62 LearnMusicTheory.net High-Yield Music Theory, Vol. 1: Music Theory Fundamentals Section 5.2 R OMAN N UMERALS Roman numerals In the roman numeral system, I (or i) means one, and V (or v) means five. Placing a one to the right of a number adds one to the value. Placing a one to the left subtracts one. So II = 2, since I + I = 1 + 1 = 2. Similarly, III = 3. The number IV means 4, since the I is to the left of the V, and 5 – 1 = 4. VI means “5 add 1,” or 6, and VII means “5+1+1,” or 7. Roman numerals Harmonic analysis uses roman numerals to indicate chords in the music. and chord quality The numeral indicates the scale degree (scale step) of the root of the chord. The format of the roman numeral indicates the chord quality, as follows: major minor diminished augmented w Triads: w w bb nw & w w & b w C major: wI ii vii° C minor: III+ M7 m7 Mm7 half-dim7 dim7 Seventh w b chords: & w w w w &b b w wM w w w w 7 w nw C major: I ii7 V7 vii¯7 C minor: vii°7 Triad roman In major keys, I, IV, and V are major; ii, iii, and vi are minor; and the numerals in leading tone chord is diminished. Notice how the format of each roman major keys numeral indicates its chord quality. M m m M M m dim w w w w & w w w w w w w wI wii iii IV V vi vii° C major: Seventh chord In major keys, I and IV are major seventh chords; ii, iii, and vi are minor roman numerals seventh chords; V is a major-minor seventh; and the leading tone seventh is in major keys half-diminished. Again, study how the format indicates each chord quality. M7 m7 m7 M7 Mm7 m7 half-dim7 w w w w w w & w w w w w w w wM w w M C major:wI 7 ii7 iii7 IV 7 V7 vi7 vii¯7 Chapter 5: Introduction to Harmonic Analysis 63 Triad roman In minor keys, i and iv are minor, III, V, VI are usually major, and the numerals in supertonic and leading tone triads are diminished. Composers almost minor keys always wrote in the leading tone accidental (below, B natural) to make the dominant triad major and the leading tone triad diminished. w bbb w w w nw w nw & w w w w w c minor: i ii° III iv V VI vii° Seventh chord In minor keys, i and iv are minor seventh chords; III and VI are major roman numerals seventh chords; V is a major-minor seventh; the supertonic is half- in minor keys diminished; and the leading tone seventh is fully-diminished. w w bb w w w w w nw & b w w w w nw w w w M M c minor: i7 ii¯7 III 7 iv7 V7 VI 7 vii°7 Variations in Because scale steps six and seven are sometimes raised in minor (see 2.4), minor keys there are several less common options for harmonies using those notes. rare! subtonic: rare! b b w b b w &b b nw &b b w &b b w &b b nw c minor: IIIw+ VII v ¾vi¯7 (goes to III) Inversion Inversion numbers (see 4.1 and 4.4 for inversions) represent intervals above numbers the lowest note; 5 means a fifth above the low note, 3 means a third, and so on. The notes may appear in any octave in any order above the low note, but always use simple interval numbers (less than 8) for the inversion. Root First Second Root First Second Third position inversion inversion position inversion inversion inversion 6 w 4 w w ? 5 6 w w ? w ww ww ww w 3 w 3 w w w w w5 w6 6 w7=F w6 6 6 C major:V3 V3 V4 V5=D V5 V4 V4 3=B 3 3 2 Use these abbreviations: Count down: 7, 6-5, 4-3, 2 w w w w w ? w w w ? w ww ww w C major:w 6 6 w7 6 4 4 2 V V V4 V V5 V3 V2 or V .