**Closely Related Partials **= two frequencies that a near to a simple fraction (2/1, 3/2, 5/3,…).

**Consonant Sound **= two notes that are simultaneously played, with frequency ratios that are simple fractions (e.g. 2/1, 3/2 or 5/4). If this is the case, then the composite wave will still be periodic with a short period, and the combination will sound consonant. For instance, a note vibrating at 200 Hz and a note vibrating at 300 Hz (a *perfect fifth*, or 3/2 ratio, above 200 Hz) will add together to make a wave that repeats at 100 Hz: every 1/100 of a second, the 300 Hz wave will repeat thrice and the 200 Hz wave will repeat twice.

**Dissonance** = two frequencies that are near to a simple fraction (2/1, 3/2, 5/3,…), but not exact. In this case the composite wave cycles slowly enough to hear the cancellation of the waves as a steady pulsing instead of a tone.

**Dyad **(in music) = a set of two notes or pitches.

**Formants** = *Overtones* in a speech sound. The basic pitch is the* fundamental frequency*. Additionaly any sound oscillates at numerous frequencies simultaneously. In music these overtones are generally near to harmonic. Not so in speech, the formants, are generally *inharmonic* to the *fundamental*. Which is also necessary, because this is the way how we can distinguish between different consonsants and vowels.

**Fundamental** = the frequency at which the entire wave vibrates.

**Fundamental frequency** = the *first harmonic* and the *first partial.* The numbering of the partials and harmonics is then usually the same; the second partial is the second harmonic, etc.

**Harmonics **(or a **harmonic partial**) = *Partials* that are perfect integer multiples of the fundamental. This includes the *fundamental*, which is a whole number multiple of itself (1 times itself).

The combination of composite waves with* short fundamental frequencies* and *shared or closely related partials* is what causes the sensation of harmony.

**Harmonic spectrum **(or **Harmonic series**) = generally used to refer to a series of numbers related by whole-number ratios. For example, the series of frequencies 1000, 2000, 3000, 4000, 5000, 6000, etc., given in Hertz (Hz.), is a harmonic series; so is the series 500, 1000, 1500, 2000, 2500, 3000, etc

If is de fundamental frequency, then a harmonic series has the form:

*.*

**Inharmonicity** = A measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial.

**Interval** = is distance between two pitches. Intervals can be harmonic, with both pitches sounding at once, or melodic, when one pitch follows another. Intervals are usually based on *scale degrees*, which refers to the relative position in the scale. However, a scale degree can be whole steps apart, but also half steps, which is the case in major and minor scales. Therefore in music theory intervals are counted by the number of halfsteps.

The following intervals are recognized:

SpecificInterval |
Size (# ofhalf-steps) |

unison | 0 |

minor 2nd | 1 |

major 2nd | 2 |

minor 3rd | 3 |

major 3rd | 4 |

perfect 4th | 5 |

tritone | 6 |

perfect 5th | 7 |

minor 6th | 8 |

major 6th | 9 |

minor 7th | 10 |

major 7th | 11 |

perfect 8th (octave) | 12 |

**Octave series**** ** = a spectrum with harmonic partials (or overtones) whose frequencies are whole number multiples, dividable by 2, of the *fundamental frequency*.

In other words, if is the fundamental frequency, then am octave series has the form* 2*, 4, 8, 16,…

**Overtones** = set of frequency components that appear above a musical tone. They can be *harmonic* or *inharmonic* partials of the *fundamental frequency*. In the first case the overtones are whole number harmonics of the fundamental, the ladder the overtones are complex partials harmonics. In music the overtones are generally harmonic. This means that wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string’s fundamental wavelength. So suppose an instrument creates a tone with a fundamental frequency of 110hz (this corresponds to the note *A*), then at the same time this vibration creates other waves at the frequencies 220hz (2nd harmonic), 440hz (3rd harmonic), 880hz (4th harmonic), etc. The wavelength on the other hand will be shorter with increasing frequency. 110hz corresponds to a max wavelength of 314cm, then 157cm, 39,5cm etc.

In speech this is different. The sounds of speech generally have* inharmonic overtones*. Which might be reason why speech is often not recognized as a musical sound.

**Partial** = all of the frequency components that make up the total waveform, including the *fundamental* and the *overtones*.

**Pitch** of a note = usually perceived as the lowest *partial* present (*the fundamental frequency*), which may be the one created by vibration over the full length of the string or air column, or a higher harmonic chosen by the player.

**T****imbre** (of a steady tone from an instrument) = determined by the relative strengths of each harmonic. Thus shorter-wavelength, higher-frequency waves occur with varying prominence and give each instrument its characteristic tone quality.

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