====== The Dimensions of Tonal Music ======

===== Harmonic (Overtone) Series Through the First Eight Partials =====

{{music_theory:overtone-series-c.png?225 |}}

512 Hz – Seventh Overtone / Eighth Partial\\ 
448 Hz – Sixth Overtone / Seventh Partial\\ 

384 Hz – Fifth Overtone / Sixth Partial\\ 
320 Hz – Fourth Overtone / Fifth Partial\\ 

256 Hz – Third Overtone / Fourth Partial\\ 
192 Hz – Second Overtone / Third Partial\\ 

128 Hz – First Overtone / Second Partial\\ 
64 Hz – Fundamental / First Partial\\ 

===== Harmony =====

The optimal vertical element – the most stable and “natural” harmonic sonority.

^ Preference ^ Interval between bass and any upper voice ^ Interval between any upper voices ^ Harmonic Quality ^ Doubling in four parts (R = Root, 3 = Third, 5 = Fifth) ^ Spacing ^
| Most preferred | Perfect Octave  | Perfect Octave  | Major Triad  | RR53  | Larger intervals between lower voices; smaller intervals between higher voices; no more than an 8ve between S-A and A-T  |
| :::  | Perfect Fifth  | Fifth / Fourth  | Minor Triad  | :::  | :::  |
| :::  | Major Third  | Major Third, Minor Third  | :::  | :::  | :::  |
| :::  | Minor Third  | Major Sixth, Minor Sixth  | ::: | :::  | :::  |
| OK, but less preferred  | Major and Minor Sixth  | :::  | Diminished Triad  | R553, RRR3  |   |
| :::  | :::  | :::  | :::  | R533, RR33  | :::  |
| Even less preferred  | Sevenths  | Sevenths  | Seventh Chord  | RR55, R555, RRR5, R333  | S-A or A-T greater than 8ve; T-B relatively low in their ranges and a 3rd apart  |
| :::  | Seconds  | Seconds  | Augmented Triad, Extended Tertian Harmony (9ths, 11ths, etc)  | :::  | :::  |
| :::  | Fourths, Augmented and Diminished intervals  | Augmented and Diminished intervals  | :::  | ::: | ::: |

===== Melody =====

The optimal horizontal element – The most perceptually coherent line.

^ Preference  ^ Generic Interval Size  ^ Scale  ^ Quality of Interval  ^ Other  ^
| Most preferred  | Second  | Within prevailing diatonic space  | Perfect, Major, Minor  | Interesting shape (such as “arch”); Maintains inertia; Goal-oriented; Leap in one direction followed by a step in opposite direction  |
| :::  | Common Tone (Octave)  | :::  | :::  | ::: |
| OK, but less preferred  | Third  |   | Diminished  |   |
| :::  | Fourth, Fifth  | :::  | :::  | :::  |
| Even less preferred  | Larger leaps (6ths, 7ths)  | Outside prevailing diatonic space  | Augmented  | Difficult to sing, Monotonous  |

===== Counterpoint =====

The optimal interaction between two lines – each line remains independent and perceptually distinct (soprano and bass counterpoint most important in textures of three or more voices).

^ Preference             ^ Relationship Between Lines ^ Lines in Close Proximity ^
| Most preferred         | Contrary motion            | No voice crossing; no lines in unison |
| :::                    | Similar / Oblique motion   | Lines move by contrary motion into or out of a unison        |
| :::   | Parallel Motion (of intervals other than 5ths and 8ths)   | :::        |
| OK, but less preferred | Similar (Unequal) Fifths (d5 to P5, or vice versa) | Lines move by similar motion into or out of unison |
| Even less preferred | Parallel perfect 5ths and 8ths | Voice crossing |

====== A Simple Theory of Voice Leading ======

> Voice leading in tonal music represents the best possible compromise among these three competing priorities: optimal harmony, optimal melodic motion, and optimal interaction between melodic lines. Each of these three priorities is as good as the other priorities will allow.