Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum Does a "Let the piano tell you" ET 5ths/4ths sequence exist?

I guess you are right. That sequence does it, it is only that it does not satisfy me. I find it cumbersome, inaccurate and error cumulative... I am looking for a simpler one.

And, for what I can see at another thread, I am not alone:

Well I am confused. I learned using 4ths and 5ths checking 6ths and 3rds major is slightly slower than minor. RBI regular beating intervals?

RBI=FBI= rapid beating interval = fast beating interval

SBI = slow beating interval

I have only a little objection.

Instead of tuning a:

1/2 bps 5th + 1 bps 4th = octave, for example F3-C4, C4-F4

I would tune the 4th in the first place:

1 bps 4th + 1/2 bps 5th = octave, for example F3-A#3, A#3-F4

That is because of the partials involved in these intervals
4:3 for the fourth and 3:2 for the fifth. So when making the fourth to beat faster than the fifth we are tuning a wider than pure 4:2 octave.

4:3 faster than 3:2 = wide 4:2

While if we first tune the fifth F-C and then the fourth C-F the partials involved don't tell us anything about what kind of octave we are getting.

3:2 slower than 4:3 = who knows?

Yes I guess you are right. I mostly talk of the way we tune, not of cts. 6:3 octaves on a Fazioli, concert grand , not at all (for instance)

I've never seen a Fazioli concert grand (except in photos). Here concert grands are mostly Ds. And they all have beautifull basses, a pleasure to tune them! All theoretical tuning stuff works to perfection in them.

I have long been offering alternative strategies to the classic Braide-White method for the reasons I have stated. I have also said that what I have to offer is not really for people who can use that system successfully. It is for aural tuning novices and those who have not been successful with the BW method. Having clearly stated that, the comments to my e-mail keep pouring in and none yet have told me that they prefer the BW method, I have only seen that on here by a few people.

Here a comments from today and yesterday's mail:

Date: Tuesday, January 19, 2010 4:21 AM
From: Stanley ***** <*****.net.py>
To: billbrpt@charter.net

Subject: Appreciation for recent Journal Article
Size: 4 KB
Dear Bill Bremmer,
I have enjoyed your series of articles on ET via Marprug Sequence.

While I attended the convention last summer in Grand Rapids, I took in 3 classes on tuning by ear. While I was there I bought the Reference Material for the 3 examinations to become a RPT. I'm thoroughly enjoying the material.

But with reference to your article in the December issue of the Journal I must say you presented specific material that is really being useful. Not only what note you tune after the other, but you included the action to take to correct things. The steps 13 to 21 in your article said to flatten this or to sharpen that. Excellent! We've had many articles on tuning but this one had something I needed.

To me that represents excellent teaching techniques.
Congratulations!
Stanley ***** International Associate Member, Paraguay

********************************************************

Date: Monday, January 25, 2010 4:36 PM
From: Jim ***** <*****@yahoo.com>
To: billbrpt@charter.net

Subject: marpurg
Size: 4 KB
Hey Bill,

Just a note to let you know that I've used the Marpurg sequence for about a month now and I find it very helpful. I have always tuned aurally. It adds some more steps but cuts down on the guess work and corrections.. I can't remember the last time I modified my temperament sequence, maybe 15 or 20 years! Thanks, Jim ***** RPT

"1 bps 4th + 1/2 bps 5th = octave, for example F3-A#3, A#3-F4"

These ratios occur on pure duodecimes (twelfths).

Bernhard Stopper

Yes as they have moderate iH you can use different stretches it chnge the type of tone. It is not as possible with a low iH piano that scream easely.

Hi Bernhard !

The next step is providing a workeable tuning sequence !. It may be easier to rely on 3:1 than on 4:2.

DO you think it is possible to switch from a 3:1 based sequence to an octave srtretch based one at some moment in the piano (treble) ?

ANY sequence starting from whatever octave width and fitting the other intervals into that width will do.

Bernhard Stopper

Yes , but your tuning is including stretch progression for at last 6 notes, my question is that it most probably does not allow to use another type of stretch aftertaht (octave based, or does it ?)

What kind of octave stretch are you talking of? Whole tone aural octave types, partial match octave types, frequency ratio octave types?

Many ways lead to Rome....

Italian octaves ! Dont know wich type but a way to keep coherence with the mediums while finding enough stretch in the high treble when feeling the desire for.

We may well stick to some kind of methodology dont we ?

Gadzar:

Congratulations again on starting a great Topic. Italian octaves, I love it! (My Grandmother would have said EYE-talian octaves…)

Let me make some general comments about 4ths and 5ths. There have been so many posts since I last posted, it is hard to sort out the questions and comments.

First let me talk about the progression of 4ths and 5ths. If we take a piano with iH and tune straight 4:2 octaves the 4ths and 5ths will increase in beat speed through most of the scale, but will less than double in beat speed per octave. Of course each contiguous 4th and 5th will beat at the same speed when the 4th is on the bottom; this is a test, or better yet a definition, of a 4:2 octave. And if the octaves are wider than 4:2 the 5th will be slower and if the octave is narrower the 4ths will beat slower. Also, if the octave partial-type narrows going up the scale (which must happen at some point or the 2:1 match will beat wildly even with straight 4:2 octaves) the 4th will progress slower and the 5ths will progress faster.

OK, your objection is that although starting with F-C at ½ bps and C-F at 1 bps is appropriate, tuning any other 4ths and 5ths with these same beat rates is not and will not produce a reliable RBI to continue the sequence. Great, we are getting down to brass tacks. Even though SBIs do not double in beat rate every octave, let’s use harmonic tones as a worse case scenario.

So what would be the error of using the same beat rates? Take a 4th that beats 1 bps and is 2 cents wide. The 4th an octave higher would beat 2 bps. And each 4th in between would beat by the 12th root of 2 faster than the one below it. And if the lower 4th was tuned to beat the same as the upper at 2 bps, the error would be 2 cents. So the error of tuning a 4th at the same speed as the one chromatically below it would be 1/8 of a cent. That is not much at all. Until we are looking at 4ths (or 5ths) that are contiguous, it may not be possible to manipulate the pin well enough, or to discern the difference in beat rates, in order to make the beats progressive. This is the reason I use the term “generally progressive” when referring to 4ths and 5ths.

And this is a worse case scenario. In reality, the beat rate of 4th and 5th do not double each octave. And if the octaves narrow sufficiently the 4ths may seem to all beat at the same speed. I believe this is how the Baldrassin-Sanderson sequence works with their use of a series of 4ths beating at the same rate. Considering the effects of iH and narrowing octaves, the 4ths may very well seem to all beat at the same speed.

So back to the “reliable” RBI. I am not saying perfect. And in cases where two SBIs are contiguous in the temperament, I believe that they should not beat the same. But even then, the errors are small and especially in the use of G-A# as a RBI rate ceiling I hold fast to it being “reliable” for continuing the sequence, not as a beat rate written in stone.

Also, there is a problem with using F-A# beating 1 bps and A#-F beating ½ bps to set an initial octave. This will fix the initial octave as ½ bps wide of a 4:2 octave. You might as well say 1 cent wide of 4:2. It does not allow the same variation due to iH that tuning F-C at ½ bps and C-F at 1 bps will.

If desired, G#3 can be tuned to F3 (instead of C#4) and this m3 should beat no slower (a tiny bit faster) than A#3-D4 which has already been tuned. Then there will be no SBIs to tune.

But I am sure I could come up with an all RBI sequence starting with an initial set of CM3s. After the initial set is tuned, M6s can be tuned with beat rates that fall halfway between the initial set of CM3s to produce a second set of CM3s. Then m3s can be tuned to beat the same as the first set of M3s (because of iH) to produce the third set of CM3s. And the fourth set of CM3s would be tuned with M6s that beat the same as M3s in the second set. At least that is how I imagine it in my head. It would have to cover more than one octave, though.

Also the sequence I designed uses only CM3 and Cm3s, but I believe 4ths, 5ths and 8ves must be always checked.

BDB,

As I promised, here is my piano tuned in ET.


Equal Temperament


My piano is a studio Petrof model P117K1, 46" tall.

There you can also see other videos where I play:

Moonlight Sonata 1st mvt, Beethoven
Pathetic Sonata 2nd mvt, Beethoven
Behind the Waterfall & Desert Rain Medley, David Lanz

I am not a pianist, so please excuse my poor interpretation.


I would be pleased to hear a piano tuned in ET by you. It is not necessary to play music, you can just play runs of intervals as I did in my video, to show the eveness of the temperament and the stretching of intervals.

Gadzar:

Here is an all RBI sequence I worked up just to see what could be done. Notice that, except for A4 while tuning the CM3 ladder, all the notes are in the temperament octave. I ran it though a simulator with a Yamaha U1 and 4:2 octaves. The result was that all RBIs were progressive, the 4ths were from 0.6 to 1.1 bps and the 5ths were from 0.6 to 0.8 bps. It makes use of an effect of iH that causes m3s to beat about ½ bps faster than they theoretically would relative to M3s in the temperament octave. I do not think this would work with harmonic tones. I did not bother figuring what checks to use, and the results would of course be somewhat different with other octave types or a different piano.

Here are the resulting offsets in cents:

F3 -1.3
F#3 -1.2
G3 -1.5
G#3 -1.4
A3 -1.4
A#3 -1.1
B3 -1.3
C4 -1.1
C#4 -1.0
D4 -1.1
D#4 -0.7
E4 -0.8
F4 -0.5

Tune a ladder of CM3s from F3 to A4.

Tune D4 to F3 to beat between F3-A3 and A3-C#4

Tune G#3 to F3 to beat between A3-C#4 and C#4-F4

Tune A#3 to D4 to beat the same as G#3-F4

Tune G3 to A#3 to beat the same as C#4-F4

Tune B3 to G3 to beat the same as F3-D4

Tune D#4 to B3 to beat the same as F3-G#3

Tune E4 to G3 to beat the same as A3-C#4

Tune C4 to G#3 to beat between G3-B3 and A3-C#4

Tune F#3 to A#3 to beat between F3-A3 and G3-B3




Now I am not saying that anyone, especially me, could actually get these results from this sequence on an actual piano. Hope you find this amusing, if nothing else.

Tooner,

As I have no U1 to try this sequence, I can not use the offsets you give, all I can do is guessing about how it would sound by the instructions you give to temper each tuned interval. Theoretically it seems to be correct, it is very similar to how I actually tune ET (CM3/Cm3). It gives a lot of available checks and it is self correcting, not error cumulative, etc. A good one, I guess.

Maybe if you tune a real piano using this sequence an give us a recording of it, we can all hear how it sounds like.