RE: harmony and small integer frequency ratios

>
> >Just intervals of small interval ratios have a uniquely pure
> > sound.
>
>Yup.
>
> >This purity is not always desirable.
>
>Right. If an n:1 frequency ratio is tuned too purely in sustained harmonic
>timbres, the upper note will disappear.
>
> >Differences of tuning as small as 1 cent do affect the sound
> >of the chord. I'm unable to try smaller intervals at present.
>
>Real musicians playing acoustic instruments don't have this level of control.
>
> >When an interval is detuned by more than a few cents, this
> > detuning has more of an impact on the sound of the chord than
> > the particular ratios involved, provided the latter are small
> >(I haven't worked out how small yet).
>
>It depends what you're listening to. If the chord occurs as a result of
>simultaneous melodic lines in a piece of music, I don't think you're right,
>unless you'd allow 20 cents to be considered a few cents. If you're listening
>for beats, then yes, you're exactly right.
>
> >All of the above depends strongly on timbre
>
>Amen. Volume as well.
>
> >The idea that dissonance increases with prime limit is
> >erroneous.
>
>I agree. The odd limit is a much better indicator. I bought a copy of
>Partch's book while in San Francisco (I last read it many years ago) and on
>virtually every page there is evidence, often strong, emphatic evidence, that
>his definition of "limit" was the odd, not prime, definition. All the Partch
>"experts" using the prime definition frustrate me to no end as they clearly
>have not listened as much as Partch and yet fail to understand the ideas he
>derived from years of listening. And for those using the prime limit
>definition to describe the resources of a tuning system rather than
>consonance/dissonance issues, what information is contained in the knowledge
>of the highest prime one is using that is more important than knowing any of
>the other primes one is or is not using?
>
>>The 3-5-7 limits happen to get progressively out
>>of tune in 12tet, though, which may be the origin of this.
>
>3, 5 and 7 are successive odd numbers, so I don't think one has to resort to
>12tet to explain the increasing dissonance of their respective intervals
>(which I clearly hear). However, since you're using a "prime," not "odd"
>definition, of limit, I think you're right; for example, 9:8 and 16:9 are
>more familiar, due to 12tet conditioning, than 8:7 and 7:4, but the latter
>would be more consonant if one could erase the conditioning. Many who cannot
>undo their conditioning therefore conclude that prime limit 3 is more
>consonant than prime limit 7, but I would say that this is not true; it is
>only true that odd limit 3 is more consonant that odd limit 7. Odd limit 9 is
>naturally slightly more dissonant that odd limit 7, though this ordering may
>be culturally altered. However, what is considered "in tune" and "out of
>tune" may have much more to do with familiar scalar intervals than familiar
>harmonic intervals, and some pure 7s hidden in inner voices will sound just
>fine to even the most culturally conditioned of listeners.


SMTPOriginator: tuning@eartha.mills.edu
From: William Sethares
Subject: psychoacoustic foundations
PostedDate: 28-10-97 16:15:45
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