Scale finder calculator: get the notes for major, minor, pentatonic, and mode scales from any root note for songwriting. Free, private, runs in your browser.
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Worked Example: D Minor, Step by Step
Set the root to D and the scale to minor. The formula stores pitch classes as an array index: C=0, C#=1, D=2, E=4, F=5, G=7, A=9, B=11. So D is index 2, and the minor scale is the interval list [0, 2, 3, 5, 7, 8, 10].
For each interval the tool computes (2 + i) mod 12. Root: (2+0) mod 12 = 2, which is D. Second note: (2+2) mod 12 = 4, which is E. Third: (2+3) mod 12 = 5, which is F. Fourth: (2+5) mod 12 = 7, which is G. Fifth: (2+7) mod 12 = 9, which is A. Sixth: (2+8) mod 12 = 10, which is A#. Seventh: (2+10) mod 12 = 12, and 12 mod 12 wraps to 0, which is C.
The output is D minor: D - E - F - G - A - A# - C. The wrap at the seventh note is the whole point of the mod 12 operation: counting 10 semitones up from D passes B (11) and lands back at C (0), one octave higher. Try the same arithmetic with root F# (index 6) and major [0,2,4,5,7,9,11]: the last step is (6+11) mod 12 = 17 mod 12 = 5, giving F, so F# major ends F# - G# - A# - B - C# - D# - F.
Limitations: Sharps Only, Intervals Not Chords
The note table names every accidental as a sharp: there is no Db, Eb, Gb, Ab, or Bb. Choose root D with the minor scale and the sixth note prints as A#, though musicians in flat keys would write the same pitch class (10) as Bb. The spelling is a display choice; the underlying pitch class math is identical either way.
The tool also reports scale membership, not harmonic function. It will confirm that B is not in C major (10 is absent from [0,2,4,5,7,9,11]) but says nothing about the dominant-seventh chord Bm7b5 that classical theory would borrow there. Similarly, the 9 blues intervals [0,3,5,6,7,10] include the flat-five at 6 semitones, a pitch that no major or minor scale contains; the calculator prints it but will not explain its tritone tension.
One practical edge case: intervals are listed as semitone offsets from the root, so a 7 always means a perfect fifth in every scale here. If you need chord spellings (thirds stacked as triads), key signatures, or the harmonic and melodic minor variants (which differ from natural minor at the 6th and 7th degrees: [0,2,3,5,7,9,10] and [0,2,3,5,7,8,11]), this tool stops at the seven notes.
