Non-Equal Temperaments

[Don Gilmore]

Pure fifth in what key?  Between what two notes?  You can't have pure fifths
between all pairs of notes that are a fifth apart.

Don

----- Original Message ----- 
From: "Conrad Hoffsommer" <hoffsoco@martin.luther.edu>
To: "Pianotech" <pianotech@ptg.org>
Sent: Friday, April 02, 2004 1:26 PM
Subject: Re: Non-Equal Temperaments


> Corte,
>
>
> >On 2-apr-04, at 15:48, Corte Swearingen wrote:
> >>Hello List,
> >>
> >>My question is this.  I'm wondering if unequal temperaments tend to
sound
> >>like they are going out of tune quicker than equal temperament.  My
> >>reasoning is that if some of the notes are already altered from equal
> >>temperament, isn't there less of a "window" of pitch shift before the
piano
> >>starts to sound out of tune?  Does this seem to be a valid question
and/or
> >>concern?
>
>
> Unequal temperaments frequently have PURE fifths, fourths and/or
> thirds.  Therefore, if the tuning starts to slip and one of these pure
> intervals is beating, it is IMMEDIATELY recognisable as being out of tune.
>
> No ifs, ands, or buts.  It _is_ or it _isn't_ PURE.
>
> Also, that pure interval is frequently the other side of one which is real
> close to being a "wolf".  One common note slipping can not only "temper" a
> pure interval, but create a REAL nasty interval out of one which had been
> only borderline nasty.
>
> Tempering is controlled mis-tuning.  In equal temperament, NOTHING is pure
> except unisons.  Not even octaves - take your pick... 2:1, 6:3, 4:2   They
> are all different.
>
> Can you listen to a major third which theoretically should beat at 9.7,
but
> happens to be beating at 9.6 or 9.5, and IMMEDIATELY tell that it is slow
> without a machine or using several checks?
>
> There is more "wiggle room" in equal temperament than in a temperament
> which uses pure intervals.
>
> My 2.1¢ - readily discernable from 2.0¢
>
>
>
> Conrad Hoffsommer - Music Technician
> Luther College, 700 College Dr., Decorah, Iowa 52101-1045
> Vox-(563)-387-1204 // Fax (563)-387-1076
>
> The man that hath no music in himself,
> Nor is not moved with concord of sweet sounds,
> Is fit for treasons, stratagems, and spoils;
> The motions of his spirit are dull as night,
> And his affections dark as Erebus.
> Let no such man be trusted.
>
> ---Wm. Shakespeare - Merchant of Venice
>
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