Meantone, my personal adventure

[Jon Page]

At 10:24 AM 3/20/99 -0500, you wrote:
>In a message dated 3/20/99 7:42:44 AM Central Standard Time,
jpage@capecod.net
>writes:
>
><< Is the 'wolf' the reason for a term I heard along time ago, I don't
>remember
> which musician or composer said it but something was referred to as the
> "pianists' vibrato".
>  
> Jon Page >>
>
>No, the "pianist's vibrato" exists even in ET.  It is essentially the
>resonance you hear from the Rapidly Beating Intervals (RBI) (not Runs Batted
>In), the 3rds, 6ths, 10ths & 17ths.  In ET, they are all distributed very
>evenly.  Every major and minor triad has its own equal share of them,
>regardless of which key you are in.  In the HT's, they are distributed in
>alignment with the cycle of 5ths.
>
>A "wolf" is a dissonant interval that is created, not by tuning it but as a
>result of tuning other intervals the way you want them. 

Ok, then so it's a sacrificed fly to left field.

> In the Meantones, you
>tune a series of 11 5ths that are *narrower* than an ET 5th.  The 12th one is
>what is left over and cannot be reconciled.  Since all the others were
narrow,
>it is wide.  In the 1/7 Comma MT, it is only slightly wide (6-8 cents
>depending on the inharmonicity) and slightly dissonant and so, it can still
>serve as a playable interval.  In 1/4 Comma MT, it is some 40 cents wide and
>extremely dissonant.  Yet, some jazz and blues players can incorporate that
>sound since they play other kinds of chords that would have seemed wildly
>dissonant in past centuries but titillate our senses today.
>
>  HT's have "wolf" 3rds too, which are again, not tuned that way but are left
>over as the result of tuning other 3rds more narrowly than in ET.  If you
tune
>a pure C3-E3 3rd and a pure E3-G#3 on top of it, the remaining Ab-C4 3rd will
>be very wide, some 26 cents.  It will sound very harsh and sour to most
>people.  It is really not a 3rd but a diminished 4th: G#3-C4.  A "wolf"
3rd is
>wider than the 22 cent "Pythagorean 3rd" which is considered to be at the
>limit of tolerance for a usuable 3rd (see Rules for Well-Tempered Tuning).
> 
>Bill Bremmer RPT
>Madison, Wisconsin
>  

Jon Page
Harwich Port, Cape Cod, Mass. (jpage@capecod.net)
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