Subject: Re: J.R Pierce paper From: Kevin Austin <kevin.austin@xxxxxxxx> Date: Mon, 11 Jun 2012 20:27:04 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--Boundary_(ID_+P1tDO6G18zaSbycPrdJ3Q) Content-type: text/plain; CHARSET=US-ASCII Content-transfer-encoding: 7BIT An interesting idea. Following from the statement: Our previous work demonstrated that chords with frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic properties of major triads (4:5:6 ratios). The traditional diatonic scale can be constructed from three major chords, the tonic, the dominant, and the subdominant chords. I took some liberties with names and numbers to simplify the results. Build a 'C major triad' , C E G. ratio 4:5:6 The 'C' is the 5th of the subdominant chord, F, and G is the root of the dominant. Using this ratio to build the F and G triads, and using foldover octave equivalence, the C 'major' scale, [starting on the arbitrary frequency of 400 Hz], seems to come out as follows: C 400 D 450 E 500 F 533 G 600 A 666 B 750 C 800 This scale may already have a name. The three primary major triads would be beat free. I think that melodies constructed from here might be quite interesting for the general population. By extension up and down, F# and Bb would be introduced. Built on the D, the notes would be D, 450Hz, F# 562Hz and A 675. This A is higher than that in the F major triad. Maybe the solution would be to split the difference and tune A to 670Hz. It would be about equally inharmonic with both triads . . . Kevin On 2012, Jun 11, at 3:32 PM, Richard F. Lyon wrote: > It does show up at their site, but it's only an abstract from a meeting; there is no corresponding paper. > http://pdfserv.aip.org/JASMAN/vol_75/iss_S1/S10_3.pdf > > d > > > At 10:02 AM -0700 6/11/12, richard duckworth wrote: >> Hi all, does anyone have this? I even have a JASA sub. but it doesn't show up on their site!! >> Four new scales based on nonsuccessive-integer-ratio chords >> J. Acoust. Soc. Am. Volume 75, Issue S1, pp. S10-S10 (1984); (1 page) >> M. V. Mathews1, L. A. Roberts1, and J. R. Pierce2 >> >> Thanks, Rich >> >> >> Rich Duckworth >> Lecturer in Music Technology >> Department of Music >> House 5 >> Trinity College >> Dublin 2 >> Ireland >> Tel 353 1 896 1500 >> >> >> It's the most devastating moment in a young mans life, when he quite reasonably says to himself, "I shall never play The Dane!" > > --Boundary_(ID_+P1tDO6G18zaSbycPrdJ3Q) Content-type: text/html; CHARSET=US-ASCII Content-transfer-encoding: quoted-printable <html><head><base href=3D"x-msg://13/"></head><body style=3D"word-wrap: = break-word; -webkit-nbsp-mode: space; -webkit-line-break: = after-white-space; "><div>An interesting idea. Following from the = statement:</div><div><br></div><div><span class=3D"Apple-style-span" = style=3D"color: rgb(45, 45, 45); font-family: Verdana; font-size: 12px; = line-height: 21px; ">Our previous work demonstrated that chords with = frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic = properties of major triads (4:5:6 ratios). The traditional diatonic = scale can be constructed from three major chords, the tonic, the = dominant, and the subdominant = chords. </span></div><div><br></div><div>I took some liberties with = names and numbers to simplify the = results.</div><div><br></div><div>Build a 'C major triad' , C E = G. ratio 4:5:6</div><div>The 'C' is the 5th of the = subdominant chord, F, and G is the root of the = dominant.</div><div><br></div><div>Using this ratio to build the F and G = triads, and using foldover octave equivalence, the C 'major' scale, = [starting on the arbitrary frequency of 400 Hz], seems to come out as = follows:</div><div><br></div><div> C 400</div><div> D = 450</div><div> E 500</div><div> F = 533</div><div> G 600</div><div> A = 666</div><div> B 750</div><div> C = 800</div><div><br></div><div>This scale may already have a name. = The three primary major triads would be beat free. I think that = melodies constructed from here might be quite interesting for the = general population.</div><div><br></div><div>By extension up and down, = F# and Bb would be introduced. Built on the D, the notes would be D, = 450Hz, F# 562Hz and A 675. This A is higher than that in the F major = triad. Maybe the solution would be to split the difference and tune A to = 670Hz. It would be about equally inharmonic with both triads . . = . </div><div><br></div><div><br></div><div>Kevin</div><div><br></div>= <div><br></div><br><div><div>On 2012, Jun 11, at 3:32 PM, Richard F. = Lyon wrote:</div><br class=3D"Apple-interchange-newline"><blockquote = type=3D"cite"><span class=3D"Apple-style-span" style=3D"border-collapse: = separate; font-family: Courier; font-style: normal; font-variant: = normal; font-weight: normal; letter-spacing: normal; line-height: = normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; = text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; = -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: = 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: = auto; -webkit-text-stroke-width: 0px; font-size: medium; "><div><div>It = does show up at their site, but it's only an abstract from a meeting; = there is no corresponding paper.</div><div><a = href=3D"http://pdfserv.aip.org/JASMAN/vol_75/iss_S1/S10_3.pdf">http://pdfs= erv.aip.org/JASMAN/vol_75/iss_S1/S10_3.pdf</a></div><div><br></div><div>d<= /div><div><br></div><div><br></div><div>At 10:02 AM -0700 6/11/12, = richard duckworth wrote:</div><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; ">Hi all, does anyone = have this? I even have a JASA sub. but it doesn't show up on their = site!!<br></blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; "><font = size=3D"+3"><b>Four new scales based on nonsuccessive-integer-ratio = chords</b></font><br><font = size=3D"+3"><b></b></font></blockquote><blockquote type=3D"cite" cite=3D""= style=3D"padding-top: 0px; padding-bottom: 0px; ">J. Acoust. Soc. Am. = Volume 75, Issue S1, pp. S10-S10 (1984); (1 = page)</blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; ">M. V. = Mathews1, L. A. Roberts1, and J. R. = Pierce2</blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; = "><br></blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; ">Thanks, = Rich</blockquote><blockquote type=3D"cite" cite=3D"" style=3D"padding-top:= 0px; padding-bottom: 0px; "> </blockquote><blockquote type=3D"cite" = cite=3D"" style=3D"padding-top: 0px; padding-bottom: 0px; = "><br></blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; ">Rich = Duckworth<br>Lecturer in Music Technology<br>Department of = Music<br>House 5<br>Trinity College<br>Dublin = 2<br>Ireland<br></blockquote><blockquote type=3D"cite" cite=3D"" = style=3D"padding-top: 0px; padding-bottom: 0px; ">Tel 353 1 896 = 1500</blockquote><blockquote type=3D"cite" cite=3D"" style=3D"padding-top:= 0px; padding-bottom: 0px; "><br><br></blockquote><blockquote = type=3D"cite" cite=3D"" style=3D"padding-top: 0px; padding-bottom: 0px; = ">It's the most devastating moment in a young mans life, when he quite = reasonably says to himself, "I shall never play The = Dane!"</blockquote><div><br></div></div></span><br = class=3D"Apple-interchange-newline"></blockquote></div><br></body></html>= --Boundary_(ID_+P1tDO6G18zaSbycPrdJ3Q)--