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I have been lurking here for awhile and coincidentally found this post in a google search of "Braid White Temperament."



I am learning to set temperaments by ear and want a basic one that uses 4ths and 5ths. Most of the beginner temperaments I am trying pivot around 3rd's which is great, but I don't hear them (or like them) as well as I do 4ths and 5ths. With the 3rds I feel like I am guessing, whereas the 4ths and 5ths are much clearer to me.

I think this temperament would be a good one for me to learn, however I have an A fork, and when transposing the sequence down a -3rd, doesn't it get a bit low?

Does anyone have a favourite temperament sequence involving mostly 4ths and 5ths that they would be willing to divulge?

I use 4ths and 5ths but start with A4.

A4 to 440 fork.
A3 to A4
E4 to A3
B3 to E4
F#3 to B3
C#4 to F#3
G#3 to C#4
D#4 to G#3
A#3 to D#4
F4 to A#3
F3 to F4

I then check for a smooth progression of 3rds starting at the F3-A3 major third through F4-A4 and correct if/where necessary. It's been my method of choice for 26 years.

*edit* typo

Congratulations on trying the aural tuning path.

I use some of the Brad White sequences in a Both-ways-from-the-Middle sort of temperament, but lately have experimented with the Marpurg sequence demonstrated by Bill Bremmer Videos The first two will apply to what you are working on, and they use 4th and 5th intervals after the contiguous 3rds exercise.

I think it has had a remarkable effect on my temperament setting. I get fewer errors and spend less time fussing. (Your mileage may vary.)

I like not dealing with G3, C4 or D4...probably makes for a much faster tuning.

Lol oops! That's probably the first time I wrote the sequence down, and it's been a long day.

When you get the temperament down, try tuning up and down the piano by fifths, checking with octaves and 10ths. Makes for a change of pace.

Definitely try multiple sequences, to get a feel for how they work, and find out which ones work for you.

Loren,

Do you proceed through the whole sequence before doing any checks?

No, I check as I go. One of the first checks I use is the F#3-A3 minor 3rd after tuning F#3 to B3. If that F# is sharp, that's an early clue that I'm not tempering enough.

Yes I do, but it starts with a C-fork. It is based on Dr.White’s method, but includes F4 and A#3 when tuning F3, G4 when tuning G3 and D4, and F#4 when tuning F#3.

Here is a link to Dr. White’s book as an ebook: http://www.archive.org/stream/modernpianotunin00whit#page/n3/mode/2up

So my sequence, with changes from Dr. White’s in bold, is:

tune C4 to a C5 fork
F3 to C4
F4 to C4 and F3
A#3 to F3 and F4
G3 to C4
G4 to C4 and G3
D4 to G3 and G4
A3 to D4
E4 to A3
B3 to E4
F#3 to B3
F#4 to B3 and F#3
C#4 to F#3 and F#4
G#3 to C#4
D#4 to G#3
A#3 to D#4 (A#3 was already tuned)
F4 to A#3 (F4 was already tuned)

There is no need to go into the detail that is already available in Dr. White’s book. I will explain the reasons for the changes I made, though.

There is much criticism of Dr. White’s method because errors can accumulate and not be noticed until later in the sequence. For me this is the value of the 4ths and 5ths method. By letting errors accumulate, they can be noticed when otherwise they would be overlooked. But by including A#3 early in the sequence, the errors can be corrected more from the ends toward C rather than more from C to one end.

On smaller pianos the 4ths and 5ths at the beginning that tune F3 and G3 can be difficult to get right because of scaling issues. This can be when there are wound strings to deal with and also when there are not. By including F4 and G4 at the beginning, a better place for F3 and G3 can be determined.

The additional notes that are above the 13 notes in Dr. White’s sequence, namely F#4 and G4, allow checks with M3s (major thirds) and M6s (major sixths) that would otherwise not be available. The first one that is available is the M6 A#3-G4. This will be the first RBI (rapid beating interval) available for a check and will always be above any serious scaling issues. This will also beat at the same speed as the M3 C4-E4 tuned later giving the first M6 outside M3 inside check. Again this check will be above any scaling issues, and just as important, includes the only true “anchor” - C4.

The most critical note is F# because it is half way around the circle of 5ths from C, and checking it to C requires a number of separate checks strung together. As mentioned before, F#4 is included to give additional checks and to help determine F#3 when there are scaling issues. And by including A#3 early in the sequence the first ladder of M3s (F#3, A#3, D4, F#4) is formed when F#3 and F#4 are tuned to tie all the needed checks together. And on top of that it will help decide just what to do with any jumps in scaling due to wound strings by providing some chromatic M3s at the bottom of the temperament octave. It is usually best to have the highest M3 that spans the wound/unwound break to beat the same speed or faster than the next M3 up. Others will disagree, but when you decide that you want the best sounding 4ths and 5ths that is what is needed.

If you prefer a 4ths & 5ths temperament sequence, that is fine; many people do. However, if what you are trying to tune is Equal Temperament (ET), the results may be something other than what you believe you are doing and intend to do. I don't believe any human being alive can really tune ET by only using 4ths & 5ths without also checking and correcting the results with the Rapidly Beating Interval (RBI) checks.

You have already said that you don't hear them well and you feel that you are just guessing. I don't wish to appear harsh in saying this but when you estimate your way through an entire sequence using only 4ths & 5ths (with no RBI checks), you are really just guessing too!

You need to expand your listening and control ability beyond just the Slowly Beating Intervals (SBI) to include the many RBI checks that are available. Some books on the subject suggest that the SBIs represent the "coarse" adjustments and the RBIs represent the "fine" adjustments. When listening to the RBIs, it will always be a matter of comparing very small differences. No two will sound exactly alike with the exception of one test which is a favorite of many tuners: the "inside third, outside sixth" test.

If there is any participant on here who can carefully and explicitly help you learn how to use these tests, it is Tooner (Jeff D.). I wish you good luck in learning to tune aurally!

Bill:

You and I will not agree on this and should not try.

When I read in TeaGirl’s OP ” Most of the beginner temperaments I am trying pivot around 3rd's which is great, but I don't hear them (or like them) as well as I do 4ths and 5ths. With the 3rds I feel like I am guessing, whereas the 4ths and 5ths are much clearer to me.” I could connect with what I perceive when tuning CM3s, also. And I do think that she was referring to CM3s because of the use of the word "pivot". It really isn’t difficult to tune a progressive set of CM3s, but I do feel like I am guessing when I do so. There is a fairly wide window of where a particular note can be placed and still have progressive CM3s. But change a 4th or 5th just ½ cent and you can hear a difference, that is, if you can hear the tempering of 4ths and 5ths.

But why are you injecting the idea of tuning 4ths and 5ths without RBI checks? That is the same old straw man you build just to knock down.

Thanks gentlemen, I will have a lot to work on today!

One day I will be able to hear the 3rds a bit better, but hope that by using a foundation of 4ths with RBI tests (of course!), that the 3rds will grow on me over time.

I will try Loren's at the moment, since I have an A fork, thanks Loren!

In the future when I try the Braid White, is it possible from an A fork or does the transposition make it too low?

In the meantime I will order a C fork...

Tea Girl,

Bill is right.

You can not tune true ET if you can not hear M3s.

It was until RBIs were introduced in the tuning sequences that true ET was achieved in the begining of XXth Century. Before that, on XIXth Century, only "Quasi ET" and "Well Temperaments" were tuned in pianos. The tuners of the time used to believe it was ET but it was not.

You can tune really nice and good sounding Well Temperaments with 4ths/5ths sequences. In fact I prefer these temperaments to the colourless ET, but to tune real ET you need RBIs, as checks or as tuning intervals, as you wish. If you can not hear them you can not tune real ET.

There is a section in Dr. White's book about using the same sequence transposed down a minor third. If you have a large piano, and D3 is not on the bass bridge, there should not be a problem. But even so, if you can recognise the jump in scaling and allow the RBIs to jump in thier progression it can be done. It's just a tough way to start. But it may work for you better anyway. If the M3s are a little too fast for you, they will be a little slower starting with A.

Tea Girl!
That’s funny…you are still doing that high tea gig? Leigh and I will drop by when we are over there.
Should be around Easter or so……

Too bad you did not ask me about this at the seminar. When the other folks were here viewing the André Oorebeek DVD on voicing last weekend we could have slipped down to the shop for some instruction on this, and I could have given you a C fork….

There has to be a starting point for you, so start where you are and the rest will come later. Use the 4ths 5ths and the rest will come as your ear develops. Just keep practicing the sequence.

There will always be people who encourage what you are learning and people who discourage. Use the useful information and the rest is not important.

Gadzar:

I guess it is a good thing that Tea Girl just prefers 4ths and 5ths and hears them better than RBIs, not that she cannot hear RBIs as you and Bill want to think. If you heard 4ths and 5ths well, you may have become a 4ths and 5ths tuner, too.

How does this sound: Unless you can hear 4ths and 5ths well, and understand what the beat speed of RBIs mean, you cannot tune true ET, only a quasi-ET. This would be apparent if the outside M6 inside M3 test was properly used.

Why start with a C fork and hope A4 ends up at 440 when that A is the critical standard? Why not set A at 440 and temper from there? I'll never figure that one out.

UnrightTooner,

Are you reading?



I don't believe it to be a good thing if a tuner doesn't want or doesn't like to hear 3rds, or prefer 4ths/5ths over 3rds. The tuner has to hear/tune/test 3rds!



This sounds perfectly correct!

You can not tune ET by merely tuning progressive 3rds, you need 4ths/5ths! To tune ET you need all of them, SBIs and RBIs.

Though, one doesn't have to use the M6 inside M3 test as an obliged way to achieve true ET. In fact I never use it because it is not a theoretically correct test: M6 inside M3 is a "quasi equal beating" test. When it sounds good you know you are on the right way, but when it sounds wrong it gives you no direct clue about the culprit(s). There are better tests available, which identify directly the wrong notes, telling you at once if they are sharp or flat and by how much.