Beat Speed Difference Ratio Test

Contiguous Major Thirds/M3's Skeleton Test

Contiguous Major Thirds/M3's Skeleton Test

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 to the other (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%).


1. Tune C#4 so that F3A3/A3C#4 and C#4F4 all change speed evenly, i.e. make the beat speeds increase or decrease by the same ratio.
(This is the first step in tuning the Skeleton, called the Lower Skeleton.)

Note: 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.

Click the TEST RESULTS link below the test to see the answers.

Your C#4 number:


Please send me your comments.

What was your C#4 number?

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P.S. When you click [Email the Results], your computer's email program will open and you will see the text of the email you are about to send.
If you primarily use an internet email service like hotmail or gmail, you can just copy the text from your computer's email program, and paste it into your internet email's webpage and send the email to mark at

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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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