source file: m1421.txt Date: Tue, 19 May 1998 10:53:13 -0400 Subject: Response to Erlich's reply to me in TD 1420 From: monz@juno.com (Joseph L Monzo) [Erlich:] >>> I think the fact that the tritone in major nearly forms a 4:5:6:7 >>> with the dominant, and that the tritones in minor nearly form >>> an 8:10:12:14:17 with the dominant, were not inconsequential >>> for the development of tonal harmony. [Monzo:] >> I don't think the fact that the tritones are close to septimal >> consonances has anything to do with the development of >> tonal harmony... >> >> The 64/45 would normally be considered the tritone which appears >> in the 5-limit Dominant 7th chord of 36:45:54:64. 4:5:6:7 is the >> same as 36:45:54:63. [Erlich:] > This whole argument smacks of what I object to in the prime-limit > theoreticians' approach. Harmonically speaking, an interval is never > more likely to be interpreted as a higher-odd-limit, lower-prime-limit > ratio than a higher-prime-limit, lower odd-limit ratio, holding the > approximation error constant. [Monzo:] I'd be interested in seeing some quantifiable info about this. Have there been experiments which prove this statement? I think this is an important and overlooked aspect of the prime/ odd debate in this forum. Lemme see some numbers. [Erlich:] > I think the four 5-prime-limit ratios you > listed have very little to do with the way a tritone is heard > harmonically, even if tuned to exactly those ratios. Although I agree > that the Pythagorean tritones, despite their low prime limit, are very > dissonant, I don't think the JI tritones are "much" more consonant. In > fact, they may even be more dissonant, since the Pythagoean tritones > approximate simple 7-limit ratios better. [Monzo:] Well, Paul, the reason you say these things is because you favor ETs, where you must be concerned with consistency, approximations, etc. In real just tuning, the differences are quite audible. The 5-limit tritones provide a biting dissonance in the "dominant 7th" chord that *demand* resolution onto the major or minor triad on the "tonic". A perfectly tuned 4:5:6:7 chord is only a tiny bit less consonant than a plain old 4:5:6 triad. There's a big difference in the sound and feel from the 3- and 5-limit "dominant 7th"s, provided they are in perfect tune also. And we're not talking about the tritone dyad by itself, we're talking about a 4-part chord. [Erlich:] > Anyway, I maintain that the fact that the tritones reinforced the > root of the dominant chord when combined with it harmonically > helped to define major and minor as the "tonal modes", while > other modes without such harmonic-melodic focus fell out of use. [Monzo:] It's important to remember that the 36:45:54:64 dominant 7th chord arose as a result of using a circumscribed set of pitches. In a 5-limit system which is using only the 7 diatonic scale pitch-classes, this particular set of proportions could only occur over the dominant. I really think that in perfect just tuning, the 3- or 5-limit chords as a whole beat too much to be nailed down as a 4:5:6:7 However, I'm am willing to grant the possibility that Erlich's idea may have some validity. I certainly agree that in hearing the music the 3- or 5-limit tritones would normally be interpreted as the much simpler 7:5 _if we are isolating the tritone_. ------------------------------------------------------------------------ [Me:] >> Chords can be tuned in JI with a variety of ratios >> that are close enough to a "target" that many of >> these ambiguities can be explored rationally. [Erlich:] > Yes, Joe, you are correct about that, but it seems > that you may have been implying otherwise in your > post about tritones. That is, I don't think 64:45 can > itself be a "target" but is instead close to several > possible targets. Other notes in the chord can clarify > which target that is, and in the case of dominant > seventh chords, only 7:5 can fit with all the other > ratios to define a simple "target chord". [Monzo:] I'm glad you didn't misinterpret me here: I should have specified that the "target" would be a lower-prime/ lower-odd ratio. You're exactly correct that any of these more complicated ratios would imply a 7:5 (or 10:7, depending on context). Joseph L. Monzo monz@juno.com _____________________________________________________________________ You don't need to buy Internet access to use free Internet e-mail. Get completely free e-mail from Juno at http://www.juno.com Or call Juno at (800) 654-JUNO [654-5866]