and chords. The typical approach is to analyze
a passage (or less) of music and select tones
from a scale that will best approximate the
desired pure intervals.
• 19 Tone: This scale has greater purity
of minor thirds and major thirds (and
conversely, minor and major sixths)
than twelve-tone equal temperament.
A disadvantage is that perfect fifths are
narrower than those found in twelve-tone
equal temperament.
• 24 Tone: Also know as the quarter tone
scale, this scale is used for variety but has
no advantage in terms of ratios that better
approximate pure intervals.
• 31 Tone: In addition to intervals that better
approximate pure intervals, this scale also
contains good approximations to Indonesian
pelog and slendro scales.
• 53 Tone: Related mathematically to the
cycle of fifths, the 53-tone scale has very
pure major and minor thirds, and fifths and
fourths.
• Partch: Harry Partch is considered the
father of modern microtonality. This scale
was devised by him and used in instrument
building and performances.
• Carlos Alpha: Wendy Carlos performed
extensive computer analysis to devise a
number of equal tempered scales with good
approximations for the primary harmonic
intervals and their inversions. This scale is
good at approximating the primary intervals
including 7/4. This scale divides the octave
into 15.385 steps forming intervals of 78.0
cents.
• Carlos Beta: This scale divides the octave
into 18.809 steps forming intervals of 63.8
cents.
• Carlos Gamma: This scale achieves perfect
purity of the primary intervals 3/2, 4/3
and 5/4. This scale divides the octave into
34.188 steps forming intervals of 35.1 cents.
• Harmonic (chromatic): This twelve-tone
scale is created in the partials in the fifth
octave of the harmonic series. The scale
degrees that correspond to the classic just
intervals are the major second, major third,
perfect fifth and major seventh.
by tuning twelve pure perfect fifths upward
and adjusting the octaves downward. This
leads to some pure intervals and some very
impure intervals.
• Just (major chromatic): a twelve-tone scale.
Just intonation tunes the most frequently
used intervals to be pure (integer ratios in
frequency). These tunings depend on the
mode (major or minor) and the key. This
scale is tuned for major mode.
• Just (minor chromatic): (See Just (major
chromatic), above)
• Meantone chrom.: a twelve-tone scale. This
tuning is a combination of Pythagorean and
just tunings so that music in a wider variety
of keys could be usable.
• Werckmeister III chrom.: a twelve-tone
scale. This scale was a first attempt (about
Bach’s time) to allow an instrument to be
played in any scale. It was in response to
this scale that Bach wrote Well-Tempered
Clavier.
• Vallotti & Young chrom.: a twelve-tone scale.
Another derivative of the Pythagorean scale
designed to allow arbitrary keys.
• Barnes-Bach (chromatic): a twelve-tone
scale. A variation of the Vallotti & Young
scale designed to optimize the performance
of Bach’s Well-Tempered Clavier.
ETHNIC TUNINGS
• Indian: This 22 tone scale is used in India to
perform ragas.
• Slendro: This five-tone Indonesian scale is
played by ensembles called gamelans.
• Pelog: This seven-tone Indonesian scale is
more interesting than Slendro and is now
the primary scale in Balinese music.
• Arabic 1: This 17 tone scale is the original
Arabic scale adopted from the Pythagorean
scale.
• Arabic 2 (chromatic): This twelve-tone scale
is the modern version of the Arabic scale
popular in Arabic music today.
CONTEMPORARY TUNINGS
Equal tempered scales with a large number
of tones are typically used to play common
tonal harmony with greater purity of intervals
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