Defining Microtonality

Definite Pitch and the Overtone Series – Pure (WNR = Whole Number Ratio) intervals and wavelength, string length, relative amplitude, and their relationship to additive synthesis and timbre

Contrasting WNR intervals with Equal temperament (12ET) – Defining cents and metrics of dissonance, other intonations / temperaments, Bach, period instruments & Classical performance practice

Alignment: Access to WNR intervals (enhanced consonance)

-       BRANCA: Symphony #5, Mov. I (1984)
-       DUMITRESCU: Movemur et Sumus (1978)
-       TENNEY: Spectral Canon (1974)

Misalignment: Dissonance against fundamental / overtones 

‘Spectral’ Music: Inharmonicity (and timbre as harmony), Spectromorphology (and timbre as orchestration) 

-       GRISEY: Partiels (1975)

Haas’ Taxonomy of Microtonal approaches

 1. The application of additional pitches to the familiar twelve-tone chromatic  system in equal temperament. This leads to equidistant sub-divisions of the  octave generating a number of pitches either larger or smaller than twelve (for  instance, the 19-tone equal temperament system which contains 19 equidistant  pitches per octave, or the 10-tone equal temperament system containing ten  pitches per octave). This approach also includes equidistant sub-divisions of intervals other than the octave. [7, 19, 22, 31] 

2. The creation of pitch systems whose (just) intervals are based on the proportions of the overtone series.

         - YOUNG: Well Tuned Piano (1964-73-81-Present)

3. The generation of harmonic beats through the application of very small yet still distinguishable intervals. 

-        LUCIER: Still And Moving Lines Of Silence In Families Of Hyperbolas (Clarinet) (1972)
-       LUCIER: Still Lives, Mov. IV Ferns (1995)

4. The creation of microtones through aleatoric means where microtones occur in a random and/or unpredictable way, for instance, by using piano preparation, certain percussion sounds, glissandi, or ad libitum detuning of strings etc.

-   LIGETI: Harmonies (1967)

Expanding on Haas:

5. Pitch structures that to re-present OR re-synthesise inharmonic overtone configurations from the acoustical world. 

6. Pitch structures that abstract numerical data (or other extra-musical data abstracted into numerical) onto the frequency spectrum (rather than the keyboard).  (NB.  Problems of abstraction… codexes etc.)

7. The use of unspecified microtones as colouristic (modulatory) devices.

-   DONALD MACLEOD AND CONGREGATION: Stroudwater Psalm 46 vv. 1-2 (r. 1975)

8. The use of microtones to gain access to other auditory phenomena (e.g. diff tones).

         - BARLOW: Until #8 for guitar (1980)
         - BARLOW: Until #7 for piccolo (1981)

9. The use of inharmonic structures as a way of interfacing with objects or other acoustical phenomena.

         - LUCIER: The Wire (1977)
         - GARSDEN: A Erice (2015)