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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108445 06/26/13 01:21 PM
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All:

Maybe we can get back on track.

One useful thing that M3s can do is fit into an octave as a set of self-checking contiguous intervals. Yes, a P4 and a P5 can also fit into an octave, but are not as useful in setting a temperment as they are not self-checking. Of course when the 9th note is tuned in a strict 4ths and 5ths temperament, a pair of contiguous M3s are formed and can be used as a check in various ways.

For example: In Dr. White's sequence when C#4 is tuned, the first set of contiguous M3s is formed (F3-A3, A3-C#4). The m6 of F3-C#4 can be chromatically compared to the m6 created when the note before was tuned (F#3-D4). And if the error is very early in the sequence, the common, implied interval to these m6s (M6 F3-D4) can be evaluated and corrected to the begining notes of C4 and G3. Then F#3-C#4 P5 can be adjusted before correcting the three middle notes of the sequence (so far) being: A3, E4, B3. I wonder if some tuner's frustration with 4ths and 5th sequences is just not understanding how infered intervals relate to the ones being tuned or checked, like chromatic M3s and the infered P4.

But 4ths, 5ths and octaves can fit into a P12 in a number of ways each of which is not only self-checking, but when used together are cross-checking.

Another possiblility is 4 m3s in an octave, but when there are more than 3 intervals within another interval, the checks are not as certain.


Jeff Deutschle
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Re: Tuning the 4ths and 5ths Temperament
Bill Bremmer RPT #2108447 06/26/13 01:22 PM
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Originally Posted by Bill Bremmer RPT
What I find interesting is that all of those who originally learned the Braide-White sequence had to supplement that knowledge with other information from somewhere else in order to actually be able to tune a true ET.


Not true.


Jeff Deutschle
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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108452 06/26/13 01:26 PM
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One always tunes 4ths and 5ths, the CM3 sequence just sets mileposts for reference and that is a great help, speaking as one that learned and tuned for a number of years the straight 4ths and 5ths sequence. How you treat the 4ths and 5ths as you fit them in the CM3 framework sets the accuracy (or lack of) in your temprement.

There are a couple of agendas here, from both sides of the border. Let's stay on topic.

Re: Tuning the 4ths and 5ths Temperament
Numbered #2108508 06/26/13 02:51 PM
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I find what Don Mannino said a while ago pertinent, especially that which I put in bold. Now here is someone with his feet on the ground and who does not have his head in the clouds and who knows his stuff.

I have quoted Don because he brings up something which Bill does like to speak about and that is "The fudge Factor".

Another way of saying that? Compromising and backtracking to make things/the temperament to work, even with the CM3 sequence.

The Fudge Factor, it really is sweet!

So, what I am trying to bring out is, no matter what sequence you use, you may and will need to fudge, whether it is the 4ths and 5ths or the CM3.

from Re: ET via Marpurg Revisited thread, 11/11/10

Originally Posted by KawaiDon

I use the contiguous 3rds to start my temperament, and the only issue that comes up when I teach others about it is that the width of the octaves is somewhat negotiable, and is a part of the tuning process that can confuse setting smooth contiguous 3rds at the start. If one decides in advance to tune precise 4:2 octaves and you verify them it works pretty easily, but I usually tune a little narrower than that, and occasionally a little wider. [/b]So this throws another fudge factor into the initial tuning process[b] that might keep me from being able to claim a truly "perfect" equal temperament. Tuners who try to simply tune a "clean" octave without using a test can then get very confused trying to make the contiguous 3rds work out. The A3-A4 octave might be 4:2, but the F3-F4 might be a little narrow and the contiguous 3rds get goofed up. [/b] And of course, small pianos with not so nice string scales kind of make one have to fudge every step of the way...[b]

Finally, it is interesting to look at a different view of tuning like this, but it is a little dangerous sometimes for people to get overly obsessed with perfection in tuning temperaments. No, I don't mean it's OK to be sloppy, but some tuners do spend an awful lot of time working out a beautiful temperament, only to spoil it with inconsistent octaves and unisons. I think that's what stops a lot of tuners from bothering with trying new temperaments - [/b]they are happy with getting something passable in some of the awful pianos they work with every day, and it just doesn't have relevence to their daily lives to worry too much about this level of perfection.[b]

[/b]I do agree it's nice to have a really well tuned temperament in a good piano that is also in great condition. Especially if the temperament is carried out well into the treble and bass with good octaves, and the unisons sing evenly.[b]

Don Mannino RPT


Last edited by Mark Davis; 06/26/13 02:53 PM. Reason: minor correction

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Re: Tuning the 4ths and 5ths Temperament
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Last edited by Mark Davis; 06/26/13 04:16 PM. Reason: off topic and unnecessary

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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108526 06/26/13 03:20 PM
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Dan, thanks for chiming in.

Also, thanks to the all who have positively contributed here too.

Last edited by Mark Davis; 06/26/13 03:26 PM. Reason: minor correction

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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108567 06/26/13 04:22 PM
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Has anyone got Arthur Reblitz's first edition book?

I think that in there he teaches the 4ths and 5ths temperament.

Would you mind posting some excerpts on what he has to say, the sequences he taught about, etc...if possible and legal.

You can PM if you like.





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Re: Tuning the 4ths and 5ths Temperament
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Originally Posted by Mark Davis
Has anyone got Arthur Reblitz's first edition book?

I think that in there he teaches the 4ths and 5ths temperament.

Would you mind posting some excerpts on what he has to say, the sequences he taught about, etc...if possible and legal.

You can PM if you like.



Wish I did. Gave mine away years ago. Public library might be an option. I do not recall the temperament in his first edition.

Clients are most likely to hear problems first in unisons and second, in octaves. Fifths are next. Accordingly, a temperament which places its primary interval emphasis on fifths (and next, fourths, and so on), is a natural. Is it perfect? No. But neither are other temperaments.

That's my two-cents worth. It doesn't get any more unscientific than this. But it works.

Last edited by bkw58; 06/26/13 06:23 PM. Reason: clarity

Bob W.
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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108657 06/26/13 06:37 PM
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There are no short cuts to setting a good temperment. If you are too scared to "back track", than you are too skeered to be a piano tuner. Find a different profession. The fourths and fifths method of setting a temperment is irrelavent. You can tune by thirds and sixths...doesn't matter. But don't be afraid to always go back to the temperment and make necessary adjustments. The results at the end are what counts.


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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108660 06/26/13 06:44 PM
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I happen to use fourths and fifths to set the temp, but I'm checking with other stuff to know I am always on track as I go along. As you get into tuning octaves outwards, it lets you know your temperment is on target. It's not unusaul for me to go back to my temperment and tweek it a bit


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Re: Tuning the 4ths and 5ths Temperament
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A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks. It all starts with a good solid octave.

An ET can be accomplished across two octaves using only 4ths, 5ths, 8ths, and 12ths. Of course that requires two good solid octaves to get started. What I find interesting is that all three notes of the double octave can be checked against the same note.


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Re: Tuning the 4ths and 5ths Temperament
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Greetings,
It might be a little misleading to say what I use for equal temperament. I don't think using fourths and fifths exclusively is going to get anybody near enough to equal to at least pass the guild test, (which is pretty forgiving).

When tuning aurally, I will listen to a fourth or fifth as the pin is moving, but once I know I am on the right side of pure, and tempered like I think it should be, I instantly use thirds and sixths to see where I am. Once I have tuned the interval, I will listen to a cascading series of tests as I progress through the 12 notes. They accumulate as I go, incorporating the 4th and 5th test, 3rd/6th steps, the 3rd/6th brackets, ascending thirds.
The first four notes I tune are C4,F3,F4, Bb3. These allow me to hear what my fifths are going to require of the octave, after that, it is a basic Holder bearing plan with Bill Garlic's refinements.
Regards,

Re: Tuning the 4ths and 5ths Temperament
Dave B #2108781 06/26/13 10:03 PM
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Originally Posted by Dave B
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks.


Or, you could just tune the 3rds and be done with it.


Keith Akins, RPT
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Re: Tuning the 4ths and 5ths Temperament
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Ed...using what fork?

Re: Tuning the 4ths and 5ths Temperament
Ed Foote #2108911 06/27/13 05:41 AM
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Originally Posted by Ed Foote
Greetings,

The first four notes I tune are C4,F3,F4, Bb3. These allow me to hear what my fifths are going to require of the octave, after that, it is a basic Holder bearing plan with Bill Garlic's refinements.
Regards,


I find that octave secured with 4ths and 5ths as the best beginning for tuning (after having played with stacked M3 for decades)Install it from A3 to A4, activity is more noticeable there.


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Re: Tuning the 4ths and 5ths Temperament
Numbered #2108939 06/27/13 06:50 AM
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All (referring to various posts):

Ah, yes. How the 5ths sound is important. On oddly scaled pianos, octaves and therefore other intervals, need to be tweaked so that the 5ths are not irritating. It happens both near the breaks and across the breaks.

I remember in my first year of tuning with Dr. White's sequence noticing how when C#4 was tuned, the M3 A3-C#4 could be compared with the M3 C#4-F4, if the F3-F4 octave had also been tuned. I thought I was onto something (this was a CM3 check ...), but soon realized that getting these intervals to be progressive did not mean the 5ths would sound good. This was in the 70's and iH was not understood very well. Heck the EFFECTS of iH are still not understood very well. Let me give my understanding of the subject.

If you consider that iH is different for every note and what the value of any particular note is not as important as the SLOPE formed by a series of notes' iH, you may be able to follow what I am saying. Well scaled pianos have an iH slope that is smooth. When a break is encountered it does not have a sudden jump. And in the lower part of the unwound trichords, there is still a slope, it does not flatten out. Oddly, some piaons have greater iH below the break rather than less.

Also, larger pianos have a steeper iH slope and therefore the difference between the 2:1, 4:2 and 6:3 octaves are small. But smaller pianos have an iH slope that is less steep and therefore there is more of a difference between the octave types. Now get this: ON SMALLER PIANOS THERE IS ALSO A GREATER DIFFERENCE IN THE 3:2 AND 6:4 FIFTHS! If you don't choose an appropriate octave, you can't have a decent sounding fifth when the slope is flatter. And on some pianos the slope even inverts across the break, as I mentioned before.

So what octave type is appropriate for the iH slope? The flatter the slope the narrower the octave type should be. And this will happen if the fifths are listened to and adjustments are made. I suppose that a sequence can rely on RBIs and then adjusted when the fifths are used as checks. But if a tuner is able to tune fifths, well why not just tune fifths that are acceptable to begin with?

I want to be fair to the use of CM3s and in particular to Mr. Bremmer's excellent ET via Marpurg sequence. For a well scaled piano, I cannot think of a more accurate and straight forward way to set the temperment. Yes, there is less going back and forth, but then again, it still takes 9 of the 12 notes (I am not including octaves) before the temperment is locked in. This is because of the temporarily tuned notes. However, I do not find it, or any other RBI sequence, useful for pianos with poor scaling. Only by tuning good fifths can you have good sounding fifths. It only takes one "raisin" to ruin a rabbit stew.


Jeff Deutschle
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Re: Tuning the 4ths and 5ths Temperament
Dave B #2108950 06/27/13 07:27 AM
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Originally Posted by Dave B
A good ET can be accomplished using 4ths and 5ths if it is backed up by a lot of Major 3rd checks. It all starts with a good solid octave.

An ET can be accomplished across two octaves using only 4ths, 5ths, 8ths, and 12ths. Of course that requires two good solid octaves to get started. What I find interesting is that all three notes of the double octave can be checked against the same note.


thumb


Bob W.
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Re: Tuning the 4ths and 5ths Temperament
BoseEric #2108991 06/27/13 09:20 AM
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Originally Posted by BoseEric
Ed...using what fork?


Greetings,
I used a C fork. tuned C4 to it. Then formed the F octave around it, and then split that octave the other way with the Bb. At this time, I could make my decision on how my octaves and fifths were going to relate. Carrying the temperament outwards from here, I listen by octave, checked by fifth and fourth, and then listened to the double octave and then how the 3rds, then 10ths progress. By that time, I am usually tired of the note, so I go to the next one...

On big pianos, the inharmonic deviation between the C5 pitch of the fork and the second partial of C4 was so far below the piano's natural variability that it was never a problem. When I went to a machine, I started seeing that there were discrepancies on the order of .2 or so cents, which means nothing except in the most clinical settings. I managed to hit the nail squarely on the Guild tests with this thing, which may have been a bit of luck.

Regards,

Re: Tuning the 4ths and 5ths Temperament
kpembrook #2109267 06/27/13 06:57 PM
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Originally Posted by kpembrook

2) Increased granularity with 3rds vs 5ths. Its simply easier to discriminate between 6 beats per second and 5bps or 7bps tuning thirds than it is to discriminate between .6 bps and .5 or .7 bps. tuning 5ths. WIth 3rds, your precision requirement is reduced by a factor of 10--not insignificant.

3) 3rds are the "check" for the 4ths & 5ths temperament and the definition of the equal temperament. The single best illustration of the equal temperament is evenly beating and slightly increasing speed with contiguous ascending thirds. So, logically, instead of hoping that this phenomenon occurs with tuning the 4th/5th system, why not simply make it happen? If you get the 3rds right, then the 4ths and 5ths will be OK. Put another way, a 1bps difference in a third is something that is audible and matters. But who cares if a 4th of 5th is a hair faster or slower than what we target?


This is exactly the reasoning I was taught, but I don't see many others embracing this logic, at least not here on this thread.

The intervals I use to tune (aurally) are M3, 5th, Octave, M3, M3, 5th, M3, M3, 5th, M3, M3, M3.

So, mostly major 3rds and Keith has already stated why.


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Re: Tuning the 4ths and 5ths Temperament
Numbered #2109347 06/27/13 09:54 PM
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If it is true that

"If you get the 3rds right, then the 4ths and 5ths will be OK,"

then it must also be true that

"If you get the 4ths and 5th right, then the 3rds will be OK."

Such is wholly predicated upon what we train our ears to detect, and where we choose to place the emphasis. The goal in temperament is equal frequency ratios between successive notes. There is more than one way to get there and to check accuracy along the way.




Last edited by bkw58; 06/27/13 09:57 PM. Reason: clarity

Bob W.
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