Electronic Music

1. Electronic Music Dr Ian Drumm

2. Perception and Realism • Aims • To review perception of musical sound by correlating objective parameters and subjective percepts • Learning Outcomes • Synthesis influencing perception of loudness, pitch and timbre. • How varying synthesis parameters overtime may be perceived • Develop ideas on perceptually guided data reduction for synthesis

3. Available objective parameters and corresponding percepts • Consider additive synthesis: • Fundamental frequency is associated with pitch • Amplitude is associated with loudness • Spectrum (harmonic series) is associated with timbre • Phase is associated with?

4. Perception of phase • Using Fourier build 100Hz square wave using the first ten non-zero harmonics. • In one line the harmonics all have the correct phase and in the other the phases are random. • Waveforms look very different • It is hard to hear the difference. • So can we neglect phase in additive synthesis?

5. Perception of parameter variations • How do we perceive changes in the objective quantities of frequency, amplitude and spectrum? • Frequency variation: • Think of frequency being modulated by another wave (perhaps a sine); • Small change (~6Hz, small amplitude) gives vibrato • Large change completely alters spectrum (see FM later on).

6. Perception • Amplitude variation: • Amplitude envelope defines individual notes; • Attack is important timbre; • Low-level modulation of amplitude envelope heard as tremolo • Spectrum: • Gives realism (can be complicated and subtle) • Or effects (e.g. wah-wah pedal is gross change of centre freq of a band-pass filter) • Or comparatively new sounds (see morphing, later on) • Phase variation: • Seems to add “life” and realism to notes with many partials like a piano

7. What is needed for realism • TVPS implies a high computational load so we need to make omissions and optimisations. Hence we should ask • What features of a real instrument are the most important to synthesis? • How do we recognise instruments to be guitars, trumpets, wood winds? • Can we say an aspect of an instrument’s timbre is it’s signature? • Can we find the minimum components needed to convey and instrument’s signature?

8. Are signatures in the spectral balance? • If we analyse a clarinet – we see the harmonics are odd corresponding to a square wave • Conversely if we build a square wave it is recognisably clarinet-like • However if we analyse a trumpet and then re-synthesise the sound is more oboe-like than brass-like • What components do we need for brass-like?

9. Risset’s Trumpet • Jean-Claude Rissets at Bell Telephone Laboratories • Analyses and re-synthesised a variety of instrument sounds • Series of subjective tests – removing key components

10. Risset’s Trumpet • The relative behaviour of harmonics in the rapid attack component (i.e. first 20ms) of the timbre was crucial for creating the recognisable signature of a trumpet sound • As the overall amplitude increases so does the relative contribution of the 3rd and 4th harmonics • i.e. centroid of the spectrum shifts up in frequency with the increase of overall amplitude of the tone.

11. Subjective Distance • A still greater understanding of how we perceive timbre can be achieved by statistical methods such as multidimensional scaling as applied by Grey (JASA 1972). • If a given pair of timbres (e.g. trumpet and guitar) sound more different than another pair (e.g. mandolin and guitar) then the first pair has a greater subjective distance.

12. Multidimensional Scaling (MDS) • Consider the relative distances between a selection of cities • Construct a table • Multidimensional scaling lets you extract the dimensions X and Y to hence represent these cities on a 2D map.

13. The steps of MDS • The technique employs a computer to try different positions for objects in a space until it eventually finds to position that fit best with the original data. • The steps are • Define a space (in this case X,Y and Z is 3D). • Arbitrarily position our objects (cities or timbres) within this space. • Form a matrix of distances between points called a Dhat matrix • Compare this Dhat with the original input matrix of distances (D matrix) using a stress function. • Adjust coordinates of each object in the direction that minimises stress • Repeat until stress values won’t get lower Reproduce distances Original data

14. Grey’s timbre space • Grey asked trained musicians to rate the similarity of pairs of synthesised emulations of real instrumental sounds • The timbres were synthesised emulations to make it easy for the researchers to present all timbres with the same loudness, pitch and duration – so that these factors don’t become part of the analysis

15. The sixteen timbres included two oboes, English horn, bassoon, clarinet, bass clarinet, flute, two alto saxophones, soprano saxophone, trumpet, French horn, muted trombone, three celli (normal playing, muted, bowed at bridge). • Each listener listened to 240=16*(16-1) possible pairs of timbres given in both directions and presented in random order. Hence each subject gave a similarity rating on a scale of 1 to 30, where 1-10 represented very dissimilar, 11-29 average level of similarity and 21-30 very similar. • Given subjective distance is clearly the inverse of the similarity rating; a suitable 16x16 input matrix of subject distances for MDS analysis was created.

16. Grey’s Timbre Space BN - Bassoon C1 - E flat Clarinet C2 - B flat Bass Clarinet EH - English Horn FH - French Horn FL - Flute O1 - Oboe O2 - Oboe S1 - Cello, muted S2 - Cello S3 - Cello, muted TM - Muted Trombone TP - B flat Trumpet X1 – Saxophone X2 – Saxophone X3 - Soprano Saxophone

17. Interpreting Dimensions • Looking at timbres a we move up I axis, can see spectral bandwidth narrows (hence axis relates to spectral energy distribution)

18. Three significant dimensions resulted • I: Spectral energy distribution – from broad to narrow • II: Synchronicity of partials in attack – from synchronous to asynchronous. • III: An-harmonisity of Attack – from high to none. • Interesting to note the importance of attack in characterising timbre