Deltadiatonic Symbology = Major , Leading Tone and the Dominant = Minor T± = Tritone "Wherever possible, we shall try to 'resolve' the dissonance (i.e. the intonation difficulty) contained in LT∆ = Leading Tone a diminished or an augmented interval. This is best done by taking the b, the 'ascending leading tone', TS = Tritone Substitute up to c, and the f, the 'descending leading tone', down to e." Schoenberg, Theory of Harmony pg. 73 R = Root b 7 = The dominant interval

The Tritone (T) occurs naturally in our as an interval containing three major seconds(whole tones). It is this unique interval that gives diatonics its dominant to tonic (V7-I) resolutionary foundation. It is the combination of the subdominant tone and the leading tone that creates what is traditionally known as an interval of an augmented fourth, or when inverted, an interval of a diminished fifth. DELTADIATONICS uses the T to refer to the tritone interval in either inversion. Note: The tritone from C is F# which divides the octave into two equal parts, each part containing three whole steps.

The Leading Tone (LT) is the tone that occurs naturally on the seventh degree of the major scale. When we examine this tone together with its neighboring tone a half-step above, we find an interval of a minor second. In the example below you will find that there are only two minor second intervals in the major diatonic scale. If we view each of the bottom tones as a leading tone, one will keep to its diatonic key and the other will move us up (modulates- tonicization) to its nearest neighboring flat key, F Major (the subdominant region, SD).

Tritone Interval (T) V7 IV Augmented Fourth, Diminished Fifth I Dominant Quality LT of C major LT of F major 7 R 3 ( To subdominant region) b ( To Tonic region) 2 2 2 2 2 2 2 C Major ± ± ∆ ± ± ± ∆ (Ionian) wœ w & w wœ w w Function wI IIw III IV V VI VII I Technical name Tonic Supertonic Mediant Subdominant Dominant Submediant Leading Tone Tonic

Resolution of the Tritone Interval (Dyads) can be outwards (rising) or inwards (falling). The minor seventh interval ( 7) of the dominant chord (V7) resolves us downwards to the major third interval (3)b of the tonic (I) while the leading tone, the major third of the dominant chord (V7) resolves us upwards to the tonic (I).

Region Tonic SD

Direction Outward Inward Outward Inward Interval T 6 T 3 T 6 T 3 Augmented ∆ Diminished Augmented ∆ Diminished Traditional fourth 6 fifth 3 fourth 6 fifth 3 wœ wœ w wœ w b bwœ w & wœ 7 3 & w w Resolutions 3 w8 wœ3 8 wœ7 3 of the 3 & 7 7 3 b3 R bwœ w b3 R b b b7 3 Function C: V7 I V7 I F: V7 I V7 I Function V7 I V7 I V7/IV IV V7/IV IV in C (Tonicization) Ron Di Salvio © 2007 Meadow Run Music ASCAP All Rights Reserved 2 The Tritone, Leading Tone and the Dominant

Root Addition By adding a root (R) to the tritone we strengthen its quality and its resolution. The root can move up a perfect 4th (P4) or down a perfect fifth (P5).This movement creates a diatonic resolution (using the dominant (V7) from its scale ) .

Chord Symbol G7 C G7 C C7 F C7 F w w & w w w w &b bw w w3 w8 7 3 w w w w3 bw3 8 7 7 3 b 3 R w b 3 R b P4 b 7 3 w w ? w ? w w w b w Root Resolution R Tonic R Tonic Rw Tonic Up a Perect 4th R Tonic

Function C: V7 I V7 I F: V7 I V7 I

Tritone Root Addition By substituting (changing) the dominant root with a root a tritone away, we strengthen its quality and intensify its resolution. Replacing the tritone root for the dominant root is know as tritone substitution (TS) This movement creates a chromatic resolution (using the dominant (V7) from the scale a tritone away) .

Chord Symbol 7 7 D b C D b 7 C G b 7 F G b F w w & w w w w b bw w w w8 3 3 & w w w3 w3 7 R b3 3 7 bw7 w8 7 R 2 b 2 b3 3 b ∆ bw ∆ w ? bw w ? bw w b bw w Root Resolution TS Tonic TS Tonic TS Tonic TS Tonic Down a Minor 2nd Function C: II I II I F: II I II I Flat Five Substitution V/Vb bV/V V/Vb V/Vb b b b b

The Phenomenon of the 3 and 7 When we use a tritone substitution the function of the 3 and 7 are reversed.b The intervals above the new root are reversed (inverted). b