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Earlier this week I tuned my piano by using Tunelab for the temperament only. The rest I tuned by octaves.

Last night during playing I noticed a 12th strongly beating. On further investigation I found that there was no 12ths beating around and within the temperament notes but many 12ths were beating outside this area.

For an ET tuning what beating is normal for 12ths?

Ian

If your temperament was correct ET then it means that your octaves are too narrow. 12ths should range from almost beatless to beatless.

What you are experiencing is precisely why aural tuners should not tune using a single interval, but should check with a variety of intervals. If when you tuned by an octave you also checked the 12th at the same time and then compromised the two so that both sound virtually beatless, then you are on the right track.

If you cannot get both sounding more or less beatless then the temperament may not be equal enough. In that case you will have to expect some 12th beating, but to be as quiet as you can get it without an obvious beat in the octave.

Chris,

Your information was very helpful. Another little step for my aural tuning progress.

thanks,

Ian

Tuning like I said will produce a reasonable degree of stretch in the octave, and do it consistently.

You may find it difficult to tune 12ths because it is wider than a hand reach. It will be necessary for a hand to leave the lever and play a note together with the other hand. You can also use one hand and play the two notes of the interval separately with the sustain pedal engaged with a bit of practice. If the piano has a sostenuto you could utilise it the keep the lower note sustained.

I should mention also that there are other methods for tuning good and consistent octaves, but since you started looking at 12ths I though the method I mentioned would be a good start and good for training the ear to really listen to the quality of the wide intervals themselves which I think is crucial to fine tuning.

If only a few 12ths were beating, then the octaves you used to expand the temperament were not consistent, and/or the temperament was not equal enough. As Chris mentioned, the 12ths are fantastic for checking even expansion of the temperament. They are also great for controlling the amount of stretch. Expanding with only octaves can be challenging due to the immediate desire to have them sound pure, which is more of an area than a point. This can lead to both insufficient and inconsistent stretch.

Myself, I strive for pure 12ths and have a wooden spanner so that I can play them as I tune in the upper part of the treble. But since it is an interval I strive to be beatless, it really needs an RBI check.

The RBI check for a beatless 12th is the M6-M17 test. Example: to test the D3-A4 12th, the beating of the F2-D3 M6 should be the same as the F2-A4 12th. The same test note is used for the M3-M17 test for the double octave (P15). The beating of the F2-A2 M3 should be the same as the F2-A4 M17 for a beatless P15. Bill Bremmer suggests expanding the temperament by making a compromise between a narrow P12 and a wide P15 and calls it "Mindless Octaves".

This of course bring up the question of how you get from an octave temperament (or a 5th temperament...) to a stretch scheme using 12ths or 15ths. If octaves are slightly, consistently, carefully stretched but still without any obvious beating, pure or nearly pure 12ths will be the result and visa versa. Myself, I expand the temperament up to about the treble break by tuning as wide a 5th I can without having an obnoxious 4th. This results in nearly pure twelfths and slightly wide 15ths when the temperament is expanded that far. At about the treble break, it is difficult to continue to expand with 4ths and 5ths and so I switch to the spanner and tune pure 12ths, but still check them with the M6-M17 test. And while I am at it, I often check on the 15ths in case something is awry.

[Edit:] Since the natural result of expanding with optimun sounding 4ths and 5ths in nearly pure 12th (nothing is perfect...) convinces me that pure 12ths should be strived for. Also when analyzing what the result of the suggested octave for a proper stretch on various sized pianos (4:2/6:3 for large, 4:2 for medium and 2:1/4:2 for small) the result is also pure 12th. Some believe that extending 12ths into the top treble will result in some loss of resonance compared to 2:1 octave. This may be so, but I haven't noticed it.

The ET shouldn't affect how you tune 12ths. There is no 12th in the temperament octave.

I consider the pure 12th as one possible stretch "temperament", much like we have different temperament octaves, well temperament, ET, etc.

It is quite possible to have pure 12ths and good octaves. As well, pure 12ths produce pure 11ths and 22nds. If the temperament supports pure 6:3's, you can have pure 19ths as well. However the 15th will be a bit wide.

If you hear beating 12ths, they are just wrong.

Pure 12ths are easily and more accurately tuned using beat speeds. M6 = M17.

I can stretch to some 12ths but not others. I guess I would need to make a tool to play both whilst tuning.

Mark I'm not clear on the procedure to use when applying your "Pure 12ths are easily and more accurately tuned using beat speeds. M6 = M17"

Ian

When a temperament octave is narrow, it doesn't affect how the 12ths are tuned?

Pure 12ths (an octave and a 5th, 3:1 partial match) produce pure 11ths (an octave and a 4th, 8:3 partial match)?

My apologies if I am incorrect, but I hope you are not confusing a 10th (an octave plus a 3rd) with a 12th (an octave plus a 5th)?

Chris,

No apology necessary as your guess is correct. Such a simple but fundamental error on my part!

By way of apology I offer this link. It has enough deep information about intervals to keep most here busy for quite a while.

https://tinyurl.com/jcgsgo4

Ian

In that case, all of the 10th intervals will beat rapidly. In fact, they should gradually increase in speed if you play them chromatically upwards. That is a good test of even expansion if the temperament is a good ET.

Good catch, Chris. When I read Ian saying "I can stretch to some 12ths but not others." I thought he meant stretching some 12ths to be pure, but not others, due to the octave growing too wide, I suppose.

Considering that you meant 10ths instead of 12ths, do you still want me to explain the pure 12th test?

Have I correctly edited your OP?

All the 10ths beat. Is it possible that you were not able to hear the beating 10ths around the temperament?

Also, there is no 10th in the temperament octave. I assume you meant "near" the temperament octave, instead of within?

I would appreciate if you could please Mark ?

So all that time you were talking about M10ths?

How can you confuse a rapid beating interval with a slow beating interval? All what you said about P12ths makes sense but if you were talking about M10ths it makes no sense at all.

It wouldn't be a bad idea for you to hire a tuning teacher at least to learn the fundamentals, don't you think?

I would be a little more charitable and believe that the mistake was in the numerical description of the interval, rather than the interval itself.

BDB, I don't think so.




As it is this makes perfect sense, as 12ths are not supposed to "strongly beat". But if you replace 12ths by M10ths in his phrase, it makes no sense at all.

No beating M10ths within the temperament but many beating outside?

M10ths are supposed to be beating everywhere in the piano's scale.

I doubt he was talking about M10ths and if he was then he has no idea of the fundamentals of tuning.

Mark,

When I said that Chris guessed correctly it was because I was trying to apply a test without analysing its principle. I had never before read about using a 12th so I should have stopped and realised that it was 3:2 near beatless test (or should I have said 3:1?)

I don't know why I incorrectly started testing 10ths for beatless but its something I would rather forget.

My piano does not have a sostenuto so I guess I will need a helper to tune using 12ths.

Ian