Subject: harmonic extraction From: "Richard M. Warren" <rmwarren@xxxxxxxx> Date: Thu, 2 Apr 2009 12:27:11 -0500 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--Apple-Mail-8-540510469 Content-Type: text/plain; charset=WINDOWS-1252; format=flowed; delsp=yes Content-Transfer-Encoding: quoted-printable In the series of auditory list comments on =93harmonic extraction,=94 =20= there has been some speculation concerning the basis for the =20 distinctive properties of odd-harmonic tones. To start with, all =20 tones lacking even harmonics have alternating polarity waveforms, and =20= all tones with alternating polarity waveforms (e.g., square waves, =20 symmetrical triangular waves, and alternating polarity pulse trains) =20 have odd-harmonic spectra. Long years ago, Warren and Wrightson =20 (1981) used iterated alternating polarity randomly determined =20 waveforms (i.e., frozen noise segments) as representative odd-harmonic =20= tones. It was found that these tones can produce a dominant pitch of =20= 2F0 with repetition frequencies up to about 100 Hz and a pitch of F0 =20 at repetition frequencies above roughly 200 Hz. Simultaneous pitches =20= were heard between these frequencies. Further experiments have shown =20= that in the ambiguous range of fundamental frequencies between roughly =20= 100 and 200 Hz, unresolved harmonics produced pseudoperiodicities, one =20= slightly more and the other slightly less than 2F0. The bases for =20 these pitches were described concisely in the abstract by Bashford and =20= Warren (1990): Previous studies have shown that tones consisting solely of odd =20 harmonics can produce two types of low pitch, one matching the =20 fundamental frequency and another approximately 1 octave higher. The =20 present study examined the bases of these pitches. Musicians provided =20= matches for odd-harmonic triads (3rd, 5th, and 7th; 5th, 7th, and =20 9th;...; 17th, 19th, and 21st) having a common, missing fundamental =20 ranging from 100 to 200 Hz. Low-order triads were matched to the =20 fundamental, whereas high-order triads produced pitches approximately =20= 1 octave higher, but deviating from exact doubling of the fundamental =20= by an amount consistent with the waveform pseudoperiodicities. =20 Interestingly, the change from fundamental to pseudoperiod matching =20 occurred with triads centered at about the 9th or 11th harmonic, which =20= have frequency separations approximating those of the dominant =20 partials in an =93all-harmonic=94 signal. These results, together with =20= neurophysiological evidence in the literature, indicate that harmonics =20= within the dominant region interact sufficiently to provide a temporal =20= basis for pitch. It appears that the dominant region is a transition =20 zone where two modes of pitch analysis overlap. The pitches of odd-harmonic tones are discussed at greater length in =20 Warren (2008). R.M. Warren and J.M. Wrightson, =93Stimuli producing conflicting =20 temporal and spectral cues to frequency,=94 JASA, 1981, 70 (4), = 1020-1024. J.A. Bashford, Jr. and R.M. Warren, =93The pitch of odd-harmonic tones: = =20 Evidence of temporal analysis in the dominance region,=94 JASA, 1990, =20= 88, S48. R.M. Warren, Auditory Perception: An Analysis and Synthesis (3rd =20 edition), Cambridge University Press, 2008 (see Chapter 3, Perception =20= of acoustic repetition: Pitch and infrapitch). --Apple-Mail-8-540510469 Content-Type: text/html; charset=WINDOWS-1252 Content-Transfer-Encoding: quoted-printable <html><body style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; "><div><div><div = style=3D"margin-top: 0px; margin-right: 0px; margin-bottom: 0px; = margin-left: 0px; min-height: 14px; "><span class=3D"Apple-style-span" = style=3D"-webkit-text-stroke-width: -1; "><font class=3D"Apple-style-span"= face=3D"Times">In the series of auditory list comments on =93harmonic = extraction,=94 there has been some speculation concerning the basis for = the distinctive properties of odd-harmonic tones.</font><span = style=3D"mso-spacerun: yes"><font class=3D"Apple-style-span" = face=3D"Times"> </font></span><font class=3D"Apple-style-span" = face=3D"Times">To start with, all tones lacking even harmonics have = alternating polarity waveforms, and all tones with alternating polarity = waveforms (e.g., square waves, symmetrical triangular waves, and = alternating polarity pulse trains) have odd-harmonic = spectra.</font><span style=3D"mso-spacerun: yes"><font = class=3D"Apple-style-span" face=3D"Times"> </font></span><font = class=3D"Apple-style-span" face=3D"Times">Long years ago, Warren and = Wrightson (1981) used iterated alternating polarity randomly determined = waveforms (i.e., frozen noise segments) as representative odd-harmonic = tones.</font><span style=3D"mso-spacerun: yes"><font = class=3D"Apple-style-span" face=3D"Times"> </font></span><font = class=3D"Apple-style-span" face=3D"Times">It was found that these tones = can produce a dominant pitch of 2F0 with repetition frequencies up to = about 100 Hz and a pitch of F0 at repetition frequencies above roughly = 200 Hz.</font><span style=3D"mso-spacerun: yes"><font = class=3D"Apple-style-span" face=3D"Times"> </font></span><font = class=3D"Apple-style-span" face=3D"Times">Simultaneous pitches were = heard between these frequencies.</font><span style=3D"mso-spacerun: = yes"><font class=3D"Apple-style-span" face=3D"Times"> = </font></span><font class=3D"Apple-style-span" face=3D"Times">Further = experiments have shown that in the ambiguous range of fundamental = frequencies between roughly 100 and 200 Hz, unresolved harmonics = produced pseudoperiodicities, one slightly more and the other slightly = less than 2F0.</font><span style=3D"mso-spacerun: yes"><font = class=3D"Apple-style-span" face=3D"Times"> </font></span><font = class=3D"Apple-style-span" face=3D"Times">The bases for these pitches = were described concisely in the abstract by Bashford and Warren = (1990): </font></span></div></div><div style=3D"word-wrap: = break-word; -webkit-nbsp-mode: space; -webkit-line-break: = after-white-space; "><blockquote class=3D"webkit-indent-blockquote" = style=3D"text-align: justify;margin-top: 0px; margin-right: 0px; = margin-bottom: 0px; margin-left: 40px; border-top-style: none; = border-right-style: none; border-bottom-style: none; border-left-style: = none; border-width: initial; border-color: initial; padding-top: 0px; = padding-right: 0px; padding-bottom: 0px; padding-left: 0px; "><font = class=3D"Apple-style-span" face=3D"Times" size=3D"4"><span = class=3D"Apple-style-span" style=3D"font-size: 15px;">Previous studies = have shown that tones consisting solely of odd harmonics can produce two = types of low pitch, one matching the fundamental frequency and another = approximately 1 octave higher. The present study examined the bases of = these pitches. Musicians provided matches for odd-harmonic triads (3rd, = 5th, and 7th; 5th, 7th, and 9th;...; 17th, 19th, and 21st) having a = common, missing fundamental ranging from 100 to 200 Hz. Low-order triads = were matched to the fundamental, whereas high-order triads produced = pitches approximately 1 octave higher, but deviating from exact doubling = of the fundamental by an amount consistent with the waveform = pseudoperiodicities. Interestingly, the change from fundamental to = pseudoperiod matching occurred with triads centered at about the 9th or = 11th harmonic, which have frequency separations approximating those of = the dominant partials in an =93all-harmonic=94 signal. These results, = together with neurophysiological evidence in the literature, indicate = that harmonics within the dominant region interact sufficiently to = provide a temporal basis for pitch. It appears that the dominant region = is a transition zone where two modes of pitch analysis = overlap. </span></font></blockquote><div style=3D"text-align: = justify;"><div style=3D"margin-left: 27pt; text-align: justify; = "><br></div> <!--EndFragment--> </div><div><div style=3D"word-wrap: = break-word; -webkit-nbsp-mode: space; -webkit-line-break: = after-white-space; "><div style=3D"text-align: justify;"></div><div><div = style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; = -webkit-line-break: after-white-space; "><div><div style=3D"word-wrap: = break-word; -webkit-nbsp-mode: space; -webkit-line-break: = after-white-space; "><div style=3D"text-align: justify;"><font = class=3D"Apple-style-span" face=3D"Times">The pitches of odd-harmonic = tones are discussed at greater length in Warren (2008).</font><span = style=3D"mso-spacerun: yes"><font class=3D"Apple-style-span" = face=3D"Times"> </font></span></div><div><div style=3D"word-wrap: = break-word; -webkit-nbsp-mode: space; -webkit-line-break: = after-white-space; "><div><div style=3D"word-wrap: break-word; = -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div = class=3D"MsoNormal"><div class=3D"MsoNormal"><font = class=3D"Apple-style-span" face=3D"Times"><br></font></div> <div = class=3D"MsoNormal"><font class=3D"Apple-style-span" = face=3D"Times"> </font><font class=3D"Apple-style-span" = face=3D"Times"><o:p></o:p></font></div> <div class=3D"MsoNormal"><font = class=3D"Apple-style-span" face=3D"Times">R.M. Warren and J.M. = Wrightson, =93Stimuli producing conflicting temporal and spectral cues = to frequency,=94 JASA, 1981, 70 (4), 1020-1024.</font><font = class=3D"Apple-style-span" face=3D"Times"><o:p></o:p></font></div> <div = class=3D"MsoNormal"><font class=3D"Apple-style-span" = face=3D"Times"> </font><font class=3D"Apple-style-span" = face=3D"Times"><o:p></o:p></font></div> <div class=3D"MsoNormal"><font = class=3D"Apple-style-span" face=3D"Times">J.A. Bashford, Jr. and R.M. = Warren, =93The pitch of odd-harmonic tones:</font><span = style=3D"mso-spacerun: yes"><font class=3D"Apple-style-span" = face=3D"Times"> </font></span><font class=3D"Apple-style-span" = face=3D"Times">Evidence of temporal analysis in the dominance region,=94 = JASA, 1990, 88, S48.</font><font class=3D"Apple-style-span" = face=3D"Times"><o:p></o:p></font></div> <div class=3D"MsoNormal"><font = class=3D"Apple-style-span" face=3D"Times"> </font><font = class=3D"Apple-style-span" face=3D"Times"><o:p></o:p></font></div> <span = style=3D""><font class=3D"Apple-style-span" face=3D"Times">R.M. Warren, = </font><i><font class=3D"Apple-style-span" face=3D"Times">Auditory = Perception:</font><span style=3D"mso-spacerun: yes"><font = class=3D"Apple-style-span" face=3D"Times"> </font></span><font = class=3D"Apple-style-span" face=3D"Times">An Analysis and Synthesis (3rd = edition)</font></i></span><span style=3D""><font = class=3D"Apple-style-span" face=3D"Times">, Cambridge University Press, = 2008 (see Chapter 3, Perception of acoustic repetition:</font><span = style=3D"mso-spacerun: yes"><font class=3D"Apple-style-span" = face=3D"Times"> </font></span><font class=3D"Apple-style-span" = face=3D"Times">Pitch and = infrapitch).</font></span><!--EndFragment--><font = class=3D"Apple-style-span" face=3D"Times"> </font></div> <div = class=3D"MsoNormal"><font class=3D"Apple-style-span" = face=3D"Times"> </font><font class=3D"Apple-style-span" = face=3D"Times"><o:p></o:p></font></div> <!--EndFragment--> = </div></div><font class=3D"Apple-style-span" = face=3D"Times"><br></font></div></div><font class=3D"Apple-style-span" = face=3D"Times"><br></font></div></div><font class=3D"Apple-style-span" = face=3D"Times"><br></font></div></div><font class=3D"Apple-style-span" = face=3D"Times"><br></font></div></div><font class=3D"Apple-style-span" = face=3D"Times"><br></font></div></div><br></body></html>= --Apple-Mail-8-540510469--