Posted by: Mark Davis

## Clean Sounding/Beatless Octaves - 12/22/12 04:46 AM

Bill Bremmer has written,

"Tuning the various Types of Octaves

Now, to achieve the optimum compromise between a 4:2 and 6:3 octave, sharpen the A3 very slightly so that neither check for a 6:3 or a 4:2 octave tests perfectly. In other words, the test for a 4:2 octave should reveal a slightly faster F3-A4 M10 than F3-A3 M3 and the test for a 6:3 octave should reveal a slightly slower C4-A4 M6 than A3-C4 m3. When you have found the spot for A3 which reveals this slight discrepancy between the 4:2 and 6:3 tests, you will hear that the A3-A4 octave has a very slow beat to it, about one beat in every two seconds. This is now considered the optimum width for the initial A3-A4 octave in Equal Temperament and what is used by

most CTE’s to set up the Master Tuning for the Tuning Exam.

It is also the equivalent to within a very small and negligible degree of a 4:2 octave plus one cent. This is the width of octave that Dr. Al Sanderson used to obtain the amount of stretch needed for optimal piano tuning when he created the calculation for his Electronic Tuning Device, the Sanderson Accu-Tuner. In this kind of compromise, note that none of the coincident partials are in tune or match exactly with each other. This may also be an example of the whole octave sound of which Virgil Smith often speaks. This, almost but not quite perfect tuning, is an example of the kind of compromise which is necessary to defeat the problem and challenge of inharmonicity, the way to achieve the finest tuning possible from the modern piano, throughout its entire range."

Now clearly a 4:2+ octave has a slight/slow beat to it. Either the 4:2+ octave has a beat or it does not have a beat, it is either beatless or it is beating, however slowly. In other words, it sounds or does not sound beatless!

I am saying that the 4:2+ octave does not sound beatless and that one definitely hear a slight swell/beat in it. Basically, it sounds like a slightly narrowed/tempered P5.

So that is why I am saying that it is the 4:2 octave which actually is the beatless octave in the middle of the piano. Please take note that I am not speaking about the so-called "optimal place of the octave", though surely this too is a moot point amongst tuners.

"Tuning the various Types of Octaves

Now, to achieve the optimum compromise between a 4:2 and 6:3 octave, sharpen the A3 very slightly so that neither check for a 6:3 or a 4:2 octave tests perfectly. In other words, the test for a 4:2 octave should reveal a slightly faster F3-A4 M10 than F3-A3 M3 and the test for a 6:3 octave should reveal a slightly slower C4-A4 M6 than A3-C4 m3. When you have found the spot for A3 which reveals this slight discrepancy between the 4:2 and 6:3 tests, you will hear that the A3-A4 octave has a very slow beat to it, about one beat in every two seconds. This is now considered the optimum width for the initial A3-A4 octave in Equal Temperament and what is used by

most CTE’s to set up the Master Tuning for the Tuning Exam.

It is also the equivalent to within a very small and negligible degree of a 4:2 octave plus one cent. This is the width of octave that Dr. Al Sanderson used to obtain the amount of stretch needed for optimal piano tuning when he created the calculation for his Electronic Tuning Device, the Sanderson Accu-Tuner. In this kind of compromise, note that none of the coincident partials are in tune or match exactly with each other. This may also be an example of the whole octave sound of which Virgil Smith often speaks. This, almost but not quite perfect tuning, is an example of the kind of compromise which is necessary to defeat the problem and challenge of inharmonicity, the way to achieve the finest tuning possible from the modern piano, throughout its entire range."

Now clearly a 4:2+ octave has a slight/slow beat to it. Either the 4:2+ octave has a beat or it does not have a beat, it is either beatless or it is beating, however slowly. In other words, it sounds or does not sound beatless!

I am saying that the 4:2+ octave does not sound beatless and that one definitely hear a slight swell/beat in it. Basically, it sounds like a slightly narrowed/tempered P5.

So that is why I am saying that it is the 4:2 octave which actually is the beatless octave in the middle of the piano. Please take note that I am not speaking about the so-called "optimal place of the octave", though surely this too is a moot point amongst tuners.