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Oboe & Oboe d’amore in Bach’s Vocal Works
Part 1

Oboe and Bach

Francine wrote (December 13, 2001):
Secular Cantata BWV 213, Hercules at the Crossroads, has a beautiful aria with Virtue (sung by tenor) singing to Hercules in unforgettable counterpoint with the oboe, though backed up by instrumental ensemble, "Auf meinen Fluegeln sollst du schweben" (upon my wings you shall soar). As a little side note, this is parodied in the Christmas Oratorio in part 4 as "Ich will nur dir zu Ehren leben". Without that distinctive oboe duet with voice, I doubt that this aria would have stayed so lovingly treasured by me.

Francine wrote (December 13, 2001):
My Grove music dictionary says that "Bach exploited [the oboe] extensively in an obbligato role." And the text also quotes from "The Sprightly Companion" that "with a good reed and skilful hand it sounds as easy and soft as the flute." (I left in original spelling) How about that?!

Thomas Boyce wrote (December 13, 2001):
[To Francine] I'm trying to think of another composer who wrote as well as Bach did for the oboe.

("And all the way (a horn!) from fjord to fjell his baywinds' oboboes shall wail him rockbound..." --Joyce, Finnegans Wake)

Francine Renee Hall wrote (December 13, 2001):
[To Thomas Boyce] Were you reading my mind? I was just going to mention that wonderful Czech baroque composer Jan Dismas Zelenka! His distinctive use of the oboe in his Orchestral works and Trio Sonatas (both on Archiv) make him stand out! And played, no less, by the wonderful Heinz Holliger!

 

Oboe solo in cantatas?

Juozas Rimas wrote (March 27, 2004):
Could you point out to any other oboe solo movements from Bach's cantatas other than these?

sinfonia from BWV 21 ("Ich hatte viel Bekümmernis")
sinfonia from BWV 12 ("Weinen...")
adagio from BWV 249 (Easter oratorio)

Thanks.

Aryeh Oron wrote (March 27, 2004):
[To Juozas Rimas] There are so many!
Walter F. Bischof lists them all in his website.
See: http://www.cs.ualberta.ca/~wfb/cantatas/ainst.html

Uri Golomb wrote (March 27, 2004):
[To Aryeh Oron] This site seems to list arias with obbligati, but not instrumental movements. At the moment, I can think of one sinfonia with oboe obbligato which is not mentioned in Jouzas' list: the opening movement of Cantata BWV 156 (Ich steh mit einem Fuß im Grabe), which has also been arranged as the second movement in the F minor keyboard concerto.

Juozas Rimas wrote (March 27, 2004):
I was also informed of an oboe-only movement in the BWV 42 (appears to be an oboe duo). So the list is as follows (quite short, though, bearing in mind the number of oboe arias):

sinfonia from BWV 12 ("Weinen...")
sinfonia from BWV 21 ("Ich hatte viel Bekümmernis")
sinfonia from BWV 42 ("Am Abend...")
BWV 156 ("Ich steh mit einem Fuß im Grabe")
adagio from BWV 249 (Easter oratorio)

I noticed the adagio from BWV 249 is also played on the flute (IIRC Koopman, Leonhardt). Perhaps there are vice versa recordings? (oboe instead of flute)

Neil Halliday wrote (March 27, 2004):
[To Juozas Rimas] Your list is complete, apart from the first movement of BWV 152, which is in the form of a fugue for flute, oboe, violin and continuo.

http://www.cs.ualberta.ca/~wfb/cantatas/minst19.html
(The numbers at the top, witout associated text, are the 'instrument only' movements).

There are many other movements (instrument only) like the 1st movement of BWV 42 for 2 oboes, as shown at: http://www.cs.ualberta.ca/~wfb/cantatas/minst20.html

The Walter Bischof homepage, sub-sections of which Aryeh pointed to, is obviously a valuable resource: http://www.cs.ualberta.ca/~wfb/bach.html

David Long wrote (March 29, 2004):
[To Juozas Rimas] Mov't 2 of BWV 131 is Oboe and Bass Soloist. "Aus der Tiefen."

 

Oboe d'amore and oboe
Oboe d'amore and oboe / “Baroque tunings”

Bradley Lehman wrote (June 15, 2004):
Douglas Cowling wrote (on BachRecordings) about the St Matthew Passion (BWV 244):
< Four oboes d'amore! No wonder the Bach family referred to it as the "Great Passion"! >
A good joke; but Bach chose oboes d'amore (vs oboes, or vice versa) primarily by being at different levels of transposing pitch, for the keys to be played...and for the slightly deeper range they have. See Bruce Haynes' article "Questions of Tonality in Bach's Cantatas: The Woodwind Perspective" in the Journal of the American Musical Instrument Society, 1986. He discusses the keys and ranges, and the "hidden" oboe d'amore parts (at least in cantatas BWV 17, BWV 29, BWV 45, BWV 94, BWV 169, BWV 193, BWV 214, BWV 215) where the music simply says "oboe" but one must use the oboe d'amore to play it, by key and/or range (the player tacitly choosing the one that works). Basically: the oboe d'amore plays the sharp keys, and the oboe plays the flat keys. (His argument is deeper than that, but this is a summary.) "We may infer that Bach did not choose the oboe d'amore primarily for its affective associations (though these were probably a secondary consideration), but because it was the most practical instrument for the tonality he had selected." He also discusses the way the Bach-Gesellschaft, the Neue Bach-Ausgabe, and other editions have treated the transposition situations in the vocal works: it's an excellent article on this complex topic. He also presents a statistical analysis of the keys employed by Bach, Telemann, and Handel for woodwinds.

Lest any self-appointed critics here scurry to books and attempt to jump upon Haynes' credibility, for whatever reason: forget it. Haynes is one of the top players in the world on these Baroque instruments, and knows his business.

For a similar pun on the name of the instrument, see my review of Bach's A-major harpsichord concerto played on oboe d'amore by Lorenz (a wonderful performance): Amazon.com "Big John Bach and his Swinging Oboe of Love".

Dale Gedcke wrote (June 15, 2004):
Bradley Lehman replied:
< 'For a similar pun on the name of the instrument, see my review of Bach's A-major harpsichord concerto played on oboe d'amore by Lorenz (a wonderful performance): Amazon.com "Big John Bach and his Swinging Oboe of Love".'

MY QUESTION:

I realize that the modern oboe is based on the key of C. I presume from what you said that the oboe d'amore was built on the key of A . I would expect that lower fundamental pitch to give the d'amore a darker tone. Are my presumptions correct? Were there any other differences between the two instruments?

Gabriel Jackson wrote (June 15, 2004):
Dale Gedcke wrote:
"I realize that the modern oboe is based on the key of C. I presume from what you said that the oboe d'amore was built on the key of A . I would expect that lower fundamental pitch to the d'amore a darker tone. Are my presumptions correct? Were there any other differences between the two instruments?"
The oboe d'amore is still in use, of course. There are modern oboe d'amores just as there aree modern oboes. I very much prefer it to the (modern oboe) for just the reasons you suggest - a darker, richer sound. And the cor anglais is even better! With the oboe family, the further the range descends, the greater my pleasure...

Dale Gedcke wrote (June 15, 2004):
[To Gabriel Jackson] From a recent encounter with a score for the English Horn (cor anglais), I understand it is based on the key of F, n'est-ce pas?

Gabriel Jackson wrote (June 15, 2004):
[To Dale Gedcke] It is indeed in F.

Bradley Lehman wrote (June 15, 2004):
[To Gabriel Jackson] And, as pundits delight in pointing out, is neither English nor any sort of horn. Was it Hoffnung who said that, or perhaps Flanders & Swann, or am I mis-remembering?

Dale Gedcke wrote (June 15, 2004):
[To Bradley Lehman] Was it Victor Borge who joked that "the oboe is an ill wind that nobody blows good"? (He was twisting that adage, "an ill wind that blows nobody good".)

When I was a teenager, I agreed with Victor Borge's pun. I didn't like the tone of the oboe. But, as I aged, I began to enjoy it much more. Now I particularly appreciate the sound of the oboe in Baroque music like Bach's. It has a quality that is unmatched by any other musical instrument. Curiously, it was also just the right sound to use in the accompaniment to "I've Got You, Babe" by Sonny and Cher in the 1960s. Take the oboe out of that song, and you have lost most of the color.

I have an up-coming concert where I have to play the oboe part of a Baroque composition on a C trumpet with a mute to get somewhat close to the oboe sound. I have tried pinching my nose between my finger and thumb as I play, but that still does not quite duplicate the nasal sound of the oboe. It's too bad that oboe players are so scarce. It is an instrument with such a beautiful sound when played lyrically.

Bradley Lehman wrote (June 15, 2004):
Dale Gedcke wrote:
< Was it Victor Borge who joked that "the oboe is an ill wind that nobody blows good"? (He was twisting that adage, "an ill wind that blows nobody good".) >
I think you're right about that one being Borge's.

< When I was a teenager, I agreed with Victor Borge's pun. I didn't like the tone of the oboe. But, as I aged, I began to enjoy it much more. Now I particularly appreciate the sound of the oboe in Baroque music like Bach's. It has a quality that is unmatched by any other musical instrument. Curiously, it was also just the right sound to use in the accompaniment to "I've Got You, Babe" by Sonny and Cher in the 1960s. Take the oboe out of that song, and you have lost most of the color. >
Mitch Miller himself made classical recordings as an oboist, apart from his sing-alongs.

1960s pop songs would also suffer if the harpsichord parts were removed.

< I have an up-coming concert where I have to play the oboe part of a Baroque composition on a C trumpet with a mute to get somewhat close to the oboe sound. I have tried pinching my nose between my finger and thumb as I play, but that still does not quite duplicate the nasal sound of the oboe. It's too bad that oboe players are so scarce. It is an instrument with such a beautiful sound when played lyrically. >
I agree!

The slow movement of the Brahms violin concerto makes my day, whenever I hear it. That oboe solo! And the opening of Bach's cantata BWV 156, "Ich steh mit einem Fuss im Grabe".

Ludwig wrote (June 15, 2004):
[To Bradley Lehman] If you think oboe players are scarce (well maybe in your area) your should try to find Oboe d'amore players. Most oboist I know will not play the d'amore instrument and if there is anyone out there who plays this instrument I need at least 4 of you to do works by Bach and my own works as (Idyll) for this.

Ludwig wrote (June 15, 2004):
[To Bradley Lehman] It is sad that many people seem to want to substitute the so-called English Horn for the Oboe d'amore. Although similar in size and both can play the same music the timbre is not quiet the same. There are manufacturers of Oboe d'amore and if you get one do not get one from a builder (as a certain one in Atlanta does) who insists on it being totally baroque in tuning and style. That is all well and good but there is just too much other music post Baroque era that can not be played, if you go with strictly Baroque tunings and style----Strauss, Ravel and my own works as "IDYLL".

Dale Gedcke wrote (June 15, 2004):
Ludwig wrote:
"........There are manufacturers of Oboe d'amore and if you get one do not get one from a builder (as a certain one in Atlanta does) who insists on it being totally baroque in tuning and style. That is all well and good but there is just too much other music post Baroque era that can not be played, if you go with strictly Baroque tunings and style ........."

MY QUESTION is:

What is the difference in tuning and style to which your refer? Is it the pitch of the individual notes, i.e., temper? Or is it the tone/timbre?

Ludwig wrote (June 15, 2004):
[To Bradley Lehman] Thanks your joke made my day.

Bradley Lehman wrote (June 15, 2004):
[To Dale Gedcke] I don't presume to speak for "Ludwig", but as for Baroque oboes and oboes d'amore, they're not built in today's equal temperament. Again, read Bruce Haynes' articles; his best-known one is the one in Early Music August 1991 where he argues that the basic normal temperament of 18th century ensemble musicianship was 1/6 comma meantone (also known as the 55-division) as corroborated by Sauveur (1707), Tosi, Telemann, Quantz, the Mozarts, and others. As Tosi and Quantz both pointed out (for singers and players, respectively), in enharmonic pairs such as G# and Ab, the notes are a [syntonic] comma apart; and that's regular 1/6 comma meantone, right there.

All the regular variants of meantone have the similar property that there are two (and exactly two) different sizes of semitones: "diatonic" (where the note-name changes, for example F# to G), and "chromatic" (where the note-name stays the same, as F to F#)--"chromatic" being a color change and "diatonic" meaning it belongs to the normal scales of Ut, Re, MI, FA.... (specifically the step MI to FA).

To spell it out even more than Haynes does (and as I'm doing in a footnote of my paper about Bach's tuning): those "55" little portions of the octave get distributed thusly on an 1/6 comma meantone keyboard: C=0, C#=4, D=9, Eb=14, E=18, F=23, F#=27, G=32, G#=36, A=41, Bb=46, B=50, C=55. That is, a diatonic semitone and a chromatic semitone are in 5:4 ratio within a tone (as Tosi pointed out), and the whole chromatic scale is built of these increments of 4 or 5 commas to build each semitone as appropriate. Stack a total of 55 of these commas together and you get very nearly an octave; hence their theoretical description as a 55-division, an "equal-temperament" (55 equal pieces) way of describing what was already common practice among 17th and 18th century musicians before Sauveur wrote down the theory in 1707. That's what he called it, "the one used by musicians in general" ("celui dont les Musiciens ordinaires se servent").

Or, go listen to the instruments. I especially recommend the set of Handel's woodwind sonatas played by Haynes himself along with Bylsma, van Asperen, and Lange; and by Bruggen in the flute/recorder pieces. In this recording Haynes plays a Stanesby Jr instrument from c1750: Amazon.com

Cara Emily Thornton wrote (June 15, 2004):
[To Dale Gedcke] You are indeed correct that the "d'amorka", as we call it in Polish, has a darker tone. It is shaped much like an English horn, only a bit smaller (so, it has that little metal lead-pipe or whatever it's called for the reed at the top, as well as a pear-shaped bell). I am not sure wheththe actual fingerings are different or not - they may well be, however. This is all off the top of my head from working with someone who uses both an oboe and a d'amorka in our performances.

Cara Emily Thornton wrote (June 16, 2004):
Dale Gedcke wrote:
< From a recent encounter with a score for the English Horn (cor anglais), I understand it is based on the key of F, n'est-ce pas? >
Yes, that's right. And the d'amore is in A, as you mentioned before.

Cara Emily Thornton wrote (June 16, 2004):
Bradley Lehman wrote:
< The slow movement of the Brahms violin concerto makes my day, whenever I hear it. That oboe solo! >
Ooh YES!!!

Cara Emily Thornton wrote (June 16, 2004):
Ludwig wrote:
< If you think oboe players are scarce (well maybe in your area) your should try to find Oboe d'amore players. Most oboist I know will not play the d'amore instrument and if there is anyone out there who plays this instrument I need at least 4 of you to do works by Bach and my own works as (Idyll) for this. >
Baroque or modern? My oboist plays both oboe and d'amore, for the moment rather modern than Baroque (although she now has her own Baroque oboe). Unfortunately, she does not have her own d'amore (it was borrowed from school) and lives in Poland. But if you can find a way around all that...

Ludwig wrote (June 16, 2004):
[To Cara Emily Thornton] The fingerings for the modern oboe d'amore are the same as for the oboe, english horn.

The fingerings for the non-boehm system are different and these for what it is worth the ones that were used in Bach's day although it makes no difference in the tonal quality when played by an expert player.

Ludwig wrote (June 16, 2004):
[To Bradley Lehman] No names mentioned but in Atlanta there is a master luthier whose instruments and particular of the oboe class have reaped laurels upon his head. He is well known by many collectors of musical instruments including such prestigious museums as the Smithsonian,

I wanted to give him a commission for four instruments (oboe d'amore) and I specified that they were to be tuned to A-440 or slightly above(standard orchestra tunings) so that could be used with modern orchestra in addition to playing Baroque music.

I am sorry to say that many oboists seem to have diva complexes and think that they determine the absolute pitch of an orchesta---that well may be except when the Organ and some unretunable percussion instruments are around (carillon for instance)---can you imagine stopping a concert to tune fifty ranks of pipes (which takes about a day or so) in an organ. No one does not stop a concert to retune for a Bach piece after playing a Strauss or Ravel piece.

To make a long story short; I withdrew the commission after he refused and kept insisting that he tune to A=420 which he claimed was the absolute baroque pitch (maybe in a cold unheated building?). The expense of the commission was just too much not to get the most music from an instrument for the bucks spent.

Studies of tunings from the Organs that Bach played and other such instruments from the Baroque period indicate that tunings in the Baroque period ranged from 410 upwards to 450. The evidence was gathered from the pipes which have to be made to speak at specific tunings. The tunings which Bach usually used were around 440 but could drop as low as 430.

Ludwig wrote (June 16, 2004):
[To Dale Gedcke] Baroque tunings are a myth projected by many HIP snobs. Mostly this means that the tunings are lower than the modern international standard of A=440.

Baroque tunings could range from A= 410 to 420 area on the lowside upwards of above and including the modern International standard. Based on the surviving original Organ pipes in the Organs which Bach played ---we know that the tunings were either A=440 or something close to this at 70 degrees F. Most buildings back then in Europe (and even today) did not have central heating. So the colder a building was the lower the tunings might fall. Some of these tunings would put Bach's Principal 32' and Posaune 32' (organ stops on some of the organs he played) into the 64' range--which is unhearable by most people although Elephants can hear these well and in fact use such subsonic sounds to communicate to other elephants located great distances away. 32' means that this sound is produced by a pipe that normally is 32 feet long and likewise 64 foot means likewise. Humans can not hear below 16 cycles per second and most can not below 2O cycles per second---which few stereo systems or speakers can deliver---this is sound that you feel rather than hear--not this is not that boombox thing you might note that homeboy has in his car. IF you have a good system that can deliver these low sounds you might want to get a copy of the Virgil Fox Memorial Concert on Gothic Records (Gothic G49122) which is recorded at Riverside Church in New York whose organ has at least 5 stop 32'based ranks in it's organ.

John Pike wrote (June 16, 2004):
[To Dale Gedcke] The oboe is one of my favourite instruments, and I particularly love the Baroque Oboe d'Amore and Oboe da Caccia.

John Pike wrote (June 16, 2004):
Bradley Lehman wrote:
< The slow movement of the Brahms violin concerto makes my day, whenever I hear it. That oboe solo! And the opening of Bach's cantata BWV 156, "Ich steh mit einem Fuss im Grabe". >
Absolutely. These are two of my favourite moments in all music. I always used to play that oboe solo myself when I practised the Brahms at home.

John Pike wrote (June 16, 2004):
[To Ludwig] Apart from the unwelcome and pejorative remark about HIP enthusiasts, which I will let pass, can I check a fact, please. I was under the impression that baroque organs were sometimes tuned as high as A=465 or even 480. Is that correct?

Bradley Lehman wrote (June 16, 2004):
John Pike wrote:
< Apart from the unwelcome and pejorative remark about HIP enthusiasts, which I will let pass, can I check a fact, please. I was under the impression that baroque organs were sometimes tuned as high as A=465 or even 480. Is that correct? >
Yes, John, that's correct.

Dale Gedcke wrote (June 16, 2004):
Bradley Lehman wrote:
"I don't presume to speak for "Ludwig", but as for Baroque oboes and oboes d'amore, they're not built in today's equal temperament. Again, read Bruce Haynes' articles; his best-known one is the one in Early Music August 1991 where he argues that the basic normal temperament of 18th century ensemble musicianship was 1/6 comma meantone (also known as the 55-division) as corroborated by Sauveur (1707), Tosi, Telemann, Quantz, the Mozarts, and others. As Tosi and Quantz both pointed out (for singers and players, respectively), in enharmonic pairs such as G# and Ab, the notes are a [syntonic] comma apart; and that's regular 1/6 comma meantone, right there."

MY QUESTIONS AND COMMENTS:

1) Is the 55-division, 1/6-comma meantone scale the same as the "Just Temperment" scale? If not, how did it differ.

2) Until the Even Temperament standard was adopted, all woodwinds, brasswinds, harpsicords and organs had to be based on the same key and played in the same key to be in tune with each other. The stringed instruments without frets on the fingerboard were more adaptable. String players could adjust the pitch of each note with their finger positions to match the pitch of the other instruments in the ensemble. Presumably, this tuning issue is why Bach wrote some compositions for the oboe (in C) and some for the oboe d'amore (in A). The concert key would be C in the first case and A in the second for that composition. The same was true of the Baroque Trumpet. It was built in keys of D and C (most common) and also in E, Eb and F. In most cases one could change the key by inserting a different "crook" or "bit" to alter the length of the tubing.

3) I understand the A400 or A440 acronym. It lists the frequency in Hertz or cycles per second for the note A. But how does one decode the AD0 and AF5 acronym?

Bradley Lehman wrote (June 16, 2004):
Dale Gedcke wrote:
< 1) Is the 55-division, 1/6-comma meantone scale the same as the "Just Temperment" scale? If not, how did it differ. >
Not at all. In "just intonation" schemes, zero intervals are tempered (and in the resulting setup, one can play in only one tonality...and even it has its problems, especially the placement of the second degree). In any of the meantone temperaments, ALL the fifths are tempered (all the same amount as one another, and the resulting twelfth fifth of a different size is really a diminished sixth).

< 2) Until the Even Temperament standard was adopted, all woodwinds, brasswinds, harpsicords and organs had to be based on the same key and played in the same key to be in tune with each other. >
Not true, but the situation is much too complicated to go into in this forum. I'm covering some of that in my paper....

< 3) I understand the A400 or A440 acronym. It lists the frequency in Hertz or cycles per second for the note A. But how does one decode the AD0 and AF5 acronym? >
Where are those used? It sounds sort of like references to spreadsheet cells somewhere, maybe? Or, maybe somebody trying to refer to "D0" or "F5" as pitches in specific octaves, numbering the octaves?

Bradley Lehman wrote (June 16, 2004):
[To Dale Gedcke] Dale, it appears something's messed up in your email program (character set or whatever): those postings by John Pike and Ludwig came through with numbers in both those places. Ludwig wrote "440" and John wrote "465" there. Specifically, "A = 465" (with no space in there), which somewhere enroute to you is getting interpreted as bytes that should be swapped out in the display.

Ludwig wrote (June 17, 2004):
[To Bradley Lehman] I am not sure of what you saying but if you are refering to so-called Baroque tunings---I gave the more conservative findings and yes they might have gone up to 465 on a hot summer day with the humidity at 70% or more. This is just one of the things that the fixated HIP folks do not consider and do not like to hear.

Bradley Lehman wrote (June 17, 2004):
[To Ludwig] Who are "the fixated HIP folks", and how would such a fluctuation of the organ's pitch affect or bother such "folks" any more than it would affect modern-instrument "folks"? And, how do you know what any other musicians "do not consider"? Players who know their instruments know what heat and humidity do to them, regardless of what type of "folks" we are; and know how to compensate in practice.

I attended a concert over lunchtime today, one where the first half was a Bach cantata (BWV 55) and then some harpsichord solos. The harpsichord had been tuned probably an hour or more before the time it was played, and the heat and humidity fluctuated in the church (as always happens when the audience arrives). Consequently, the top octave went pretty far out of tune on both manuals, and the resulting discord obviously threw the performer's concentration off a bit; still, she played very well and I enjoyed hearing her. I do wish, though, that there had been a 5-minute intermission between the cantata and the harpsichord program to allow any touch-up of that octave, eliminating these problems; the player deserved better treatment than the concert situation today dealt to her.

Ludwig wrote (June 17, 2004):
[To John Pike] John you could be right (I mean no disrespect to HIP folks---it is just a few of them act like that their opinion is THE ONLY opinion or fact. I might mention I am a moderate HIP person) especially when temperature and humidity conditions are correct and that happens even today when the central air is turned off and a poor organ, harpsichord is left to fluctuate its tunings.

Cara Emily Thornton wrote (June 17, 2004):
[To John Pike] I have solved the mystery. It is an encoding problem. I have made small corrections which should solve it.

John Pike wrote (June 17, 2004):
[To Dale Gedcke] Somehow, the characters have got muddled up. I actually wrote "A equals four hundred and sixty five or even as high as four hundred and eighty" in figures. The problem of characters getting adulterated is quite common on this list. parts of Thomas' e mails are so badly messed up with strange characters. Maybe it is a conversion from german characters on his keyboard, but I don't get that problem with other e mails I receive containing German characters, which are usually displayed correctly. Perhaps you and Thomas could check your keyboard settings.

Dale Gedcke wrote (June 17, 2004):
Dale Gedcke wrote:
"2) Until the Even Temperament standard was adopted, all woodwinds, brasswinds, harpsicords and organs had to be based on the same key and played in the same key to be in tune with each other."
and Brad Lehman commented:
"Not true, but the situation is much too complicated to go into in this forum. I'm covering some of that in my paper...."

MY CONTINUED INQUIRY (D. GEDCKE):

Last night I quickly scanned the information I have on the Pythagorean, Just, 1/6th Comma, and Even temperaments. As a consequence, I am puzzled by the "not true" statement, because it seems to conflict with explanations given elsewhere, and my own logical understanding. Let me describe a few hypothetical situations, and you can advise me on what I am overlooking.

First, let's consider the even temper scale that is in common use today. An octave is defined by the frequency of the note at the top of the octave being a factor of 2 times the frequency of the note at the bottom of the octave. For even temper, the octave is divided into 12 equal half-tone intervals. Each half-tone step changes the frequency by a factor given by 2 raised to the power of 1/12th. That factor turns out to be approximately 1.059463. Full-tone steps are the square of that factor or 2 raised to the power of 2/12ths. The full-tone frequency ratio is approximately 1.122462. With even temper, those ratios are the same no matter what key an accurately-tuned piano is playing in.

Now consider the hypothetical experiment where one piano, (a), is tuned with it's middle C at 261.63 Hz, the normal modern pitch with A440. Piano (a) is tuned to play in the concert key of C (no flats and no sharps). Now tune another piano, (b), so that all its white and black keys are exactly a half-tone below the corresponding key on piano (a). Piano (b) will be tuned to play in the concert key of B (5 sharps). Choose a composition to play on piano (a) that is written in the concert key of C (no sharps or flats). If you play that same composition on piano (b), but transpose it up a half-tone to the written key of Db (5 flats), the two pianos will sound identical in pitch for all notes. This conformity is possible because all the half tone intervals have exactly the same frequency ratio, no matter what key the composition is in, and the same applies for the whole-tone intervals. This was the important advantage claimed for the even temper scale. A composition sounds the same in any key, and instruments built on different fundamental keys can transpose to match each other in any composition.

Now run back to the old Pythagorean scale. The half-tone intervals are not a constant half-way between the whole-tone steps. So when I tune piano (b) so that its white key for middle C matches the frequency for the white key for B on piano (a), I can no longer transpose up a half-tone on piano (b) to play in tune with piano (a). The pitch on some notes will match, and on others it won't match.

Before even temper became the standard, the mismatch caused by uneven intervals created two limitations. 1) If you transposed a composition into a different key, it might sound different, because of the different interval spacings.
2) to play in perfect unison pitch, all the instruments in the ensemble had to be based on the same fundamental key.

Now, turn to the 1/6th Comma tuning, where the octave is divided into 55 intervals instead of 12. Correct me if I am wrong. But, my understanding is that two half-tone increments don't necessarily completely span the whole-tone increment that brackets the two half-tone steps. In other words, two half-tone intervals still don't exactly equal a whole-tone interval, and the interval pattern is not uniform (equal steps) throughout the scale. That screate the same difficulties as ascribed to the Pythagorean scale.

Does your "not true" statement mean that the 1/6th comma intervals are so close to equal that most human ears don't detect the mismatch? The commonly held belief is that the typical human can only notice mismatches that are greater than 5 cents. This amounts to the note being off pitch by a factor of 1.00289. Another way of stating it is: a half-tone interval in the even-temper scale is denoted by 100 cents, and a detectable discrepancy in tuning is 5 cents out of 100 cents. Are 1/6th comma intervals equal within 5 cents?

Footnote: Most on this list already know this, but if there is any neophyte who is wondering what a cent is, here is a working definition. One cent converts to a frequency ratio computed by 2 raised to the power (1 cent/1200 cents). There are 1200 cents in an octave, and for the even-temper scale: 100 cents in a half-tone, and 200 cents in a whole-tone interval.

Bradley Lehman wrote (June 17, 2004):
[To Dale Gedcke] Good questions, Dale.

The fundamental issue here is the behavior of regular meantone: ANY variety of regular meantone, of which 12-note equal temperament is a limiting case. That's why it transposes, and that's why they do too: whether we're talking the 1/4 or 1/5 or 1/6 ("55-division") or versions even more exotic.

In all these regular meantone temperaments, the naturals are evenly spaced: being generated by fifths of the same size as one another, consistently. The accidentals are also evenly spaced, coming from chains of fifths at either end of the naturals (F-Bb-Eb-Ab-Db etc, or B-F#-C#-G#-D# etc): BUT these intervals don't split the naturals exactly in half. There are two different sizes of semitones, as I explained earlier.

Music is completely transposable in all these meantone temperaments PROVIDED THAT the keyboards have those particular notes on them, and not only their enharmonic not-quite-equivalents...or if keyboards are not involved in the piece at all. That is, for example, a piece in G minor (G-A-Bb-C-D-Eb-F#-G...) can be played readily in B minor (B-C#-D-E-F#-G-A#-B...) as long as everybody agrees really to use A# and not Bb's anymore: they can't be swapped willy-nilly because they don't sound anywhere near the same as one another. The players can't simply finger a Bb on their string fingerboards or oboes or whatever, and expect it to sound passable as an A#.

Indeed, as Haynes' 1991 paper showed brilliantly, when keyboards are not involved the orchestra simply plays in some variety or other of meantone, and anything can be transposed as necessary (while allowing that the woodwinds, especially, sound best in the keys closest to the tonic in which they are built, as the alternate enharmonics need various forked fingerings and other work-arounds...it's not ONLY a keyboard problem here). It is the constraint of having 12 (and only 12) notes on standard keyboards that necessitates most of the issues of temperament, where the irregularities create the key differences.

With regard to your specific question: "Now, turn to the 1/6th Comma tuning, where the octave is divided into 55 intervals instead of 12. Correct me if I am wrong. But, my understanding is that two half-tone increments don't necessarily completely span the whole-tone increment that brackets the two half-tone steps. In other words, two half-tone intervals still don't exactly equal a whole-tone interval, and the interval pattern is not uniform (equal steps) throughout the scale."

The two half-tone increments (the diatonic semitone plus the chromatic semitone) DO span the whole-tone increment completely and exactly; but they're different sizes from one another. The ratio between them depends on the amount of tempering that was applied consistently to all the fifths, generating the entire temperament. For example, in 1/6 comma meantone, the semitones end up splitting the tone in 5:4 ratio amongst themselves, and the tone is therefore 9 of these little pieces, completely. Looking only at the natural notes of the 55-division, they are: C 0, D 9, E 18, F 23, G 32, A 41, B 50, and C 55. All those whole steps in there ARE equally spaced: 9 of those pieces each. That's 196 cents each. (And the half steps in there come from the older theories related to hexachords and mutation...way too much to go into here. Last night I enjoyed reading Gerd Zacher's paper "Zum Tonalitaetsverstaendnis bei Johann Sebastian Bach" (1993) about that hexachord background; the New Grove article about hexachords is good, too, as a place to start.)

For the question/suggestion: "to play in perfect unison pitch, all the instruments in the ensemble had to be based on the same fundamental key."...no, that's not true. To play in perfect unison pitch, all the instruments simply have to be able to play, in some manner or other, the subset of pitches that is agreed upon, whether that's a regular meantone scheme or something else. The musicians have to know what to listen for, and then know how to get the results, and then know when they've got them. It's a software issue, mainly, not a hardware one: musical training and experience, and knowing how tonal music behaves.

On harpsichords it's almost trivial to retune all the Bb's to A#'s in just a few minutes, if the goal is to remain in some regular meantone layout or other (a good musical goal for some and execrable to others: Bach being of this latter opinion). But, on organs and fretted clavichords it's anything but trivial to do such a conversion quickly. Hence the practical need for systems that are reasonable compromises, instead of the limited regular meantone systems. Plus, even on harpsichords, the expectation of meantone still limits composers not to use pairs such as D#/Eb both in the same piece; and the 17th and 18th century composers did not let themselves be restricted in that way, anyway, most of the time. For example, yesterday I played through an organ piece by Froberger (from 1649) that is based in G-Dorian but visits the triads of both A-flat major and B major within this same piece. That simply can't be done without first chucking the expectation of regular meantone out the window, or else building the organ with split keys (which was sometimes done).

Again, there are further levels of complication that I simply cannot go into here with regard to all the possible Chorton/Cammerton situations. I appreciate your interest, but this isn't an appropriate forum for me to explicate all this. The musical side of all this intonation business must be HEARD to be understood, in musical practice; internet chats do it hardly any justice at all.

Last night I had a friend over to play through the Bach violin sonatas BWV 1014-19. I tuned my harpsichord to my Cammerton (i.e. the normal) reading of Bach's temperament, using A 440 since that's the normal pitch of my friend's violin. I could have used the transposed Chorton version (simulating the Leipzig cantata situation, with keyboardist reading a whole step below everybody else or transposing mentally on the fly) but that would have distorted the interval relationships in THESE particular pieces, the violin sonatas. The point of our session was to explore the question of how easy Bach's tuning is to play with, from the other person's perspective: and it worked marvelously. He said it was the easiest tuning to match that he's ever played these pieces with, finding the spots on his violin fingerboard to sound good with the harpsichord's intonation in the various keys. Of course it was; Bach knew what he was doing, both as a tuner and as a composer, and my friend knows how to listen well as a good violinist. In the cantatas, with the expectation that the organ was essentially a transposing instrument in D (from the perspective of the orchestra and singers), Bach composed the music differently to take that into account, favoring a different set of keys: again, Bach knowing what he was doing with the available instruments and not being a victim of circumstances, but turning it all to musical advantage.

=====

One thing to watch out for here is: the cents measurement itself is deeply biased towarequal temperament, that expectation that even 100s are somehow better than an even series of some other number. As I mentioned above, the whole steps in 1/6 comma meantone are 196. Pythagorean fifths generate a scale whose whole steps are 204. So what? Equal temperament's steps of exactly 200 aren't better in any way, except that the measurement system is biased to assign them that exactness. The division of an octave into 1200 cents is arbitrary, a logarithmic assignment of convenience to make equal temperament more easily understandable. There are other ways to think more productively and musically about other temperaments, than to measure them as deviations from the post-industrial-revolution standard of equal temperament. That's a fundamental flaw of Murray Barbour's otherwise very well researched book: his penchant to measure everything as deviations from E.T., and to assign musical value directly according to the lowest deviations. Tonal music simply does not work that way, in practice. E.T. is atonal. All the other meantone temperaments are tonal, according to the selection of the subset of notes they have in them. E.T., that limiting case, is the exception. And, it brings biasing expectations to the table....20th/21st century expectations being read back into historical situations, where they don't really belong.

Ludwig wrote (June 17, 2004):
[To Dale Gedcke] Thanks Dale but I must agree with Brad that for this list the matter of physics and music is a little too complicated to go into unless you can make it not seem so dry which is often the problem with mathematical problems.

The same proceedures apply to the design of Pipe Organs in designing pipes and the pitches to which they will speak. Many of Organs that Bach played had Organ Pipes come to the ration of the Golden mean 8/5 or 1.666666666----- for the Principal stops. From this scales were narrowed or opened up according to the timbre that the builder and voicer/pipe maker wanted.

Dale Gedcke wrote (June 17, 2004):
Bradley Lehman wrote:
"........The point of our session was to explore the question of how easy Bach's tuning is to play with, from the other person's perspective: and it worked marvelously. .........."

MY COMMENTS:

Thanks for the elaboration on the tuning used in Bach's era. That explanation helped.

I presume Bach composed for a particular tuning. A lot of the composing skill is the intuitive feel for how good it will sound, and that presumes a particular tuning in the composer's mind.

Having experimented with the tuning you think Bach used, do you feel that playing in even temperament has dulled some of the more brilliant colors in Bach's compositions?

The rationalization for the Pythagorean tuning is that humans like to hear pitch progressions in simple ratios (2:1, 3:2, 4:3, 5:4, 6:5, etc.) with the first few ratios in that list being the most desirable. There must be some truth to that rationalization. But it is not obvious how much deviation from the pure ratios is enough to significantly degrade the appeal. Have you developed an opinion on that issue after trying different temperaments?

Bradley Lehman wrote (June 17, 2004):
[To Ludwig] Translation of that "8/5" business: regular 1/4 comma meantone in the minor sixths.

But, that's not the Golden mean, and 8/5 does not work out to 1.66666666.... 8/5 is 1.60. The Golden mean is Phi, 1.6180339...., i.e. the solution of the equation (Phi - 1) = 1 / Phi. From a rectangle of that proportion, Phi to 1, hack off a square and you're left with a new rectangle of the same proportion as the original. (SQRT(5) + 1) / 2.

What evidence is there that anybody ever tried to tune specifically to Phi in their minor sixths?

Or, if 1.6666666 (i.e. 5/3) is to be pure in the major sixths, then that's regular 1/3 comma meantone. That's too extreme for organs. An interesting harpsichord recording in that, however, is Edward Parmentier's CD "17th Century French Harpsichord Music", Wildboar 8502. Since all the major sixths are pure in that temperament, the minor thirds are also; and therefore the diminished triads and 7ths are also pure, a startling sound.

Bradley Lehman wrote (June 17, 2004):
Dale Gedcke wrote:
< I presume Bach composed for a particular tuning. A lot of the composing skill is the intuitive feel for how good it will sound, and that presumes a particular tuning in the composer's mind. >
In the paper I show that Bach was not only "intuitive" about this but knew scientifically and demonstrated in explicit examples that he understood exactly how it sounds and why it works. That is, his composing skill was a blend of both intuition and analytical work.

< Having experimented with the tuning you think Bach used, do you feel that playing in even temperament has dulled some of the more brilliant colors in Bach's compositions? >
I say it more strongly than that, and feel it more strongly than that. Listening to equal temperament in a tonal piece of music is like looking at a black-and-white reproduction of a color painting: ALL the color has been washed out. And, listening to Bach's music in the variously incorrect unequal temperaments is like having most of the color right in a color print from a painting, but incorrect balances in the printing inks.

< The rationalization for the Pythagorean tuning is that humans like to hear pitch progressions in simple ratios (2:1, 3:2, 4:3, 5:4, 6:5, etc.) with the first few ratios in that list being the most desirable. There must be some truth to that rationalization. But it is not obvious how much deviation from the pure ratios is enough to significantly degrade the appeal. Have you developed an opinion on that issue after trying different temperaments? >
Of course; over the past 20 years of experimentation and reading. I also subscribed for a while to the Just Intonation Network's newsletter, "1:1"; and am a fan of Lou Harrison's music. But, there are others who take that side of things a lot farther than I care to. Bach's student Kirnberger was into that stuff, too, and deserves better treatment in the press than he has received. His goal was different from Marpurg's, and that's why Marpurg didn't understand or respect him.

As for degrading the appeal in impure ratios, it all depends on the music to be played. For atonal music, equal temperament is obviously the way to go. For tonal music, so much varies by time/place/style that dozens of other options really can't be ruled out.

 

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