Re: consonance of MELODIC intervals (Eckard Blumschein )


Subject: Re: consonance of MELODIC intervals
From:    Eckard Blumschein  <Eckard.Blumschein(at)E-TECHNIK.UNI-MAGDEBURG.DE>
Date:    Mon, 26 Jun 2000 14:28:20 +0200

Dear Piet Vos, I just respond because I see your question related to my opinion that harmony is based on coincidence detection. I am not aware of any deviation from Zarlino's simple fraction rule. So I naively read the well known figure by Buser and Imbert 1992 after Wood 1944 after Helmholtz 1883, showing hardness of the sound of two violins as a function of frequency ratios, roughly as follows: C4-C4: 1:1 (prime) 0/12 1 C4-C5: 2:1 (octave) 12/12 2 C4-G4: 3:2=1.5 (fifth) 7/12: 1.49831 diff. -0.00169 C4-F4: 4:3=1.33 (fourth) 5/12: 1.33484 diff. +0.00151 C4-A4: 5:3=1.66 (sixth) 9/12: 1.68179 diff. +0.01512 very large C4-E4: 5:4=1.25 (major third) 4/12: 1.25992 diff. +0.00992 large C4-Dis4: 6:5=1.2 (minor third) 3/12: 1.18921 diff. -0.01079 large void 7:4=1.75 C4-Fis4: 7:5=1.4 6/12: 1.41421 diff. +0.01421 very large C4-Gis4: 8:5=1.6 8/12: 1.58740 diff. -0.01260 large void: 9:5=1.8 void: 7:6=1.166 void: 8:7=1.14857 etc. C4-D4: 9:8=1.125 2/12: 1.12246 diff. +0.00254 C4-Ais: (16:9=1.777) 10/12: 1.78180 diff. +0.00402 C4-B4: (17:9=1.8888) 11/12: 1.88775 diff. -0.00114 C4-Cis4: (17:16=1.0625) 1/12: 1.05946 diff. -0.00304 It is just my guesswork that people may mainly differ with respect to tolerance against deviation from the matching frequency at equally tempered scale. In case of a third, that difference amounts about 0.01 times 256 Hz = 2.56 Hz, it is, in terms of period about 32 microseconds. This is of the same order as enlargement of perceived octave with respect to the real one. Has anyone looked for an similar effect on fifth and third? I realized that octave enlargement equals an first-order ISI perception error of about 16 microseconds, independent of frequency, that might correspond to width of action potential. Regards, Eckard Blumschein At 15:36 20.06.00 +0200, you wrote: >Hi, > >Does someone know how to order the 13 within-octave MELODIC intervals >(prime, minor 2nd,... octave) as a function of consonance. I believe to >know that there are more than one different possible orderings, in >dependence of the theory on consonance (psycho-acoustical, mathematical, >... theory). Thanks in advance for any help! > >Piet V. > >Piet G. Vos >section Perception NICI, U. Nijmegen >P.O.Box 9104 >6500 HE Nijmegen NL >tel: +31 24 36126 31/20; fax: +31 24 361 60 66; vos(at)nici.kun.nl >home-page: http://www.nici.kun.nl/~vos > > >"et altissimus humilissimum facere debet" >


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