what does 6:3 single octaves mean?

Just a short question in Tune Lab Pro, I cannot understand what is the meaning for 6:3 single octaves and 4:1 double octaves. I am not an English native speaker (I had my postgraduate study in UK), it takes me too long to find the answer to this question, could anybody help me? May be an example can give me a clear understanding.

Every note is made up of partials. For example the A at the bottom of the staff in the bass clef actually sounds that A, the A an octave above, then the E above that, then the A above, then the C# above....

The partial ladder continues up, but if you get the pattern of
fundamental (first partial)- note name
2nd partial - octave
3rd partial - octave plus fifth
4th partial - 2 octaves
5th partial - 2 octaves plus major third
6th partial - 2 octaves plus fifth
7th partial - 2 octaves plus seventh
8th partial - 3 octaves

So.... when tuners discuss partial matches in different octaves, the numbers correspond to different partials of two notes that line up on the same place (note name)

A 6:3 simply means a matching of the 6th partial of the bottom note and the 3rd partial of the top note an octave above.

Similarly, a 4:1 double octave matches the 4th partial of the lower note with the fundamental (first partial) of the upper note.

This is difficult at first, but once understood becomes clear and helps with tuning theory. Please ask more questions if my language is not clear.

Ron Koval
Chicagoland

Thanks Ron, I think I totally got your idea.

the 6:3 single octaves means for instance,
the comparison of 6th partical of an A0 and the 3rd partical of an A1, step by step, like 6th #A0 to 3rd #A1, and so on and so on?

then 4:1 double octaves, with the comparison to 4th partical of C5 to fundamental of C7, and so on and so on?

Am I right?

yes! It is a way to get a uniform framework to tuning using single partials from two different notes to check. It was the standard way to allow the machines to tune using only one partial to "hear" during the tuning process - that is, before the Verituner was developed.

Ron Koval
Chicagoland

I'm glad this question was raised, because it's something I've never quite understood. The Potter course alludes to different octave ratios but doesn't explain it well. Does it really only apply to ETD tuning? I was under the impression that different octave ratios yielded slightly wider or narrower octaves, but lately I'm not sure of this (and not sure if it applies if one is not using an ETD).
Thanks,
Anne

OK, it occurs to me that different octave ratios might yield different tests/checks? Please explain.

3:6 means compare a fifth with and octave and a fifth, as best I can understand. So if you are tuning C5 to C4, compare them both with F3. [Although that is really (3:2):3.]

Poof! and it's gone.... I hate when I write something up, click a button, only to have it disappear into the ether!

So, as I just tried to write...

This topic is a common source of confusion, even for very experienced techs! One good online resource is the manual for the Sanderson Accutuner. Appendix H deals with octave tuning, written by Rick Baldassin.
http://www.accu-tuner.com/SATIIImanual/aph.html

Here you can read that both machine and ear can be used to check and set octaves using different partial matches.

One thing to remember is that using these checks allows for us to set the octave pure, contracted, or expanded. The best tuning for a particular piano may not be found by placing one partial match pure between two notes.

New Tunelab users run into this often as that program has a nice graphical view of both the tuning and the chosen partial matches. While striving to get the second graph to zero out provides a nice exercise, it may not lead to the "best" tuning for that instrument.

Anne, it's possible to tune aurally without much awareness of different octave types, but having this knowledge makes possible a great deal more fine-tuning and customization to fit different situations.

A good example of what I'm talking about is tuning the tenor and treble with the 3rd-10th-17th test: When I first learned to tune, theory taught that all three should beat equally. There was mention that inharmonicity often made that impossible, but not much information more specific than that. So for awhile I noticed these inconsistencies but didn't have a very clear picture of what to do about it, other than just do what sounded best.

Now we know that the inconsistencies in the 3rd-10th-17th test can be used consciously to get well-regulated but varying degrees of stretch depending on what we want, based on the different octave types. I've found that to be a very valuable skill to have, since I've had customers want both more stretch and less than I tended to naturally do at a given time.

Ron brings up an interesting point, at least to me. Nothing against the TuneLab program, but that's a basic thing about its method I don't think I could be happy with. Its model (as far as I can tell, anyway) is to base a tuning around getting a single type of octave/interval beatless in each half of the piano. It feathers the two together in the center, but I wouldn't like to be limited by orienting a tuning around just two octave/interval types. I haven't tried it, but I think it might be possible, as one is working through a TuneLab tuning, to use aural checks and the temporary offset feature to get a somewhat consistent curve between octave/interval types. To its credit, TuneLab does offer a very large selection of octave/interval types to choose from for each half of the scale.

I think as far as the single-partial-based ETDs go, the most versatile in this particular respect -- at least regarding pre-tuning programming -- might be Reyburn Cybertuner. Its custom EQ function allows setting all seven octaves separately, to different octave/interval types and degrees of variance from beatless.

Verituner can do something similar to that, but also allows the user to program specific percentage mixes of up to three different octave/interval types, and also to decide how many set points to have and where to locate them on the scale. Exactly how this custom style function relates to Verituner's inbred calculations derived from multi-partial evaluations of each note, I'm not certain.

Accu-Tuner III allows on-the-fly adjustment of the double octave beat rate by tenth-of-a-beat increments, or pre-tuning alteration of the calculated tuning's DOB rate. Its basic calculated tuning integrates predetermined expansions of beatless octave types in different parts of the piano.

So, there are interesting differences in how the major ETDs approach this area.

In aural tuning I use a lot of tests for different types of octaves, but they seem more and more to be just reference points rather than hard and fast targets to tune to.

Jeff

(Specific post references to TuneLab and RCT functions slightly edited.)

For Hongzhi Mo:

6:3 octaves in the bass and 4:1 double octaves in the upper half will produce an average tuning, that you may or may not like. It's at least a good starting place. If you learn about the different octave/interval types offered by TuneLab, you'll be able to choose a tuning that sounds more expanded or contracted, depending on your taste.

Good luck,

Jeff

Thanks Jeff, I am an amateur pianist and tuning my own piano, and so of my best pianist friends including my piano teacher (who is a professional).

Currently I am useing Tune lab pro trial, try all my best to do with 6:3 octaves in the bass and 4:1 double octaves in the upper half. It sounds excellent in Beethoven and Chopin but not that good in Mozart and Bach. I am actually trying to find what will be the best fit for Mozart and Bach. It seems within a short period of time, I will have to own two piano, for different composers

Jeff, thanks for that very clear explanation.

I've noticed that when I tune my piano using TuneLab set to 6:3 in the bass and 4:1 double octaves in the treble, the treble sounds flat to me (and the bass sounds sharp, relative to the treble). I asked my mentor about this and he suggested switching to 2:1 octaves in the treble. He also said I could be losing my hearing!! And that he could tell how old tuners were by how sharp they tuned the treble! (I'm not that old really, unless you consider 45 old!) I haven't had a chance to try the 2:1 yet.

Anne

Glad you got something from my explanation, Anne. With all due respect to your mentor, 2:1 will produce an even more narrow octave than 4:1, so if you want a bit more brightness in the treble you need to go in the other direction. I'd try 3:1, which would produce beatless twelfths. I believe that's the next degree of brightness TuneLab offers after 4:1.

For what it's worth, the one piano I tried 6:3 and 4:1 on (an older Baldwin Hamilton studio) produced a result that sounded to me just like you describe. Many people would feel that way I think, and hearing loss isn't required. Of course it depends on how much of the keyboard you want to sound reasonably harmonious together.

Jeff

Tunelab can place the octaves anywhere you'd like... It's just so easy to look at the graph and think that the line should end up on the zero line. If you switch back and forth between partial matches, you can see where the different matches will be, based on the current tuning curve. As you nudge the top higher and lower, observe the effect that change has on the other partials. Many times, the best choice is to NOT end up on the zero line, based on a single partial.

Anne, once you have the middle tuned, try finding a good placement for A6 and A7. (where your ear wants) Then play with the graph to see if you can get it to cross those locations. Same works for going down into the bass. Both will depend on how wide/narrow your middle octave(s) are set. I never did find a real easy way to adjust the middle...

For reference purposes, I just experimented with the Steinway D and Average files in TuneLab. I zeroed out the bass around 6:3, reading beats, and did the best I could to zero out the treble around the different octave/interval choices. Here are the cents readings I got at C8. A higher cents reading indicates more stretch.

Steinway D

2:1 31.64
4:1 33.21
3:1 37.18
4:2 37.71
6:1 38.66
8:1 39.51
3:2 48.20

Average

2:1 26.72
4:1 30.87
3:1 33.70
6:1 38.36
4:2 41.15
8:1 41.23
3:2 51.08

The only difference in order between the two charts is that 4:2 and 6:1 change positions. TuneLab also offers 8:2 double octaves and 6:4 fifths, but these were off the scale at C8.

Jeff

Please forgive the very naive question I'm about to ask.

Does nobody tune 6:3 octaves in the treble?

-- Robert

Only in the bass and midsection. Aurally the 6:3 tests become impractical after a point as one works up the scale, and in the case of ETDs I think there could be a problem tuning the high treble using the 3rd partial of an octave's top note.

Jeff

As a side note, if you silently hold down A 2 (with out playing it) and then firmly play A3 above it and let off so the damper makes it quiet, you will hear the second partial of A2 vibrate sympathetically. If you continue holding A2 and play E4 in the same staccato manner, you’ll hear the third partial of A2, and so on, hitting all the intervals Ron mentioned above. This is also a valuable way to check the bass section 6:3 octaves.

There’s an interesting article on “Ghost Tuning” in the PTG Journal from a few years back that would be worth doing a search for, if this concept interest you.

I never expected this short question will lead out so many answers, I learned much more than I can image. Thanks all

How practical for a ghost tuning? I mean the precision? Within how much errors can trigger a ghost sound reaction?

An example of the way I Ghost Tune C2 to C3 in the bass: While holding C2 and D#2, I play G4 and let up immediately, I hear the beats coming from 6th partial of C2 and the 5th partial of D#2. Both are approximately G4 in pitch. I then do the same while holding down D#2 and C3, listening to the 5th partial of D#2 as it beats against the 3rd partial of C3. Both are approximate G4 in pitch. When the beats from C2-D#2 waver at the same rate as D#2–C3, it is in tune with C3.

Hongzhi, tuning with ghost notes is very accurate, but it does take some time to learn. Often there is more than one set of beats happening, and you have to focus your hearing on the beats sounding at the proper frequency.

The ghost reaction can be set off if the partials involved are just in tune within a certain range of variance.

The natural partials of any single string aren't usually exactly in tune with their corresponding notes on the keyboard, partly because of the compromises involved in equal temperament (our system of twelve equally-spaced semi-tones). But ghost testing requires playing pure non-tempered partials together with notes that are tempered. The fact that the ghost reaction still occurs is proof that the partials don't have to be exactly in tune for the reaction to occur.

But that doesn't affect the accuracy of the test. Tuning this way with precision just depends on hearing the right set of beats and making sure the two test intervals produce beat rates of exactly the same speed.

Practically speaking, I think ghost testing on lesser-quality pianos can be be too time-consuming and not worth the effort. In the low bass of nicer pianos it can really help, particularly when other tests still leave doubt or don't work.

Of course ghost testing is an aural tuning technique. You may be interested to know that the same results can also be gotten electronically: The electronic alternative to the 6:3 test Dave described would be to first set TuneLab to G4. Then play C3, adjusting the temporary offset until the display stops. Then play C2, and tune that note until the display stops.

If any of the above is unclear, just say so and I'll try again.

These are nice things to experiment with when learning how the partial series is used in tuning.

Jeff

This is something I cannot understand. What does this mean? You cannot possibly mean that the first overtone of a fundamental on a Steinway D is an octave plus 31.64 cents, can you? That would be absurd!

No it certainly does not mean that. It means that if you adjust the tuning to produce beatless 2:1 octaves on that piano, then the cumulative effect of that stretch from A4 to A5, A5 to A6, A6 to A7, and A7 to C8 would make C8 31.64 cents higher than if you were using a no-stretch tuning all the way (440, 880, 1760, etc.).

Robert Scott
Ypsilanti, Michigan

That still does not make any sense. There is no way one would come up with a C8 that high based on any theory of inharmonicity that I know.

I also do not understand what is meant by "Average." Is that an average piano? Most of those numbers are smaller. Again, there is no way that an average piano is going to be purer than a concert grand.

I measured a digital piano once because it sounded like it had an unusual amount of stretch. C4 was near 0 cents deviation as I remember, by the time I hit C8 it was running around 30+ cents sharp. That is, I had to off set the dial by 30 some cents to stop the lights. I know digital is not a suitable example for this discussion, but the sample was an actual recording of a concert grand using that much stretch.

Hmmmm....

Here's the partial measurements for a single string A4 on a Baldwin studio.
1st partial 0.0 - 440hz
2nd partial 1.08 - (A5 fundamental 880hz + 1.08 cents)
3rd partial 3.51 -
4th partial 7.10 (A6 fundamental 1760 hz + 7.1 cents)
5th partial 11.7
6th partial 16.72
7th partial 23.52
8th partial 32.79 (A7 fundamental 3520hz + 32.79 cents)

So if you want to tune the A7 to "sound" in tune with the A4, where ya gonna put it?

Even if you take a very conservative route, here's where you will end up:

A4 set to 440 (measured second partial = 1.08)
A5 set to 1.08 (measured second partial is 7.1)
add 1.08 and 7.1 to get
A6 set to 8.18 (measured second partial 20.54)
add 8.18 and 20.54 to get
A7 set to 28.72

So even setting 2:1 octaves from the middle up brings us to an A7 setting of about 29 cents.

A lot of the older uprights need to have the top C set over 50 cents (from a strict mathematical doubling model) to get them in tune with the middle.

The only thing I can assume is that the measurements are wrong. There are too many people who can detect a quarter of a semi-tone difference.

It's tough when science gets in the way of our beliefs...

So the second partial of A 440 is 440*2*1.08 = 950.4, a bit higher than A# 932.32.

Yeah, sure!