source file: mills2.txt Date: Tue, 16 Jul 1996 12:05:49 -0700 Subject: Next Post from McLaren From: John Chalmers From: mclaren Subject: the audility and audible coherence of inharmonic progressions of inharmonic tones Part 2 of 2 -- Inharmonic timbres are the final frontier of microtonality. Thus it's important to be clear on whether they are musically useful or not. We have seen why experiments on inharmonic tones gave deceptive results prior to the 1970s. Before the wide availability of computers, it was not practical for most auditory researchers to generate inharmonic tones digitally. Thus, most early experiments with inharmonic tones were done with analog circuits. These circuits offered early researchers almost no control at all over the fine structure of the inharmonic tones thus produced. In particular, researchers couldn't specify detailed amplitude or frequency envelopes for each inharmonic partial, nor did early researchers have even crude control over the exact frequencies of the inharmonic partials used. Typically, FM or AM techniques were used to generate inharmonic timbres. These methods generated large sets of audibly unrelated and individually uncontrollable partials from an input periodic waveform. Prior to the use of computers, there was thus no scale-like relationship twixt adjacent inharmonic partials, as is found (say) in an inharmonic tone produced by setting each partial to the closest value in 19-tone equal temperament. By the 1980s the notion that inharmonic sounds necessarily failed to fuse into a single percept, or necessarily exhibited a fundamental pitch unrelated to the pitches of the partials, had been disproven. Geary, for example, points out that "This paper examines the hypothesis that pairs of strongly inharmonic sounds can also cause the perception of a kind of consonance if the two have frequency components in common, and dissonance if components at each make near misses. This hypothesis is verified by experiments in which subjects were asked to choose which of two inharmonic sound pairs seemed more consonant. The data show significant agreement with predictions based ont he missing and matching of spectral components." [Geary, J. M., "Consonance and dissonance of pairs of inharmonic sounds," J. Acoust. Soc. Am., Vol. 67, No. 5, May 1980, pg. 1785] Geary goes on to conclude: "Clearly, it cannot be claimed that the perceptions are exactly the same, since inharmonic and harmonic tones themselves sound different to the ear. However, the experiments do establish a similarity between the consonance-dissonance phenomenon in harmonic and inharmonic sounds. Most of the subjects had prior familiarity with the conventional meanings of the words consonant and dissonant (especially the latter) and conventional harmonic intervals were played and identified for each subjec before the experiment. Consequently one would expect the subjects' judgments to be made according to the conventional sensations of consonance and dissonance. The similarity of perceptions in the harmonic and inharmonic cases is further established by the high scores of people with substantial musical experience. (..) That such people chose the predicted dyads in spite of their conventionally dissonant relationships between their fundamentals, and rejected other dyads with conventionally consonant fundamental relationships, is strong confirmation of the hypothesis of this paper." [op. cit., pg. 1788] Geary further mentions that "the concept of inharmonic consonance and dissonance raises intriguing possibilities for experimentation in electronic and computer music. Consonance and dissonance are responsible for much of the structure of conventional music, such as that in scales, chords, and harmonic practice. If this structure is due to the configuration of spectral components of harmonic sounds, then it might be possible to alter such structure by electornically relocating the spectral components to inharmonic positions. New intervals, scales, and chords might be possible, as well as timbres unobtainable with harmonic spectra." [op cit., pg. 1789] By the mid-1980s, with many computer-generated inharmonic progressions in many different compositions as audible examples, it had become clear that inharmonic tones could and did exhibit consonance, dissonance, modes and cadences akin to those found in harmonic-series-based compositions. Examples include James Dashow's compositions --take your pick: Whispers Out Of Time, Sequence Symbols, etc.,; Risset's compositions, against take your pick: Mutations II, Inharmonique, Songes, etc. Jonathan Harvey's Mortuos Plango Vivos Voco, and so on and so on. Slaymaker, in 1970, described some perceptual & musical characteristics of harmony and melody which uses inharmonic tunings and inharmonic timbres: "Not all musical instruments [use harmonic series timbres], however. The cast bell carillon and tubular chimes, for example, have tones that are not made up of harmonics. Many of the intervals traditionally defined as consonant sound quite dissonant on these instruments; therefore, true chords are seldom played on either of them, and chimes are usually used in the orchestra only for special effects. Conversely--a situation seldom realized--some of the intervals that have been classed as dissonant can sound quite smooth on these inharmonic instruments. Consonant sounds can also be produced from synthetic tones having partials that are spaced by a constant ratio, as long as the partials appearing in a chord are not spaced closer than the critical bandwidth of the ear." [Slaymaker, F. H., "Chords From Tones Having Stretched Partials," J. Acoust. Soc. Am., Vol. 47, No. 6, 1970, pg. 1569] Slaymaker goes on to describe the effect of increasing timbral inharmonicity while playing a traditional chord sequence: "The impression of traditional predictability still persisted, though the tone quality gradually became more chime-like and the intervals of the scale became more noticeably different from the familiar tempered scale; i.e., the sequence began to sound 'out-of- tune.' The change in the S value from 1.083333 to 1.261839 resulted in a completely different impression for the chord sequence, compared to tfe impression for the values of S nearer unity. All of the traditional predictability was gone. The chords sounded smooth and nondissonant but strange and somewhat eerie. The effect was so different from the tempered scale that there was no tendency to judge in-tuneness and out-of- tuneness. It seemed like a peek into a new and unfamiliar musical world, in which none of the old rules applied and the new ones, if any, were yet undiscovered." [ op. cit., pg. 1569] With the advent of William Sethares' landmark paper "Local consonance and the relationship between timbre and scale," J. Acoust. Soc. Am., Vol. 94, No. 3, 1993, pp. 218-1228, those rules became clear. Demonstrations like Slaymaker's sounded "out-of-tune" as the inharmonicity of the timbres increased, because the chord progressions were based on traditional Western musical intervals...which are themselves closely related to low members of the harmonic series. If instead the chord progressions of inharmonic tones are based on an *inharmonic series* (and not simply a set of arbitrarily stretched members of the harmnic series, but rather a coherent self-contained inharmonic series- viz., the vibrational modes of the free-free metal bar, or of the free metal tube) then the inharmonic chord progressions will produce a sense of finality and cadence. This is also the reason why Mathews and Pierce reported that extreme values of partial stretch resulted in a destruction of the finality of the cadences--Mathews and Pierce were also using cadences whose triadic root movements were based on *harmonic-series-related* intervals. However, I have used the commercial resynthesis package FdSoft to analyze and resynthesize sampled sounds. Although this package is greatly inferior to the LEMUR Fourier analysis/ resynthesis software available for the Macintosh (which I cannot run since I have only a Mac Plus), FdSoft does analyze and resynthesize some timbres relatively well. For instance, solo brass instruments, strong (not whispered) vocal timbres, and some solo woodwinds and double reed instruments retain their identity well upon Fourier analysis/resynthesis without modification. Using FdSoft, I have determined that most timbres retain their identity well when resynthesized with slightly inharmonic partials--for example, setting the partials of a resynthesized trumpet or trombone or clarinet or english horn note to the closest values available in 41-TET produces an inharmonic sound which is virtually unchanged perceptually from the original sampled sound, yet exhibits subtly increased sensory consonance when used in 41-TET triads. Warping the partial frequencies by larger values (for instance, setting them to the nearest approximations available in 11-TET or 13-TET) produces a slight perceptual distortion of the trumpet or trombone or clarinet or english horn note upon resynthesis... The effect is somewhat similar to very slight ring modulation. These timbres, however, exhibit greatly increased sensory consonance upon resynthesis. Pushing this method to its uttermost extreme, I have determined that some sounds even retain their identity well upon radical timbre-mapping. For example, a trombone note retains its identity very well even when mapped into the closest partials of the free-free metal bar scale (with all partials not close to members of the metal bar scale deleted). The resulting timbre sounds slightly denatured and empty because large numbers of partials have been deleted, but the sound is still recognizably a trombone--but, weirdly, it sounds like a trombone crossed with a chime. The effect is very strnage--as though you could somehow put a mouthpiece on a metal bar and instead of striking the bar, produce sound by blowing through the mouthpiece. (A perceptual paradox I've also heard in the Yamaha series of physical modelling synthesizers, which allow you to "put a mouthpiece" on a bowed string instrument and "blow" instead of bow a violin or cello or viola.) Most sounds do not retain their iden well when their component partials are mapped into such a radical non-just non-equal-tempered scale, but *all* such resynthesized sounds retain the sense of spectral fusion--no doubt because all the original auditory cues are still present: synchronous fluctuations of amplitude envelope in each partial, the slight trajectory in frequency for each partial, the initial identical "blip" of the attack of all the partials, the overall synchrony of the partial envelopes and the ensemble effect produced by their synchronized decay, etc. My experiments in this area, however, pale before William Sethares' investigations. William Sethares has produced many musical examples using inharmonic timbres and inharmonic tunings. The tunings sound convincing, consonance and dissonant are present, and cadences exist--yet they are unlike those present in harmonic-series- based music. With typical clarity, Sethares points out that "One subtlety that arises when dealing with nonharmonic partials is that it is important for the partials to fuse, to be perceived holistically as a single entity rather than as a collection of oddly placed sine waves. Fusing is greatly helped by commonalities in the partials: similar pitch vibrato, similar amplitude fluctuations, similar onset times and similar envelopes." [Sethares, W., "Local Consonance and the Relationship between Timbre and Scale," J. Acoust. Soc. Am., Vol. 94, No3., Sept. 1993, pg. 1227] William Sethares' music is the most convincing example yet of the falsity of Erlich's contention. From now on, people, please read the literature before making these kind of claims. Please get the facts straight, and do the reserach. Let us hear no more of verifiably false claims that inharmonic timbres cannot spectrally fuse, or that they necessarily produce (via virtual pitch) unrelated and bizarre fundamental pitches: anyone who doubts that inharmonic timbres can be used to produce convincing and entirely musical cadences & harmonies need only e-mail William Sethares and ask for a copy of his demonstration tapes. Or, if you prefer, simply persue the article "Applying Psychoacoustics in Composition: `Harmonic' Progressions of `Nonharmonic' Sonorities," Parncutt, R. and H. Strasburger, Perspectives of New Music, Vol. 39, Nos. 1-2, 1995, pp. 88-127 --mclaren Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Tue, 16 Jul 1996 22:48 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id NAA14010; Tue, 16 Jul 1996 13:48:19 -0700 Date: Tue, 16 Jul 1996 13:48:19 -0700 Message-Id: <199607162047.VAA12564@gollum.globalnet.co.uk> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu