Apple Logic Pro X - Manual (Page 887)

Chapter 25 Preferences, project settings, and key commands 887
The comma and equal temperament
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
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.
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.