Piano World Home Page Forums Our Most Popular Forums Piano Tuner-Technicians Forum A question about twelths

Ian, I think "too many cooks are spoiling the broth". I am going to drop out. I suggest you pay attention to what Chris has to say the most. He knows the subject thoroughly, communicates well, and has no other agenda that trying to help you understand.

3:2 is a P5

3:1 is a P12



I don't remember anything about that ;-)



No. You can use two hands to judge the quality but you won't know which way to tune a note is the P12 beats.

You can use the P12 test that someone already mentioned and I did too.

I will reply to another post where someone asked me to explain it.

Let's test the F3C5 P12

Here are the partials. (You need to understand the Harmonic Series - See here: http://howtotunepianos.com/podcast-6/)

F3:F3-F4-C5
C5:C5

So when playing F3C5, the C5 is common.

We say that C5 is the coincidental partial.

I will use F3(C5) to mean the frequency of the C5 partial that belongs to F3.

So, if F3(C5) = C5(C5) then each partial frequency is the same, and there will be no beating at C5. We say F3C5 is pure.

<> "means does not equal"

But, if F3(C5) <> C5(C5), then there will be beating at C5. F3C5 may be wide or narrow, we don't know.

We use G#2 to test.

Here is the partial series above G#2.

G#2:G#2-G#3-D#4-G#4-C5

So, we see that G#2 has a partial equal to C5 as well.

We tune G#2 flat so that it produces beats with F3 and C5.

The speed of the beats tells us how sharp F3(C5) and C5(C5) are from G#2(C5).

If they are both sharp of G#2(C5) by the same amount, then they are equal to each other.

Think of it like this: If I am 10 feet ahead of you on a sidewalk, and my friend is also 10 feet ahead of you on that same sidewalk, then my friend and I are beside each other.

So, when I play G#2F3 and G#2C5, I know that

G#2F3 and G#2C5 are beating because

F3(C5) is above G#2(C5) and

C5(C5) is also above G#2(C5).

But, if G#2F3 = G#2C5 then

F3(C5) and C5(C5) are both above G#2(C5) by the same amount, meaning F3C5 is pure.

If G#2F3 <> G#2C5, then whichever is faster, is sharper. [Remember Faster = Sharper]

If G#2F3 is faster, then

F3 is sharper,

and bottom sharper means F3C5 is narrow.

If G#2C5 is faster, then

C5 is sharper,

and top sharper means F3C5 is wide.

(I usually stick to the Faster=Sharper rule to make analysis simpler, although Slower=Lower works as well.)

So, now knowing that a non-pure P12 F3C5 is wide or narrow, and assuming you wanted to make it pure, just do the following:

To make a non-pure interval pure:
Narrow? Raise top or lower bottom.
Wide? Lower top or raise bottom

F3C5 narrow? Raise C5 or lower F3.

F3C5 wide? Lower C5 or raise F3.

That's all the theory. Now the next step is to get to a piano and practice.

Hearing the beats clearly is the key. Here's a post where I give you some tricks to do just that:
http://howtotunepianos.com/2014/04/14/how-to-hear-beats-when-tuning/

Have fun!

Mark,

I appreciate the detailed reply you gave me. Just now I am working through your podcasts so that I have not missed something fundamental.

I see how the G#2 fits being the 6th partial but it is not obvious to me how you knew to choose this particular partial?

Ian

Very good question.

Here is how you find the check note. (The G#2 in the F3C5 P12, for example, is the P12 check note for the F3C5 P12)

Just go down two octaves and a M3 from the coincidental partial.

Any slow beating interval (P4, P5, P8, and their compounds - compounds being P8+P4, P8+P5, P15, P15+P4, etc, ) will have a coincidental partial, maybe even two. And the note two octaves and a M3 below that coincidental partial can be used as I explained, if you set it flat so that is produces reasonable beats with each interval note.

When I tune I listen to the octave, 12th and double octave and make them all sound as pure as I can get them. This makes the piano sound very clean and clear.

I use more intervals than that.

Mark,

Understood.

thanks,

Ian