed-pitch instrument can play in more than one key. The bending is written against the names of the notes, not a tonic. It needs only the reference A, which anchors the system in hertz. Equal temperament is the one on every keyboard: twelve identical steps, no note more at home than another, and the right answer when a piano is in the room.
Just intonation in cents, degree by degree.
Each degree's distance from where a keyboard would put it. Positive is sharp of the piano, negative is flat of it. wabetune measures against these numbers when you name a tonic. It computes them from the ratios, because a table of twelve numbers copied by hand picks up a typo nobody finds.
| Degree | Ratio | Cents from equal | In which scale |
|---|---|---|---|
| 1 | 1:1 | 0 | both |
| ♭2 | — | no target | neither |
| 2 | 9:8 | +3.9 | both |
| ♭3 | 6:5 | +15.6 | minor |
| 3 | 5:4 | −13.7 | major |
| 4 | 4:3 | −2.0 | both |
| ♯4 | — | no target | neither |
| 5 | 3:2 | +2.0 | both |
| ♭6 | 8:5 | +13.7 | minor |
| 6 | 5:3 | −15.6 | major |
| ♭7 | 16:9 | −3.9 | major |
| ♭7 | 9:5 | +17.6 | minor |
| 7 | 15:8 | −11.7 | major |
The three degrees that move most are the third, the sixth and the seventh, and they are the ones a teacher spends years on. That is not a coincidence. They are where the two systems disagree, so they are where a student is most often told they are out of tune by a device that is measuring the wrong thing.
Two degrees have no target, and we do not invent one.
The flat second and the tritone belong to neither the major nor the minor scale. Over a C tonic they are the D♭ and the F♯, and no scale that lacks them yields a ratio. Every published value for those two is a convention. The tritone has three well-known candidates spanning thirty cents, and they disagree even about the sign.
So wabetune declines. Those cells stay unlit, and a student playing there sees where equal temperament puts the note, the only honest answer left. Blank is not zero. Zero claims the note sits where the keyboard has it. Blank says this system does not pronounce on that note. The map draws them differently.
The flat seventh is the one degree where the table has to ask a question, and it is why wabetune offers just intonation twice, once for a major tonic and once for a minor one. Elsewhere the two keys want different degrees: the major third and the minor third are the 3 and the ♭3, and both fit in one table. The flat seventh belongs to the minor scale, and a major key borrows it all the time (the B♭ of a C7), so both keys need a value for it and each wants it somewhere else.
In a minor key it belongs to a chord you play: the fifth above the flat third, an E♭ to a B♭ over a C tonic. That fifth is pure at 6:5 × 3:2, which is 9:5. In a major key no such chord needs protecting. The degree is chromatic there, the B♭ of a C7 on its way to F, and the plain answer is two pure fourths up, 16:9. The two sit a syntonic comma apart, twenty-two cents, far outside any tolerance a student can set. For a while the app gave the major value to every tonic and told minor-key players their perfect E♭–B♭ was sharp.
That is why the flat seventh is the only thing the major/minor switch decides. Other tuners ship two just tables that differ in three degrees: the flat seventh, the flat second and the tritone, the last two settled by the quality of the tonic. The tonic cannot settle them. The chord a tritone belongs to decides whether it is 45:32 or 36:25, a dominant seventh or a diminished chord, and both turn up in major pieces and minor ones. The key answers with confidence a question it cannot decide, so wabetune leaves the cell blank.
Accuracy needs a reference. Consistency does not.
When the target is arguable, accuracy (distance from the target) is a fragile number. A product that reports it with confidence hands its own assumptions back to you.
Consistency holds up. It is the spread of your own repetitions of one note, and it ignores which system you had in mind. Twenty attempts at an F♯ within four cents of each other mean you control that note, whether you aimed at 386, 400 or 408. Twenty attempts spread over twenty cents mean you do not, and no reference rescues that number.
wabetune reads it first, and the report keeps off by and swing in separate columns instead of adding them into one score. At equal deviation, swing is harder to correct, and a score that hid it would flatter you about the easier problem.
Where this stops being true.
Just intonation is defined against a fixed tonic and holds as long as the music stays there. When a piece modulates, the ratios count from a tonic that has moved, and a target computed from the old tonic is wrong by an amount a musician hears, with no warning.
The same limit shows up inside one key. The second degree has two defensible values: 9/8 (203.9 cents) over a dominant chord, and 10/9 (182.4 cents) over the chord built on the second degree. They sit 21.5 cents apart, one syntonic comma, and no table of twelve fixed values holds both. wabetune uses 9/8. Tune a D to a D minor chord in C and the map shows it 21 cents flat.
wabetune applies your declaration to the whole recording. That fits scales, arpeggios and the studies that fill a practice room, because none of them modulates. It does not fit a concerto movement, and we say so here so you do not find out from a graph. Declare equal temperament for those and read the swing, not the deviation.