All the parts in each of these scales, from the first tonic to the second, relate to the same parts of the scale below them in the simple ratio of 2:1; and serially to the first tonic in the following ratios:— 8:9, 4:5, 3:4, 2:3, 3:5, 4:7, 8:15, 1:2. _First Series of Scales._ ----+------+-------+-------+-------+-------+-------+------+-------+------- |Tonic.| | | | | | | | | |Supertonic. | | | | | | | | |Mediant. | | | | | | | | |Subdominant. | | | | | | | | |Dominant. | | | | | | | | |Submediant. | | | | | | | | |Subtonic. | | | | | | | | |Semi-subtonic. | | | | | | | | |Tonic. ----+------+-------+-------+-------+-------+-------+------+-------+------- I. |(¹⁄₂) |(⁴⁄₉) |(²⁄₅) |(³⁄₈) |(¹⁄₃) |(³⁄₁₀) |(²⁄₇) |(⁴⁄₁₅) |(¹⁄₄) |Red. |Red- |Orange.|Yellow-|Yellow.|Yellow-|Green.|Blue- |Blue. | |orange.| |orange.| |green. | |green. | ----+------+-------+-------+-------+-------+-------+------+-------+------- II. |(¹⁄₄) |(²⁄₉) |(¹⁄₅) |(³⁄₁₆) |(¹⁄₆) |(³⁄₂₀) |(¹⁄₇) |(²⁄₁₅) |(¹⁄₈) |Green.|Blue- |Blue |Blue- |Purple |Red- |Red |Red- |Orange. | |green |hue. |purple |hue. |purple |hue. |orange | | |hue. | |hue. | |hue. | |hue. | ----+------+-------+-------+-------+-------+-------+------+-------+------- III.|(¹⁄₈) |(¹⁄₉) |(¹⁄₁₀) |(³⁄₃₂) |(¹⁄₁₂) |(³⁄₄₀) |(¹⁄₁₄)|(¹⁄₁₅) |(¹⁄₁₆) |Red |Red- |Orange |Yellow-|Yellow |Yellow-|Green |Blue- |Blue |hue. |orange |hue. |orange |hue. |green |hue. |green |hue. | |hue. | |hue. | |hue. | |hue. | ----+------+-------+-------+-------+-------+-------+------+-------+------- IV. |(¹⁄₁₆)|(¹⁄₁₈) |(¹⁄₂₀) |(³⁄₆₄) |(¹⁄₂₄) |(³⁄₈₀) |(¹⁄₂₈)|(¹⁄₃₀) |(¹⁄₃₂) |Green |Blue- |Blue- |Blue- |Purple |Red- |Red- |Red- |Orange |hue. |green- |toned |purple-|hue. |purple-|toned |orange-|hue. | |toned |gray. |toned | |toned |gray. |toned | | |gray. | |gray. | |gray. | |gray. | ----+------+-------+-------+-------+-------+-------+------+-------+------- V. |(¹⁄₃₂)|(¹⁄₃₆) |(¹⁄₄₀) |(³⁄₁₂₈)|(¹⁄₄₈) |(³⁄₁₆₀)|(¹⁄₅₆)|(¹⁄₆₀) |(¹⁄₆₄) |Red- |Red- |Orange-|Yellow-|Yellow-|Yellow-|Green-| Blue- |Blue- |toned |orange-|toned |orange-|toned |green- |toned | green-|toned |gray. |toned |gray. |toned |gray. |toned |gray. | toned |gray. | |gray. | |gray. | | gray. | | gray. | ----+------+-------+-------+-------+-------+-------+------+-------+-------