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Hi all, I'm currently working on setting the temperament aurally, I have a 5'3" yamaha, and I've been working on C3-B3.

Came across something strange and did not know what to do

The C3 is a copper winding bass string, does that affect the beating speed in relation to the treble strings? Because when I first tuned the whole octave to tune lab, I went ahead and listened to the 3rd, 4th, 5th, 6th. it seems like the beating speed is always out of sequence when comparing to the neighboring intervals (usually faster than it should be).

Should I trust tune lab or should I trust my ears? This is to get ready for the RPT exam.
Thanks!

That's a normal occurrence at the change from plain to wrapped strings, because there's usually (always?) a change in inharmonicity between the two. This means that only some, not all, of your tests will be able to have a smooth progression.

You need to trust your ear - keep in mind the master tuning you are graded against is determined aurally - but since not all tests will agree you have to understand which ones are more important. For C3 that's going to be your 4th, 5th, and octave (check both the 2:4 and 6:3 octaves).

Also, are you planning to use C3-B3 as your temperament octave? If so that's unusually low, and will surely cause you problems if your practice piano has a break there. You really want to keep your temperament on the plain strings (granted on spinets this is sometimes not practical).

Edit: if any of the terminology I'm using doesn't make sense don't hesitate to ask...

I use beat speed windows. The trade off is the octave may suffer but the benefit is pure 11/12/22 and maybe 19.

Using a 4/5/8 criteria is too limited for me because I want the big chords to sound in tune. I.e the 4/5/8 might not be offensive but the 12/22 could be awful.

Here's how I would tune C3. (You have to tune the whole piano like this for it to work)

G#3C4 <= G#3C5 < G#3C6 = G#3F4 = C3G#3
M3 <= M10 < M17 = M6 = m6 down

This window sets all these intervals and/or confirms their size. Very powerful because pitch is always sliding around on the piano and in this way, I catch a lot of drifters.

M3 <= M10 (pure or wide 4:2, whatever fits)
M10 < M17 (wide 2:1)
M17 = M6 (pure 12th)
M6 = m6 down (pure 11th)
M10 = m6 down (pure 22nd triple octave)
M3 < M17 (wide 4:1 double octave)
M10 < M6 (narrow fifth)
M17 = m6 down (pure 22 triple octave)
M3 < M6 (wide fourth)
M10 < m6 down (narrow 8:2 double octave)
M3 < m6 down (narrow 8:4)

If the octave also tests as a pure 6:3, possible on many pianos (within aural limits) you can also have a pure 19th.

Hmm the thing is on the exam, you tune C3-B4 as a section, then that is scored before you proceed. So C6 isn't going to be available; technically C5 won't either although I suppose you could go ahead and tune it...

Oh and just to be clear, when I say to do the 4:2 and 6:3 octave checks, I mean the fast beating ones, i.e. g#2c3 to g#2c4 and c3d#3 to d#3c4. You do of course have to rough in g#2 for that to work.

Yes, but you still have the "Little Window"; M3 <= M6 = m6 down. That "sets up" the eventual larger window for all those pure intervals. I just love tuning this way. It is like I am imagining what I want the piano to sound like, what intervals will be in tune and then work backwards from that.

I'm having a hard time puzzling out how one could tune equal temperament with both pure 11ths and pure 12ths... Wouldn't an 11th (octave + 4th) fundamentally have to be wider than a 12th (octave + 5th)?

EDIT: Oh, I think I get it. The pure 11th is lower than the pure 12th -- you're tapering from wider intervals in the bass to narrower ones in the treble, as most tunings do?

At any rate,





I have no doubt this produces a beautiful, musically useful tuning. But I must stress that compromising the octaves will probably cost you points on the tuning exam. They're looking for clean sounding octaves in the midrange, usually right around pure at the 4:2 level, perhaps a little wider toward the bottom -- but definitely no wider than 6:3 anywhere, even in the bass! They're not doing this as a statement against compromising the octaves to make other intervals sound better, it's just a way of keeping the exam objective. If any CTEs are reading, perhaps you can chime in on this?

Wow this is a lot of information to chew on, I truly appreciate all the inputs, I'm going to experiment On the suggested tunings here, very excited!

Perhaps we could summarise by saying that you should try to trust your ears, but be aware that M3rd, M6th and M10th progressions through the area of the piano that you are proposing for the temperament may not be progressive due to the inharmonicity changes associated with different string types and the break. For this reason it is better to restrict the temperament area to plain steel strings in which even progression will then be an indicator of a good equal temperament. As Nathan said, the priority is to ensure clean sounding octaves as you expand.

Ascc, you came across something I think is very important, rarely talked about and misunderstood: How does the bass/tenor scaling break affect the beatrates of the tuning intervals? If a reasonable octave is used on a typical piano, you can expect the M3s and M6s that straddle the break to beat faster than the ones wholly above and below the break, while the m3s and m6s will be slower.

Consider the iH curve on this Ludwig 5' grand, which is typical:



Notice how the lowest strings of the tenor have a higher iH? This means their upper partials will also be much higher resulting in slower M3s and M6s above the break and faster M3s across the break.

Now consider the iH on this Wurlitzer 4'10" grand, which is not typical (Btw, tuning one of these is a memorable experience...):



Here the upper strings of the bass have a higher iH than the lowest part of the tenor. With reasonable octaves, you can expect the M3s and M6s across the break to be slower than the ones wholly below the break.

So here is the thing to remember. You can't expect a smooth progression of RBIs across a scaling break. It is best to set the temperament wholly above the break, for that matter, don't use the bottom two notes above the break.

If this makes the RBIs in the temperament octave beat too fast to be able to discern, consider tuning the temperament within just a tempered fifth then expand this upward with 4ths and 5ths. There may be errors that will need to be corrected as further checks are made, but that can be expected regardless of the temperament octave.

Thanks Jeff, I think those kinds of charts are the best way to understand what's going on at the break.

By the way, exam pianos have to meet pretty tight requirements designed to keep these factors to a minimum. For ex. I'm fairly sure they have to have all plain strings in the mid section. So ironically the exam pianos are usually much better behaved than the ones we practice on

Not only better than the ones we practice on, but better than the vast majority of pianos that are tuned! So is the purpose of the test to show proficiency or to gain credentials? (I took and passed my exam before ETDs were invented, but even then found little use for the credential and let my membership expire.)

Jeff, you have no idea how those charts solved one of the most confusing thing thats been bothering me: how is it that sometimes I'm tuning a spinet piano according to tune lab, the lower octaves still sound terrible even if tune lab says its in tune (yes I do measure the inharmonicity before I start). much appreciated

The point of using a good piano is to keep the exam as fair and objective as possible. Uneven scaling certainly makes a piano harder to tune, but it also makes it harder to prove that the examinee made an error! The idea is to show proficiency by pricing you can control what you're doing.

Disclaimer: I'm just speaking from personal experience and what I've read. I'm not a tuning examiner.

Ah, well, lower octaves on a spinet. Can I suggest that you tune the first string of each bichord to both the 5th and the 8th above, like G2 to D3 and G3, playing all three notes at once? Listen for the best resonance. The partials tend to be all over the place and so specific octaves and their tests can be a shot in the dark. For the single strings, just aurally tune the octave best you can.

So if I'm just practicing for setting the temperament of c3-b4 not worrying about the rest of the Piano yet, should I just try to have w/e option that gives the cleaner octave?

A clean octave is a subjective thing, and with a would string sometimes you can only go for a less bad, rather than a more good, option. See, with an octave there are many audible partial matches, and it can be hard to decide what sounds clean, especially across a break.

Myself, because I am a 4ths and 5ths tuner, I strive to make those intervals sound good and consistent. If the result is a bad octave, then I know there is a tuning error somewhere.

But, hey, if you are just practicing, why not tune C#3-C5?

Dear ascc,
You have a great opportunity to expand your understanding of relative inharmonicity!
I'm assuming that C#3 is a plain wire string. If not, transpose my suggestion to the first adjacent wound and plainwire notes.

Wedging off unisons so you have one open string of C3 and one of C#3, try to tune them as a unison (tune C# down to C.)

Now the inharmonicity of the plain wire will be much higher, relative to the wound string. You will not get a clean unison. You will be able to chase beats up and down the partial series, but only one pair will be beatless. As you do this, try aural test intervals, comparing the beat speeds between the two strings. The results should show you that the frequency differences between the partials of the plain wire are greater than the comparable differences on the wound string.
You can also try tuning various intervals from the two strings as C3, octaves, fifths, thirds, etc., to see how the greater relative inharmonicity influences the tuning.
No end to this quest! Have fun! You will understand a lot more about tuning when you're done.
Ed Sutton

Ohhhh I totally misread the exam notes, i thought they want us to tune c3 to b4, but it's actually any 13 consecutive notes within that range of keys... I think I'll try either d3-d4 or f3-f4 and avoid the wound strings


Do you all think it's safe to reference TuneLab as a "master tuning" when I'm checking my temperament?


Ed, yes! as of right now it feels like a headache but I'm sure it will be very rewarding at the end. To actually UNDERSTAND the tuning rather than just following what's on the acreen

Well, you tune the entire midrange (c3-b4) in one uninterrupted block of time. However, the temperament octave is scored separately from the rest of the midrange. You get to specify which octave you want scored as your temperament -- if I remember right the temperament notes end up counting for more as far as your overall score goes. You don't even have to decide until after you're done tuning the midrange, so you're allowed to pick a section outside of your original temperament octave if you think you really nailed it.

My personal suggestion would be to settle on the temperament octave you're going to use long before you take the exam and have all your checks nailed down. IMO trying to game it by picking which section you did best after the fact is going to be a problematic distraction.



In my personal experience, no! I actually was doing this for a while when I was preparing, and came to find out (after reviewing my tunings with RPT's in my chapter) that my ear was closer to the exam spec than TuneLab's calculated octaves. Again, that's not a judgment about which tuning is "better" (personally I think they both have their own merits). It may be possible to fiddle with the octave sizes in the TuneLab settings to get you closer to an exam tuning, but in my experience that was an uphill battle. I did however find TuneLab very useful for checking the evenness of my tuning.