Chromatic scale common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale (). Due to a different tuning technique, the twelve semitones in this scale have two slightly different sizes. Thus, the scale is not perfectly symmetric. Many other tuning systems, developed in the ensuing centuries, share a similar asymmetry. In Pythagorean tuning (3-limit just intonation) the chromatic scale is tuned as follows, with sharps higher than their enharmonic flats: These are 17-EDO Pythagorean tuning approximations. In 5-limit just intonation the chromatic scale, Ptolemy's intense chromatic scale, is as follows, with flats higher than their enharmonic sharps,
Tonic sol-fa latter more directly represents the intervals between pitches in any given key signature. In Curwen's system, the notes of the major scale (of any key) are notated with the single letters d, r, m, f, s, l, and t. For notes above the principal octave, an apostrophe follows the letter; notes below the principal octave have a subscript mark. Chromatic alterations are marked by the following vowel, "e" for sharp (pronounced "ee") and "a" for flat (pronounced "aw"). Thus, the ascending and descending chromatic scale is notated: Such chromatic notes appear only as ornaments or as preparation for a modulation;