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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.

Not true.

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.

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

Dan, thanks for chiming in.

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

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.

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.

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

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.

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,

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

Ed...using what fork?

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.

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.

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,

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.

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.