Tuning Settings

About Alternate Tunings

The 12 tone scale used in Western music is a development that took centuries. Hidden in between those 12 notes are a number of other microtones—different frequency intervals between tones.

To explain, by looking at the harmonic series:  Imagine that you have a starting (or fundamental) frequency of 100 Hz (100 vibrations per second). The first harmonic is double that, or 200 Hz. The second harmonic is found at 300 Hz, the third at 400 Hz, and so on. Musically speaking, when the frequency doubles, pitch increases by exactly one octave (in the 12 tone system). The second harmonic (300 Hz) is exactly one octave—and a pure fifth—higher than the fundamental frequency (100 Hz).

From this, you could assume that tuning an instrument so that each fifth is pure would be the way to go. In doing so, you would expect a perfectly tuned scale, as you worked your way from C through to the C above or below.

To simplify this example:  Imagine that you are tuning an instrument, beginning with a note called C at a frequency of 100 Hz. (A real C would be closer to 130 Hz.) The first fifth would be tuned by adjusting the pitch until a completely clear tone was produced, with no beats. (Beats are cyclic modulations in the tone.) This would result in a G at exactly 150 Hz, and is derived from the following calculation:

• The fundamental (100 Hz) x 3 (= 300 Hz for the second harmonic).

• Divided by 2 (to drop it back into the same octave as your starting pitch).

This frequency relationship is often expressed as a ratio of 3:2.

For the rest of the scale:  Tune the next fifth up:  150 x 3 = 450. Divide this by 2 to get 225 (which is more than an octave above the starting pitch, so you need to drop it another octave to 112.5).

The following table provides a summary of the various calculations.

As you can see from the table above, there’s a problem.

Although the laws of physics dictate that the octave above C (100 Hz) is C (at 200 Hz), the practical exercise of a (C to C) circle of perfectly tuned fifths results in a C at 202.7287 Hz. This is not a mathematical error. If this were a real instrument, the results would be clear.

To work around the problem, you need to choose between the following options:

• Each fifth is perfectly tuned, with octaves out of tune.

• Each octave is perfectly tuned, with the final fifth (F to C) out of tune.

Detuned octaves are more noticeable to the ears, so your choice should be obvious.

The Comma

The difference between a perfectly tuned octave and the octave resulting from a tuned circle of fifths is known as the comma.

Over the centuries, numerous approaches have been tried to solve this mystery, resulting in a range of scales (before arriving at equal temperament—the 12 tone scale).

Other historical temperaments that have been devised emphasize different aspects of harmonic quality. Each compromises in some way or another. Some maximize pure thirds (Mean Tone) while others emphasize pure fifths at the expense of the thirds (Kirnberger III, for example).

Every temperament has its own character, and a given piece of music may sound fine in one key but awful in another. Transposing a piece to a new key can completely change its character.

Careful attention must be paid to the selection of temperaments for authentic performances of historic keyboard music. The wrong choice could result in an unsatisfactory and historically inaccurate musical experience.

About Equal Temperament

Equal temperament takes the tuning error (the comma), and spreads it equally between each step of a chromatic scale. The result is actually a scale of equally mistuned intervals, with no interval grossly out of tune, but none in perfect tune. Equal temperament has become the de facto standard for two main reasons:

• Convenience: Retuning an instrument to a temperament that is better-suited for a particular piece of music is a hassle. Many instruments are not capable of being alternately tuned (fretted string instruments, for example).
• Portability: All Western musical pieces can be performed (adequately) on an instrument tuned to equal temperament. Obviously, some of the nuances may be missing in pieces that were originally performed in another temperament.

What Is Hermode Tuning?

Hermode Tuning automatically controls the tuning of electronic keyboard instruments (or the Logic Pro software instruments) during a musical performance.

In order to create clear frequencies for every fifth and third interval in all possible chord and interval progressions, a keyboard instrument would require far more than 12 keys per octave.

Hermode Tuning can help with this problem:  it retains the pitch relationship between keys and notes, while correcting the individual notes of electronic instruments, ensuring a high degree of tonal purity. This process makes up to 50 finely graded frequencies available per note, while retaining compatibility with the fixed tuning system of 12 notes per octave.

How Hermode Tuning Works

Frequency correction takes place on the basis of analyzed chord structures.

The positions of individual notes in each chord are analyzed, and the sum of each note’s distance to the tempered tuning scale is zeroed. In critical cases, different compensation functions help to minimize the degree of retuning, at the expense of absolute purity, if necessary.

For example:

• The notes C, E, and G form a C Major chord.

• To harmonically tune these, the third (the E) needs to be tuned 14 cents higher (a cent is 1/100th of a tempered semitone) and the fifth (the G), needs to be 2 cents higher.

It should be noted that Hermode Tuning is dynamic, not static. It is continuously adjusted in accordance with the musical content. This is done because, as an alternative to tempered, or normal, tuning, fifth and third intervals can also be tuned to ideal frequency ratios:  the fifth to a ratio of 3:2, the major third to 5:4. Major triads will then sound strong.

With clean (scaled) tuning, Hermode Tuning changes the frequencies to values that are partly higher or partly lower.