The Radio 3 Boards Forum from myforum365.com
08:30:25, 02-12-2008 *
Welcome, Guest. Please login or register.

Login with username, password and session length
News: Whilst we happily welcome all genuine applications to our forum, there may be times when we need to suspend registration temporarily, for example when suffering attacks of spam.
 If you want to join us but find that the temporary suspension has been activated, please try again later.
 
   Home   Help Search Login Register  

Pages: 1 2 3 [4] 5 6
  Print  
Author Topic: What does Well-Tempered mean anyway?  (Read 2391 times)
roslynmuse
*****
Gender: Male
Posts: 1615



« Reply #45 on: 15:07:40, 01-11-2007 »

Ena - many thanks indeed for all this! Looking forward to reading and rereading at leisure and starting to get an insight into this whole area, about which I am (shamefully) ignorant...

Re some of the earlier posts - I know a lot of choral trainers who also insist on high leading notes, and I have to say that is how my ears have become conditioned recently for good or ill...
Logged
Reiner Torheit
*****
Gender: Male
Posts: 3391



WWW
« Reply #46 on: 15:17:29, 01-11-2007 »

Ena, I am agog at the time and effort you have spent on this monumental posting!  Thank you for sharing this depth of insight into this matter with us here so freely!  I've read it once, but I think it deserves a bit of rumination and re-reading of individual sections.  I wish I had an electronic pitch-generator to hear the results "live" (or even better a harpsichord, but that's a luxury beyond my wildest hopes).

Could I ask the moderators to make sure this thread gets saved to an archive?  There's extraordinarily worthwhile information in here!

Meantime, to Roslyn...  yes, I know choral trainers who push the leading-notes up all the time, as though they're merely flattened-off versions of the tonic Sad
Logged

"I was, for several months, mutely in love with a coloratura soprano, who seemed to me to have wafted straight from Paradise to the stage of the Odessa Opera-House"
-  Leon Trotsky, "My Life"
Bryn
*****
Gender: Male
Posts: 3002



« Reply #47 on: 00:52:17, 02-11-2007 »

I concur most readily with RT. Many thanks, Ena. It occurs to me that there are several keyboard instrument players of considerable repute who read and sometimes contribute to this forum. There are also several practitioners in the field of electronic music making around here. Perhaps they could combine forces to attempt to put at least some of your solution into practice, Ena? I would certainly be eager to hear the results.
« Last Edit: 08:57:03, 02-11-2007 by Bryn » Logged
C Dish
****
Gender: Male
Posts: 481



« Reply #48 on: 02:53:21, 02-11-2007 »

F major is also the most unpleasant scale to practice on the piano.
Why should F be any worse than G? I am mystibaffled
Better than being baffified. Since e-f# is a whole step and a-b flat is a half step, the former flows more naturally than the latter (in ascending pattern, that is).

A: I don't mean that F major is itself unpleasant, just playing the scale evenly is harder relative to the other 11.
Logged

inert fig here
C Dish
****
Gender: Male
Posts: 481



« Reply #49 on: 03:01:47, 02-11-2007 »

I wish I had an electronic pitch-generator to hear the results "live".
Have you tried a free program called Scala? Easy to learn and free to install (but not in that order!)
Logged

inert fig here
Reiner Torheit
*****
Gender: Male
Posts: 3391



WWW
« Reply #50 on: 05:21:13, 02-11-2007 »

No, but I will now!  Thanks, CD Smiley
Logged

"I was, for several months, mutely in love with a coloratura soprano, who seemed to me to have wafted straight from Paradise to the stage of the Odessa Opera-House"
-  Leon Trotsky, "My Life"
Sydney Grew
Guest
« Reply #51 on: 06:30:52, 02-11-2007 »

Have you tried a free program called Scala?

Thank you for one of the most interesting links to have come our way for some time.
Logged
Ena
Guest
« Reply #52 on: 08:35:51, 02-11-2007 »

I wish I had an electronic pitch-generator to hear the results "live".
Have you tried a free program called Scala? Easy to learn and free to install (but not in that order!)

Thanks for this CD. I retuned my clavichord last night to Bach WT (i.e. his own 'Mixed 1/8th-Comma Mean Tone Temperament'). Each key sounds a) delightfully in tune, and b) quite different from every other key! I now need to download Scala to 'check it out'!
Logged
C Dish
****
Gender: Male
Posts: 481



« Reply #53 on: 10:52:48, 02-11-2007 »

'Easy to learn' may have been a bit too enthusiastic -- but it's certainly not forbidding. And extremely versatile, though I haven't tried everything out.
Logged

inert fig here
oliver sudden
Admin/Moderator Group
*****
Posts: 6411



« Reply #54 on: 11:26:29, 02-11-2007 »

All the same it does seem only fair to mention that a real live instrument has resonances which a computer program is going to have trouble emulating but which do affect our perception of tuning.

(piano stretched octaves being one: I'm led to believe they have not so much to do with the desire of our ears to hear higher things sharper as with the need for the instrument to be in tune with its own overtones - I'm told the resistance of the metal of the strings to vibration stretches the overtones somewhat...)

I must say that while the Lehman inversion of the diagram is certainly a sticking point for me, what I do find compelling about his line of reasoning (as someone with no specialist knowledge in this area) is that he does find a specific meaning for the double loops which is directly related to the tuning process.

There's certainly something about the shape of the capital D though - as calligraphy it would be an utter shambles but the O'Donnell interpretation of it as combining the names of Eb and D# does seem to have something going for it.
Logged
C Dish
****
Gender: Male
Posts: 481



« Reply #55 on: 21:11:49, 02-11-2007 »

All the same it does seem only fair to mention that a real live instrument has resonances which a computer program is going to have trouble emulating but which do affect our perception of tuning.
True dat, but perhaps we can build an automated tuning-peg crank that is connected to a computer running Scala.
Logged

inert fig here
Sydney Grew
Guest
« Reply #56 on: 15:06:07, 05-11-2007 »

If we had ever before considered Bach's squiggles it was only to dismiss them as a piece of eighteenth-century irrelevance, so we stand now agape in simple wonderment at all these revelations.

But to return to this:

If a major-third sequence is played using only ‘pure’ intervals (i.e. C-E, E-G#, G#-B#) the last note (B#) lies horribly flat from the expected C.

One would seldom wish to do that in diatonic music would one? We suppose the Member to have had in mind something like this:


or even of this kind:


but neither of those sequences is much like real music. When one moves for example from E to G# that would would it not normally be thought of in a context of tonal harmony i.e. A to E then A to G# and not really E to G# at all. The A's may be there still in the musician's mind even if they are not sounded that is what we are saying; and it would be his the musician's duty to harmonise the other notes with the tonic (i.e. with the context) rather than with each other, thus:


or thus:


The following four-part sequence even would be altogether more natural and harmonious then than any of the above would not it?


Let us now for a moment address the point about the a capella singers' "pitch drops":

It seems that when the music modulates, the right singers have to adjust the crucial intervals so that Pythagorean tuning is maintained but the pitch does not drop. In Palestrina's music, the modulations are relatively straigh[t]forward and pitch drops don't generally occur. But in some other music of that period, special care must be taken at critical moments. Late Gesualdo is probably the ultimate test.

We suppose that were the work not designed to return to its original key one would really expect its pitches to move around as a result of the journey it contains or embodies - rather than as a fault this should perhaps be regarded as a necessary phenomenon arising from the nature of sound and the progression of the music. A requirement in other words. Of course though were it something of Mozart we should expect balance, but other composers have other, non-Mozartian ideas.

Finally we draw the attention of Members to the possibility of getting away from it all on a canoeing trip. This was the dream of the little Austrian here depicted, renowned may we say for his extreme neatness:


In the seminal year 1908 he produced this - "moving tenderly" as he put it:


We wonder how much if at all it is modelled upon the music of Heinrich Isaac (1450 - 1517)?

Certainly the composer was at this time (1908, as we say) an enthusiastic follower and setter of Stefan George the renowned Homosexualist and Symbolist poet.

The music contains rather a lot of snags does it not? Can any Member recommend a performance?

Here to end up with is George dressed up as Dante (second from the left), with a selection of his little friends and disciples.

« Last Edit: 23:10:49, 05-11-2007 by Sydney Grew » Logged
Ena
Guest
« Reply #57 on: 15:40:41, 05-11-2007 »

If a major-third sequence is played using only ‘pure’ intervals (i.e. C-E, E-G#, G#-B#) the last note (B#) lies horribly flat from the expected C.

One would seldom wish to do that in diatonic music would one? We suppose the Member to have had in mind something like this:


or even of this kind:


but neither of those sequences is much like real music...

But the point was a mathematical one, not a musical one (as such). Taking one of your examples...


... if the three successive thirds are rendered as pure (i.e. 5:4) thirds, they fall short of an octave. This is because (5/4) x (5/4) x (5/4) = 125/64 (i.e. 1.953125, which is less than 2 by a factor of 0.046875).

Furthermore, if one adds back to these thirds the Syntonic comma that has been removed (i.e. 81/80), these thirds now are increased from 6/5 (=80/64) to the Pythagorean size of 81:64. Now if your example is again tried, this time with the Pythagorean values, it will overshoot the octave. This is because (81/64) x (81/64) x (81/64) = 531441/262144 (=2.027287, thus exceeding the octave by 0.027287).

So in order to accommodate three conjunct major thirds into exactly one octave (no matter how composers may then go on to use or abuse them!), their value will have to be larger than a pure third, but smaller than a Pythagorean third.
« Last Edit: 16:37:26, 05-11-2007 by Ena » Logged
thompson1780
*****
Gender: Male
Posts: 3615



« Reply #58 on: 23:19:15, 05-11-2007 »

A bear of very little brain writes:
Not all of us fully understand it even now Sad

I had to do some numbers to get a feel for it.  It should tie in with Ena's maths.

A Harmonics
1. A24 has a frequency of 55hz
2. A16 = 110 Hz
3. E = 165 Hz
4. A8 = 220 Hz
5. C# = 275 Hz - REMEMBER THIS ONE
6. E = 330 Hz
7. G = 385 Hz
8. A = 440 Hz
9. B = 495 Hz
10. C# = 550 Hz REMEMBER THIS ONE TOO

Let's now say we want to construct the E harmonics so that they are in tune with the Dominant E in the A harmonics above....

E Harmonics
1. E = 82.5
2. E=165 (to match the 3rd harmonic of the A-series.  Being the 2nd of the E-series, this leads to all the 2/3 business)
3. B = 247.7
4. E = 330 (which neatly matches the 6th harmonic in the A series)
5. G# = 412.5
6. B = 495

Let's now say we want to construct the B harmonics so that they are in tune with the Dominant B in the E harmonics we’ve just created....

B Harmonics
1. B = 61.875
2. B= 123.75
3. F# = 185.625
4. B = 247.5 to match the 3rd harmonic of the E series
5. D# = 309.375
6. F# = 371.25
7. A= 433.125  WHOOPS! THIS IS SUPPOSED TO BE 440Hz
8. B = 495
9. C# = 556 875 (WHOOPS! THIS IS SUPPOSED TO BE 550Hz)

And if you take this further to the F# Series….

F# Harmonics
1. F# = 92.8125
2. F# = 185.625
3. C# = 278.4375  WHOOPS! THIS IS SUPPOSED TO BE 275 Hz
4. F# = 371.25
5. A# = 464.0625
6. C# = 556.875 WHOOPS! THIS IS SUPPOSED TO BE 550 Hz

It all just gets too messy!

Tommo
Logged

Made by Thompson & son, at the Violin & c. the West end of St. Paul's Churchyard, LONDON
oliver sudden
Admin/Moderator Group
*****
Posts: 6411



« Reply #59 on: 11:31:01, 06-11-2007 »

We wonder how much if at all it is modelled upon the music of Heinrich Isaac (1450 - 1517)?

Certainly the composer was at this time (1908, as we say) an enthusiastic follower and setter of Stefan George the renowned Homosexualist and Symbolist poet.

The music contains rather a lot of snags does it not? Can any Member recommend a performance?

From wiki: "Webern attended Vienna University from 1902. There he studied musicology with Guido Adler, writing his thesis on the Choralis Constantinus of Heinrich Isaac." So it would be foolish to discount the possibility entirely.

We find the performance by the BBC Singers under the direction of M. Pierre Boulez (recorded by the German Gramophone Company) to be very pleasing. We were unaware that the key signature of Entflieht... was Herr von Webern's last! In the same box



are to be found the songs to texts of George (opera 3 and 4, and ohne Opuszahl from 1908-09) for voice and piano, gloriously sung by Christiane Oelze. These are simply ravishing things. One really must take advantage of any opportunities which may be presented one to play these songs to those who think Webern's music too unpleasant for them. Although such persons have as often as not not actually heard anything of Webern anyway.

George also produced the most satisfying German renditions of the Shakespeare sonnets we know. Umdichtungen he called them rather than Übersetzungen and we could not agree more.

Verbrauch von geist in schändlicher verzehr
Ist lust in tat • und bis zur tat • ist lust
Meineidig • mörderisch • blutig • voll unehr •
Wild • tierisch • grausam • roh • des lugs bewusst.

Genossen wo gleich drauf verachtung trifft •
Sinnlos erjagt und gleich nach dem empfang
Sinnlos gehasst wie ein verschlucktes gift •
Eigens gelegt dass toll wird wer es schlang.

Toll im verfolg und im besitz zumal •
Erlangt und im und beim erlangen wild •
Glück beim versuch und wenn versucht nur qual •
Erst: freudig hoffen • nachher: schattenbild.

     Dies weiss jedweder . . doch nicht wie man flieht
     Den himmel der zu dieser hölle zieht.


But this is by the by: we find Webern and for that matter Debussy extremely apt for if tangential to this topic in that their music is for us a necessary consequence of equal temperament - when the contrasts between the keys are removed (which we understand did indeed not occur until the late 19th century) the harmonic variety which is thereby lost must needs be replaced somehow, and with harmonic resources inherent to the tuning system. We find it far more fruitful to think of music springing in the first instance from its resources - we doubt very much that either Gesualdo or Bach wrote his harmonies without a firm idea how they sounded.
Logged
Pages: 1 2 3 [4] 5 6
  Print  
 
Jump to: