10.6

1051Logic Pro User Guide
As you can see from the table, 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. As a workaround, 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 and equal temperament in Logic Pro
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.
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.
Hermode Tuning in Logic Pro
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.