Beat Speed Difference Ratio Test

Tuning the Skeleton F3A3C#4F4A4

Tuning the Skeleton F3A3C#4F4A4

When tuning contiguous major thirds - that is, major thirds that share a note, easily imagined as an augmented chord such as F3A3C#4 for example - the beat speeds of these thirds in equal temperament change about 26% from one interval to the next (when no inharmonicity is considered.).

The Skeleton (See HERE) is a method I teach that requires the tuner to tune one beat speed exactly between two other beat speeds.

Exactly between means so that the beat speed ratios are the same. For example, 10, 11, and 12 are not even because 10 to 11 is 10%, but 11 to 12 is 9.1%. The correct beat speed progression would be 10, 10.95(9.5%), and 12(9.5%).

The steps for tuning accurate skeleton notes - F3, A3, C#4, F4, and A4 - are:

1) Tune A4
2) Tune A3A4 beatless
3) Tune F3A3 about 7bps
4) Tune F3F4 beatless
5) Tune C#4 so that F3A3, A3C#4, and C#4F4 all change speed by the same amount.

That means the speeds work out to:
F3A3 - A3C#4 - C#4F4

In each case above, the change in beat speed from F3A3 to A3C#4 equals the change in beat speed from A3C#4 to C#4F4.
I.e. SLOW - MEDIUM is the same increase as MEDIUM to FAST.
VERY FAST to MEDIUM is the same decrease as MEDIUM to VERY SLOW.

Notice that A3C#4 is always MEDIUM.
Since A3 is never touched, then C#4 is always at the same pitch if we preserve that the changes in beat speeds are constant.

Also, understand that the pitch of F3 determines which situation we end up with (FAST - MEDIUM - SLOW, or whatever).
We cannot force a beat speed progression onto the lower skeleton.

The hard part is tuning the C#4 so that each pair of M3's changes by the same amount, exactly.

Many technicians deride this method but that is because they are not being picky enough when tuning that first C#4.

The test below has F and A octaves tuned so that they will produce a SLOW F3A3, MEDIUM A3C#4, and FAST C#4F4, when C#4 is tuned correctly.

Each M3 pair must increase in speed by about 22%, in this case.

Tune the C#4 so that each M3 pair increases by the same ratio, 22%.
(22% is not audible. You just have to compare each M3 pair and judge that they change by the same amount.)

Click the SCORE button when you are done and see how close you got.

Have Fun!


The waveforms take time to load into your cache.
You may have to play them a second time
so that both notes sound at the same time.

Each time C#4 is changed, A3C#4 will play at the new speed.

Remember, because of the way F3 was set in this test, each M3 must increase in speed.

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4 Responses to “Beat Speed Difference Ratio Test”

  1. Tommy black says:

    Difficult for me to make the 3rds sound together. I guess I wasn’t sure how to use the system.

  2. Michael says:

    Hello Mark – You start to explain OK but then take such a long time to get the message across that I lost you. Many years ago I published a tuning system similar to yours on the PTG. You’ll find it under the subject of ‘Pitch Raising’ and my ‘system is called ‘Quadrant’ tuning. However whereas your ‘skeleton’ only takes in the M3’s of one of my ‘Quadrants’ my system shows how to extend into the four ‘Quadrants’ which together will set the bearings for all the notes within a ’10th’ – which is, of course, the natural extension using an M3 base.
    Good luck!
    Michael UK

  3. ray says:

    you’re running a brilliant website

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