The Altered scale is sometimes called the ‘Diminished Whole-Tone scale’ due to its similarity to these two structures: Diminished is based on whole-tone-half-tone steps, while Whole-Tone is a series of two-fret gaps. Altered scale is: root-half-whole-half-whole-whole-whole-whole; then second octave, half-whole b7th and so on. So, from the 3rd to the octave we have five notes as in the Whole-Tone scale; and from the b5th to the is a six-note pattern of alternating whole and half steps, with six of the seven notes as you would find them in the Half-Whole scale. This makes it easy to go from Altered to Whole-Tone or Altered to Half-Whole; simply replace the 2 and #2 with a major 2nd for a complete Whole-Tone scale, and replace Altered’s #5 with a perfect 5th and major 6th for Half-Whole scale. Easy!