Klarinet Archive - Posting 000561.txt from 2004/11

From: "Keith" <100012.1302@-----.com>
Subj: [kl] RE: pitch standard
Date: Fri, 19 Nov 2004 09:26:34 -0500

Tony,

Sorry for the delay in replying. That was an oops! You are quite right, the
major thirds in the diatonic scale, constructed from the triads, all have
necessarily the same ratio (4:5). I should have said *minor* thirds. The
minor thirds from III-V, VI-VIII and VII-IX (=II) are part of the triads on
the tonic, dominant and subdominant and will all have the same ratios (5:6).
But the minor third from II-IV (D to F in the scale of C) is not part of
those triads. It comes (according to Helmholz' convincing arguments) from
the fifth of the dominant, and the subdominant, and has the ratio 6:7, a bit
narrower. Seconds are also not the same through the scale.

Ratios are not the whole story. Joe Fasel has pointed out that choirs tend
to sharpen thirds. According to Eskelin, this is only in a triad, ie when
the fifth is also sounding, and when the third is sung on its own, the
interval is sung close to the "pure" 4:5 ratio to eliminate beats. Do you
have this experience also? It may be emphasis of the major character of the
chord, but this is speculation and needs research on perception.

Another curious perception is that if a tone is generated with a constant
known frequency (including with partials), and increased in volume, it
sounds as if it is going flat.

Keith Bowen

Date: Tue, 09 Nov 2004 12:13:30 +0100
To: klarinet@-----.org
From: Tony Pay <tony.p@-----.org>
Subject: Re: [kl] RE: pitch standard
Message-ID: <5f651a0b4d.tony.p@-----.org>
On 9 Nov, "Keith" <100012.1302@-----.com> wrote:
> The construction of the scale is most sensibly seen (I think!) by the
approach
> first given by Helmholz (in Tonempfindung, available in Dover "On the
sensations of tone").
> We can tune octaves, fifths and triads easily by absence of beats. So
> we get the scale by the major triads based on the tonic (I), the dominant
(V)
> and the subdominant (IV). The subdominant is tuned a fifth below the
tonic.
> Note that in this method, which is probably used instinctively in
orchestral tuning,
> the major thirds in the scale (eg C to E, F to A and G to B) do not have
> the same ratios. So how they are tuned will depend on the harmonic
context.

I don't understand this bit. If you use the major triads to get E, A and B
(and D) from C, F and G in C major, you *do* get those major thirds in the
same ratios, surely?

Tony

--

_________ Tony Pay

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