historical vs. equal temperament

Billbrpt@aol.com Billbrpt@aol.com
Fri, 3 Jul 1998 01:08:34 EDT


In a message dated 7/2/98 11:12:55 AM Central Daylight Time,
 pianotoo@IMAP2.ASU.EDU writes:

<< My friend Bill:
 
 I'm sorry to have to break this news to you, but for once in your exciting
 life you are wrong. In your note below you mention that pure 5ths tuning is
 a departure from ET. ABsolutely wrong. It is the only equal temperament
 which also includes tempering the octaves.>>

Thanks for your note, Jim, I am looking forward to your class.  I want to talk
 to you about doing a full day in Madison or Milwaukee next year.   Far be it
 from me to want to prove the notion that some have that I am a person who
 thinks he is always right, here is what I said,  
 > It is no secret that the Steinway Hall tuners have long used the so-called
 "ET
> with pure 5ths" variation from true ET.  There is only so far you can go
 with
> any modifications to ET before it stops being ET.  In this arrangement, the
> intervals within the octave are all equal but the octave itself is tempered.
> It cannot be considered a true ET because of this.  It might be called
 "Quasi
> Pythagorean ET".

I have to admit that Owen Jorgensen told me that it could still be considered
 ET and in a way, I concede that in what I said, "...the intervals within the
 octave are all equal..." but it is difficult for me to accept that ET can be
 anything but *one* thing and *one* thing only, otherwise it would not be ET.
 We start getting into the "more equal" arguments.  I used the words
 "variation" and "modification", not "departure".  The latter might apply to
 the Quasi-ET's.  When I used the word "Quasi", I used it as a modifier to the
 word "Pythagorean".

<< You do not get pythagorean 3rds.>>

I am well aware of this and it is not what I implied.  A so-called
 "Pythagorean 3rd" is one which is wide by a full syntonic comma (21.5¢) or
 more.  In the ET/pure 5ths,  I think they  are all about 15¢ wide, more or
 less.


<< All intervals progress evenly in beat speed as you ascend the scale. Pure
 5ths tuning on a modern piano has nothing to do with HT. It is merely an
 approach to dealing with inharmonicity of which the ancients had no or 
 little knowledge.>>

This, I have no argument with.  I used to tune this way 15 years ago. I had
 read Lucas Mason's book, The New Tuning (by the way, he graduated from the
 University of Wisconsin, Madison), and thought that it supported what I had
 been inclined to do anyway.  I talked to Bill Garlick at Steinway about this
 idea in 1986.  He confirmed my hypothesis that one could use the Inharmonicity
 of a piano to one's advantage in making the octave as large as might be
 tolerable to the ear in order to make the 5ths be less tempered.  

He confirmed the idea but admonished me that, in his words, "would produce a
 very bright sound".  I responded that such a sound was my goal.  He replied
 that there might well be circumstances where a more contracted sound might be
 preferred.  I will always remember that.  It was the beginning of the end of
 the idea that I had that there was only one very best way to tune a piano. 

 To accept the premis that there might be any number of different styles and
 variations that one might use in any given circumstance became my new field of
 exploration.  I first experimented with the width of the temperament octave in
 ET, then with the rest of the octaves.  I came up with a bone-head simple way
 of tuning the 5th, 6th& 7th octaves with what I consider to be *optimum*
 stretch.  When you heard those octaves, you were interested and to that I am
 deeply flattered.  But to me, it is so natural and so simple, anyone can learn
 to do it aurally, as I did for many years or with the SAT and get the same
 results.  I will be using this approach with the Walter Grand in Providence.
 
 
<< As you well know (and do an excellent job of tempering your octaves when 
 using your favorite HT version), one of the beauties of your concert tuning
 was that your upper octaves sounded so good with the rest of the piano. The
 only way they can sound that good is through a careful stretching of the
 octaves immediately below in order to accomodate the greater stretch which
 is required in the top octave in order to blend with the mid section of 
 the piano.>>

Thank you so much but as I said, it is very simple and completely natural.  I
 was to the point as an aural tuner that I could consistently do the same kind
 of beautiful octaves no matter what my physical or mental condition might be.
 Even if I was tired or feeling ill but still needing and wanting to work, I
 could stil tune these kinds of octaves consistently, effortlessly, even, I
 would say, mindlessly.  Any skilled tuner can use the same technique and get
 just as good of results.

 <<You have told me yourself that that is the area where you can
 stretch out the wolf 5ths.>>

In Meantone temperaments,  such as the 1/7 comma Meantone, the "wolf 5th" is
 actually wide so it does not need stretching. What you can do however is tune
 the sharp note of that interval in 2:1 octaves to the top and the flat note,
 stretch as much as can be justified.  You reverse this pattern below the
 temperament octave.  This tends to close the widened 5th in the outer octaves,
 leaving the only dissonance in the temperament octave itself.  My tempered
 octaves method serves to "pull the tempering out" of the rest of the tempered
 5ths of the 1/7 comma Meantone while retaining the basic balance of harmony
 which is the goal of the temperament.

The more Inharmonicity there is, the more that the tempering of an octave can
 be used to absorb the Comma.  That is why I really like tuning a Steinway or
 other high Inharmonicity scale, especially in 1/7 comma Meantone.  To me, the
 more Inharmonicity there is, the "sweeter"  (as they have called it here on
 the List recently) I can make the tuning sound.  The Walter Grand I will tune
 is of moderate Inharmonicity but I will make that work quite well with my
 Equal-Beating Victorian Temperament.  The Walter console, one of which I own,
 has a relatively high Inharmonicity scale.  I can really make it *sing*!
 
<< Take courage my dear brother, I've been wrong more than once (even on this
 list). It is not the end of the world for you. You are still valuable. I'm
 looking forward to hearing your work in Providence. Incidentally. I will be
 doing a pure 5ths tuning in the last half of my class on Advanced Tuning.
 Hope to see you there also.
 
 Jim Coleman, Sr. >>

No need to bolster my ego, Jim, I've already become hardened to the ways of
 this List.  I use your "sticky note" solution.  Anybody who wants information
 or to discuss HT's with me will get an appropriate response.  Anybody who
 wants to tell me that what I am doing is wrong will be wasting time and
 energy.

My sincerest regards,
Bill Bremmer RPT
Madison, WIsconsin



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