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)