Re: Meantone, Well-temperament, Equal Temperament, Just Intonation, Just Temp...

After eMailing this post, I decided to send it to Tuning as well--PWP

> Meantone (MT), Well-temperament (Werckmeister--WM),
> Equal Temperament (ET, 12-ET),
> Just Intonation (JI), Just Temperament (JT)
>
> Class,
>
> Below are abridged posts in response to several posts in the Yahoo! Tuning
> forum by George, who's writing a book on tuning. The quotes left in are by
> me, Pauline. This post, which I also sent to my JI forum, and to George, is
> more technical than what is usually posted in my organ forum.
>
> But one member asked for more JI info a while back. What George says is so
> close to my own thinking and experiments on the JT organ I'm building, I
> asked his permission to post some of what he said in my music forums. He
> agreed. His eMail address is: <A HREF="mailto:gdsecor@yahoo.com">gdsecor@yahoo.com</A> .
>
> Pauline
> ______________________
> George:
>
> For me, if you can count them, it's tempered. (If you're doing it by
> ear, then you set a temperament by counting beats, right?) However,
> if they're so slow that it's difficult to count them, then it's just.
>
> I think that no beating sounds stagnant or dead, but very slow
> beating is like letting in a bit of fresh air. Microtempering a JI
> set can accomplish this, while making consonances out of some near-
> misses. (My upper limit is about 3.25 cents error for most
> intervals, but half of that for 2:3's. And 217-ET does considerably
> better than that.)
>
> When I first investigated alternative tuning systems in 1963, one of
> the things I did was to retune my electronic organ to the meantone
> temperament, which is practically the same thing as a subset of 31-
> ET.
>
> I kept the organ tuned this way for several weeks and was absolutely
> delighted with the way older organ music (such as Bach and Handel)
> sounded, as long as I didn't try to make enharmonic substitutions (in
> order to avoid the "wolf" fifth). Particularly intriguing was the
> fact that augmented seconds and diminished sevenths sounded different
> from (i.e., more dissonant than) minor thirds and major sixths,
> something that we don't have with 12-ET.
>
> But I did miss the ability to modulate freely, and so I put the organ
> back into 12-ET. I was totally unprepared for the shock that I
> received when, after playing no more than two or three chords, I
> found my ears literally assaulted by dissonant triads that would find
> no resolution or rest until, in desperation, I omitted the third of
> the chord, leaving an open fifth.
>
> In meantone I could easily flee the wolf by playing in another key, but in
> 12-ET there was no escape. Not only did the thirds and sixths have a
> jarring effect,
> but everything sounded out of tune. It suddenly became obvious to me
> why organs were not generally tuned in equal temperament in England
> until after 1850; if I found the change hard to accept after only a
> few weeks in meantone, how difficult it must have been for those who
> had spent all their lives with it to put up with 12-ET, in which you
> have three times the error in the major and minor triads.
>
> The out-of-tune sensation of equal temperament left me after a short
> while, but I have never been satisfied with its unending dissonance
> since that time. I soon solved the problem by devising a well-
> temperament that would give me more consonant-sounding triads in at
> least a few keys, until such time as I was able to obtain an
> instrument with more than twelve keys per octave. So I now have the
> meantone sound in 31 different keys (plus 7 and 11 harmony).
>
> The lifeless or stagnant effect that some have objected to with just
> intonation is a result of the absence of disturbances caused by
> beating harmonics or non-coincident combinational tones, so interval
> size has a lot to do with it.
>
> But any lack of life you might perceive in just intonation with sine
> waves would have more to do with the just major third being smaller,
> which makes the leading [tone] lower in pitch and less effective
> melodically. If you were to try 17-ET with sine waves; I suspect you
> would find that it makes 12-ET sound lifeless and bland by
> comparison. (At least that has been my experience with it.) So I
> would say that 12-ET is about as good melodically as it is
> harmonically -- a compromise that does both about equally well (or
> badly, depending on your point of view).
>
> > >Mutation stops on pipe organs are tuned to just intonation.
> > >When the rest of the organ is tuned to ET, the 1 3/5'
> > >stops are way out of tune with the major thirds!
>
> . . . then they [mutation stops tuned to ET as suggested by a poster, and
> as is done on some electronci organs] wouldn't be in a true harmonic
> relationship with the pipes sounding the fundamental pitch and would beat
> against the harmonics of those pipes, causing each and every single note to
> be literally out of tune all by itself.
>
> > >Any theoretical just interval can be tuned +/- 2
> > >cents the theoretical value and still sound normal
> > >to the ear. And +/- 3 cents still sounds in tune,
> > >but has a celeste (vibrato) quality.
>
> The beating of the thirds in 12-ET is so fast that it's not even a
> vibrato; I would describe it as more of a grating effect. But you
> don't fully realize how bad it is until you've spent a little time
> with something that has (harmonically) better thirds.
>
> > >out-of-tuneness destroys the natural Difference
> > >and Sumational Combinational tomes. These are
> > >obviously destroyed, or at the wrong pitch, via
> > >ET tuning!
>
> In JI the combinational tones are in exact mathematical
> relationship with the fundamental, but in 12-ET they're quite
> discordant (by practically anyone's definition of the term). This is
> in addition to the fast-beating harmonics in the thirds, so 12-ET
> leaves a lot to be desired.
>
> --George
> __________________
>
> Comments by Pauline:
>
> Perhaps now you can see the sense in Johannus digital-sampled organs
> providing both MT, WM and ET tuning in one instrument! Something individual
> pipe organs can't provide.
>
> MT will play in 0-2 #/b, providing the B-major chord, and certain flat
> chords, aren't used.
> WM will play in 0-3 #/b generally, and in some cases 4 b.
> ET is needed to play in many 4 b, 4 #, or 5 b.
>
> In scoring hymnbooks for Johannus organs I accomodate the above in the
> suggested Tune/Pitch/Intonation.
>
> Sincerely,
> Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool">Johannus Organs eSchool</A>
> Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
> organs.
> Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>