Tuning Beatless Octaves

Words in italics are subjects you need to know in order to understand this article.

When tuning a piano by ear, one of the first steps is to tune a clean octave. For example, after tuning A4 from the fork or sound source, many methods advocate tuning A3 by tuning the A3A4 octave as clean as possible. Many methods do not really say how to do that other than “make it clean”.

Some methods advocate tuning a pure 4:2. Some say tune a wide 4:2/narrow 6:3. The problem with these methods is that they do not always produce the best sounding octave due to the different inharmonicity of different pianos.

We need a method that allows us to measure the inharmonicity of a specific piano. That would allow us to know which octave size sounds best for that piano.

The following flow chart shows you how to tune the first octaves of a temperament when you do not have any other criteria other than “make it sound as clean and pure as possible with itself.”


Because of the different 6:3 octave sizes associated with each octave, each octave proves a different m3/M3 equality and that equality is listed below the octave scale size.

2 Responses to “Tuning Beatless Octaves”

  1. Cobrun Sells says:

    I brought this up in an email before, but I still believe this is another obstacle for me. I tuned my own Baldwin Hamilton 45″ console vertical piano. After using your “Tuning a beatless Octave” chart above I deemed my piano a Large Scale Octave piano. So, I first tuned A3A4 to a Pure 4:2 octave…it didn’t sound good because there was rough beating at the 6:3 partial. So, I tuned A3A4 to a “wide 4:2/narrow 6:3.” This means that 4:2 and 6:3 were beating slightly, but neither sounded good enough (both still beated roughly). So, I “tuned BACK to a pure 4:2.” Let me reiterate…A3A4 octave started small…went big…went BACK to small. This means 4:2 is pure just like the Small Scale Octave, but the 6:3 is beating horribly. Now, since you do indicate in your chart to “tune BACK to a pure 4:2” this to me means that you want me to tune the octave small once again so that the 4:2 is pure. But, doesn’t this mean that the entire temperament will be compromised? Since there is large inharmonicity in the temperament register of the piano (the evidence being the Large Scale Octave) the intervals will want more space within one octave to “breath.” But, because I LESSENED the size of the A3A4 octave (and the F3F4 octave) by “tuning BACK to a pure 4:2” (just like the Small Scale Octave) we give less room for the largely inharmonic notes within the temperament octave leaving room for at least one interval to beat horribly in comparison to the others. So…what are your thoughts? Am I not following the chart correctly? When you say “tune BACK to a pure 4:2” are you really wanting me to INCREASE the size of the A3A4 octave even more so that 6:3 is more pure or DECREASE the size of the A3A4 octave so the 4:2 is more pure? Let me know. Thanks.

    • First, you can’t tune a small scale octave. The terms Small, Medium, and Large, are terms I defined to indicate the amount of beating at the 6:3 when tuning a pure 4:2. It is an indication of the scale inharmonicity of that particular piano in that particular section of the piano.

      Each piano, and octave, may have a different scale, but that can’t be changed without changing strings.

      So, let me get this straight.

      You tuned a pure 4:2, checked the 6:3, found a huge difference between the m3 and the M6, assumed it was a Large Scale Octave, but hated the sound. I.e. Didn’t like the fast beating 6:3. Then tried a wide 4:2/narrow 6:3 and that didn’t sound any better.

      Here are some possible descriptions of the problem:

      1) The pure 4:2 is the best for that piano but you are not accustomed to the sound of a pure 4:2 on that style of piano. Perhaps focus your ear more on the clean sound of the 4:2 and attribute the beating 6:3 as the “tone” of the octave, much like we attribute beating M3 and M6 as having a specific piano style tone.

      2) This piano may not fall into small, medium, or large. Some pianos sound better as a pure 2:1, narrow 4:2. Try tuning the octave directly, without checks. Just listen to A3A4 and tune A3 until it sounds as pure as possible. Then check the 2:1, 4:2, and 6:3 for size. Based on the size of the 6:3, you can make some assumptions about what m3/M3 equality may fit.

      I hope that helps.

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