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The Learning
Pyramid
Visual Music SoundScenes' great strength
is its flexibility. It can be just as useful for a musical beginner
as it can to some who has studied music for decades. We use the metaphor
of a pyramid in a desert to describe ViMS' flexibility advantage
The ViMS Learning Pyramid
'Vox clamanti in
deserto'
(A voice crying in the wilderness)
The four faces of the pyramid represent "Performance," "Theory," (the
two shown above on the two visible faces of the pyramid), Musical
Creation, and Musical Education (the latter two being hidden on the
back side of the above pyramid).
There are also four levels of attainment
in music, as shown in the above illustration of a pyramid on its
surrounding desert. The lowest level belongs to the "Uninitiated," who
live without music on the desert; the second level, at the bottom
of the pyramid, is for beginners, who learn here the fundamental
elements of music; the next level up is for "Intermediates," who
learn to apply the principles learned in the first level to performance,
theory, creation or education--or to any combination of these. The
top level is for experts, who will soon graduate from the pyramid
entirely.
The four levels are as follows:
Musical Learning: A.S.S.U.M.E. [The Art, Skill
and Science of Understanding Music Easily].
(Instruct reader on use of hypertext links to read essays)
The Principal Elements of
Music
In the beginning, musical learning proceeds
as a purely aural experience. Only as the basic concepts begin to
form in the listener's mind through careful listening practice does
the musical masterpiece become an aesthetic, and, eventually, an
intellectual, or cognitive experience. Initially, the beginner
responds to musical rhythms and melodies as sequences of individual
sounds in patterns that make sense.
Rhythmic pulses, recognized simply
as varying durations and accentuations of sounds, seem to require
least training, perhaps because rhythms are a familiar part of every
day life. Heart beats, breathing, walking, talking, time-telling--all
these and many more daily activities involve rhythmic patterns we
live with. This is fortunate, for rhythm is the philsopher's elan
vital of music-- a force that moulds even the basic frequencies
of the individual tones that make up melodies and harmonies. For
practicing listeners who seek continuing growth in musical understanding,
this ease is doubly fortunate, for rhythmic patterns serve as clear
mnemonic labels by which to quickly recognize motives, subjects and
themes essential to the understanding of musical forms and formulas. Ability
to recognize these marks a vital set of skills for understanding
musical masterpieces, such as those which make up the repertoire
of Visible Music SoundScapes. Without this ability, the dramatic
significance of such great forms as 'Sonata Allegro,' 'Concerto Allegro,'
'Rondo,' 'Sonata Rondo,' 'Theme and Variations,' etc., will
be lost upon the listener. oIn short, musical forms are very
important to the art of listening.
However, for the beginner, the concept
of musical form establishes a difficult conceptual barrier. How
can music, the invidible art, have form, which is a visible entity?
Actually, musical form is a figment of human musical memory, both
for the creater and for the listener. Thus the term musical
form can have no meaning for the novice until such time as his musical
learning has progressed sufficiently to enable his or her musical
memory to recognize formal elements. To recognize form, the
listener must have achieved sufficient ability to parse the music
being heard, to identify recurrence, whether specific, varied, or
even quite vague. Visible Music SoundScapes really aid this
process by making vivid all the main actions of music, such as rhythmic
patterning, melodic, harmonic, and tonal progressions, and
such advanced concepts as thematic transformation, motivic disintegration,
etc. Once the learner has made progress with recognizing rhythmic
patterns,m as described above, he or she is ready to develop more
advanced skills in musical intuition.
Recognizing the patterns of melodic sequences
is the next skill in order of difficulty for developing musical awareness. For
the rare individual blessed with 'perfect pitch' such recognition
is made easy, since the ear automatically registers the names of
notes for the listener. For most, however, parsing of melodies
requires the development of the sense of relative pitch whereby the
listener measures the intervals between pitches that make up a given
melody. Though seeming difficult at the outset, the skill for
measuring melodic intervals is rather easily formed, as Guido of
Arezzo discovered nearly ten centuries ago. His method, which no
doubt originated in the liturgical practiceof 'solmization,' is learned
with ease, by means of solfeggio, as the Italians named it, or 'Sol-fa-ing'
it was known after the seventeenth century in England. In developing
this skill, the listener first identifies the key-note of a given
melody as 'Doh,' then
names the other notes in ascending order as 'Reh,'Mih,Fah,Sol,Lah,Tih, and
then again 'Doh.' The
popular show-tune, 'Doe, a deer, a female deer' makes the acquiral
of this skill very easy;
Doh: Doe,
a deer, a female dear,
Reh: Ray,
a drop of golden sun,
Mih: Me,
a name I call myself
Fah: Fa,
a long, long way to run.
Soh: Sew,
a needle pulling thread,
Lah:
La, a name to follow Sew,
Tih: Tea,
a drink with jam and bread,
Doh:
Which takes us back to Doe.
Here is a sample of the way this song
reads in Visible Music Notation.
By clicking on this button "Demos" you may both see and hear
the music:

The above-described sol-fa names are
colored in accordance with a color-coding scheme which not only is
helpful in identifying melodic notes, but is equally helpful with
harmony- and tonality-identifications, as discussed below. Each
of these colors identifies an absolute pitch. That is to say,
all "C's," (or "Doh's")
are always blue; all "D's," (or "Reh's")
are always green; all "E's," (or "Mih's")
are always yellow; all "F's" (or "Fah's")
are always orange; all"G's" (or
Soh's") always red; all "A's" (or "Lah's")
always purple; and
all"Tih's" always
grey. The
intervals between these notes, as shown in the following table, also
are absolute, as shown in the following:
Table of
intervals from Doh
| Doh: |
Reh |
Mih |
Fah |
Soh |
Lah |
Tih |
Doh: |
Reh |
Mih |
Fah |
Soh |
Lah |
Tih |
| Doh: |
Maj. 2nd |
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Maj. 3rd |
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| Doh: |
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Perf. 4th |
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Perf. 5th |
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Maj. 6th |
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Maj. 7th |
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Perf. 8ve |
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Maj. 9th |
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Maj.10th |
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P. 11th |
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P. 12th |
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M. 13th |
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M. 14th |
Table
of intervals from Reh
| Reh |
Reh |
Mih |
Fah |
Soh |
Lah |
Tih |
Doh: |
Reh |
Mih |
Fah |
Soh |
Lah |
Tih |
| Reh |
Prime |
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Maj 2nd |
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| Reh |
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Min 3rd |
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Perf. 4th |
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Perf. 5th |
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Maj. 6th |
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Min. 7th |
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P. 8ve |
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Maj. 9th |
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Min. 9th |
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P. 11th |
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P. 12th |
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Similar tables may be constructed from all other notes
of the scale. And it will be useful for the learner to conbstruct
tabulations for all remaining scale tones. As a first assignment,
continue the above process by constructing intervallic tables from
the rest of the scale. Maintain the color schemes, and figure
out the intervallic sizes as best you can.
Actually, intervallic recognition is built into the Sol-Fa
system intuitively. Practicing Sol-Fa only a few moments each
day, the learner quicly develops necessary skills for identifying and
tuning intervals. (For a more detailed and more technical discussion
of this subject, see ASSUME, Essay 1. Scales, Intervals, Intonation
and Temperament).
READING
HARMONIC PROGRESSIONS
As these notes and intervals become familiar
to the listener, chords, or harmonies next become part of musical
awareness. Harmonic combinations present the listener with
simultaneous patterns of sound that at first seem difficult to identify,
if only because of the wide variety of harmonic combinations that
exist, the infinite variability, and the intrinsic complexity of
each. However, utilizing the color-coding discussed above greatly
simplifies the matter for the beginner. Since the name of a note
appears also in the name of a chord, more or less the same color
coding applies throughout, the only differences arising from the
need to distinguish between major, minor, augmented and diminished
chords. Quite simply, our recourse is to change the appearance,
or texture, of the polygon surfaces--i.e. the "walls of the
structures" that represent harmonies, whereby major harmonies
will be identifed by the same colors as the notes upon which they
are based, while minor harmonies will show stippled versions of the
same colors. Diminished triad structures bear one downward
chevron; diminished sevenths, two, and dimnished 9ths, three. In
similar fashion, augmented triads are shown by one upward chevron,
augmented 7ths by two, and augmented 9ths by three. When we
come to extensions of these structures, particulaly in the works
of Wagner and Debussey, other chevrons will be added for 11th-chords,
13th-chords, etc. Here is a simple table for identifying chords,
or harmonies:
Table of Harmonies Classified in
Major Key
| Major |
Minor |
Diminished |
Diminished 7th |
Diminished 9th |
Augmented |
Augmented 7th |
Augmented 9th |
| C: Doh |
c-minor (with stippling) |
c-diminished, with 1 downward chevron |
c-7th-diminished, with 2 downward chevrons |
c-9th-diminished, with 3 downward chevrons |
C-augmented, with 1 upward chevron |
C-augmented, with 2 upward chevrons |
C-augmented, with 3 upward chevrons |
| D: Reh |
d-minor (with stippling) |
d-diminished, with 1 downward chevron |
d-7th-diminished with 2 downward chevrons |
d-9th-diminished, with 3 downward chevrons |
D-augmented, with 1 upward chevron |
D-augmented, with 2 upward chevrons |
D-augmented, with 3 upward chevrons |
| E: Mih |
e-minor(with stippling) |
e diminished, with 1 downward chevron |
e-9th diminished with 2 downward
chevrons. |
E-augmented, with 1 upward chevron. |
E-augmented: with 2 upward chevrons |
E-7th-augmented: with 2 upward chevrons |
E-9th -augmented, with 3 upward chevrons |
| F: Fah |
f-minor (with stippling) |
f-diminished, with 1 downward chevron |
f-7th-diminished, with 2 downward chevrons |
f-9th-diminished, with 3 downward chevrons |
F-augmented, with 1 upward chevron |
F-7th-augmented, with 2 upward chevrons |
F-9th-augmented, with 2 3 upward chevrons |
| G: Soh |
g-minor (with stippling) |
g-diminished, with 1 downward chevron |
g-7th-diminished, with 2 downward chevrons |
g-9th-diminished, with 3 downward chevrons |
G-augmented, with 1 upward chevron |
G7th-augmented, with 2 upward chevrons |
G9th-Augmented, with 3 upward chevrons |
| A: Lah |
a-minor (with stippling) |
a-diminshed, with 1 downward chevron |
a-7th-diminished, with 2 downward chevrons |
a-9th-diminished, with 3 downward chevrons |
A-augmented, with 1 upward chevron |
A7th-Augmented, with 2 upward chevrons |
A9th-Augmented, with 3 upward chevrons |
| B: Tih |
b-minor (with stippling) |
b-diminshed, with 1 downward chevron |
b-7th-diminished, with 2 downward chevrons |
b-9th-diminished, with 3 downward chevrons |
B-augmented, with 1 upward chevron |
B-7th-Augmented, with 2 upward chevrons |
B-9th-Augmented, with 3 upward chevrons |
So much for the complexity of the harmonic element. In actual listening
practice, the problem of parsing harmonies is much simpler, for almost
all harmonies fall into one of three classes--the "Doh[C]" harmonies
the "Tih[B]" and the "Reh", or
super-tonic harmonies. The listener may identify each class by simply
humming the basic note. If singing "Doh" produces
no sense of "Discord discomfort," the harmony belongs to the
first class. If there is discomfort, the harmony is probably a "Tih" chord. Once
the listener has established this classification, the next step must
be find the sub-classification, for which purpose Sol-Fa-ing
also comes into play.
For "Tih" harmonies there are
four possible basic chords to check: Beginning with the most frequent,
the listener first sings the chordal melodic pattern, Tih-Soh-Re. If
those sounds satisfy, the chord is the 'Dominant,' or "G
Chord." If however, this pattern seems
to fit, but creates the sensation that something is missing, the listener
should then try "Tih-Soh-Re-Fah." If
this fulfills, the chord is the "Dominant
7th," or "G-7th-Chord." If
neither of these patterns seems to fit, the listener should next try "Tih-Soh-Mih," the
pattern that identifies the "Mediant" harmony, if there is
a fit. If not, the one remaining pattern to try is "Tih-Reh-Fa," to
check for the diminished triad on the leading tone.
For "Doh"-class harmonies there are also
four basic patterns, plus a fifth "modulatory chord pattern." First
comes the "Tonic" pattern which the listener identifes by
singing Doh-Mih-Soh-Mih-Doh. If
that pattern fits, the harmony is the Tonic chord of C-Major. If
not, the next pattern to try is "Doh-Lah-Fah," which
spells the sub-dominant, or F-Major chord.
Here, as in the case of the Dominant seventh chord, there seems a need
for one more sound, the listener should try "Doh-Lah-Fah-Teh" or
sub-dominant 7th chord, the Teh representing
the lowered leading tone in the original key. This harmony often
triggers a modulation to the sub-dominant key. In the process of
modulation, the lowered sub-tonic becomes the fourth step of the new
key, F Major,
if departing from C-Major. (See "Spelling
Modulations," below). If that pattern does not fit the next pattern
to try is "Doh-Mih-Lah" for
the "Sub-mediant," or "a-minor" chord.
Finally, within the class of major tonalities, there
are two basic "Super-Tonic," or "d-minor
chords," firstly "Reh-Fah-Lah" which
spells the regular super-tonic. The second, the four-note chord on Reh-Fih-Lah-Doh, or
major Super-Tonic 7th chord often triggers a modulation, this time
to the "Dominant" or "G-Major" key,
(which is Soh-Tih-Reh" from
the perspective of the key of C-Major).
Table of Harmonies Classified in
Minor Keys
| Minor |
Major |
Diminished |
Diminished 7th |
Diminished 9th |
Augmented |
Augmented 7th |
Augmented 9th |
| c-minor (with stippling) |
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c-diminished,with 1 downward chevron |
c-7th-diminished, with 2 downward chevrons |
c-9th-diminished, with 3 downward chevrons |
C-augmented, with 1 upward chevron |
C-augmented, with 2 upward chevrons |
C-augmented, with 3 upward chevrons |
| d-minor (with stippling) |
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d-double-diminished, with triangle. |
double-diminished 7th with downward chevron & triangle |
double-diminished 9th-with triangle, 2
downward chevrons |
d-minor-augmented, with 1 upward chevron |
d-minor 7th -augmented, with 2 upward
chevrons |
d-minor-augmented, 9th with 3 upward chevrons |
| e-flat minor: with stippling |
E-flat Major |
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E-flat-augmented: with 2 upward chevrons |
E-flat-7th-augmented: with 2 upward chevrons |
E-flat-9th -augmented, with 3 upward chevrons |
| f-minor (with stippling) |
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f-diminished, with 1 downward chevron |
f-7th-diminished, with 2 downward chevrons |
f-th-diminished, with 3 downward chevrons |
f-minor-augmented, with 1 upward chevron |
f-minor7th-augmented, with 2 upward chevrons |
f-minor 9th-augmented, with 2 3 upward
chevrons |
| g-minor (rare) |
G-Major & G-Major 7th chord |
g-diminished, with 1 downward chevron |
g-7th-diminished, with 2 downward chevrons |
g-9th-diminished, with 3 downward chevrons |
g-minor-augmented, with 1 upward chevron |
g-minor 7th-augmented, 2 upward chevrons |
g-mnor 9th-Augmented, with 3 upward chevrons |
A-flat minor (rare)
with stippling |
A-flat -major |
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A-flat-augmented, with 1 upward chevron |
A-flat-7th-Augmented, with 2 upward chevrons |
A-flat-9th-Augmented, with 3 upward chevrons |
| B: Tih |
b-minor (with stippling) |
b-diminshed, with 1 downward chevron |
b-7th-diminished, with 2 downward chevrons |
b-9th-diminished, with 3 downward chevrons |
B-augmented, with 1 upward chevron |
B7th-Augmented, with 2 upward chevrons |
B9th-Augmented, with 3 upward chevrons |
Here, the "harmonic spelling bee" more or less follows the
steps shown in connection witht he major tonalities, as discussed above.
However, there are new Sol-Fa syllables, as shown in the following chromatic
scales, rising and descending
Syllables in Rising Chromatic Scale: Syllables on Descending Chromatic
Scale:
Doh-Dih-Reh-Rih-Mih-Fah-Fih-Soh-Sih-Lah-Lih-Tih-Doh
Doh-Tih-Teh-Lah-Leh-Soh-Suh-Fah-Mih-Meh-Reh-Rah-Doh-Duh
C C# D D#E FF#GG#A A#B C C B Bb AAbGGb FE EbD Db C Cb
Spelling harmonies in minor modes is somewhat more complex, given broad
use of both variables on the sixth and seventh degrees of the scale. There
are still, however, mainly three test-tones, namely Doh, Tih and Reh,
as before. The "Doh" harmonies
closely follow the Major model, now playing out as: Doh-Meh-Soh(C-Eb-G)
for the minor tonic chord, Doh-Meh-Leh(C-Eb-Ab)
for the Major Sub-Mediant on flatted root, and Doh-Leh-Fah(C-Ab-F )
for the minor sub-dominant. Infrequently, the Major Sub-Dominant
(F-A-C)
will be encountered, its sound being easily self-evident.
The first and last of the "Tih" chord
patterns, the Dominant and the leading tone diminished triad remain the
same as in the Major keyes. While the Mediant chord, Tih-Soh-Meh emerges
as an augmented triad, Eb-G-B, so
spelled.
The Super-Tonic chord emerges either as a diminished
triad, Reh-Fah-Leh (D-F-Ab),
or as a minor triad: Reh-Fah-Lah. The
modulatory forms, Reh-Fih-Lah & Reh-Fih-Lah occur
quite frequently.
MODULATION
Modulation is also fairly easy to learn to understand. To
modulate either to the "Dominant Key" of the Subdominant
Key, a resident triad is altered so that it will conform to the Dominant
7th harmony of the new key. When modulating to the Dominant, the composer
merly sharpens the 4th degree of the scale (conferting Fah to Fih)
using the new harmony to affirm the new key, and repeating it one or
more times to confirm the same. To modulate to the Sub-Dominant,
the mere process of adding a flatted seventh (hence, the pattern Doh-Mih_Soh-Teh,
or C-E -G-Bb )
to the Tonic Triad affirms the Sub-Dominant as the new key. With
just a little practice, the listener soon learns to spot modulations
merely by the frequent appearance of the altered tones, Fih instead
of Fah, or Teh as a part of the Tonic harmony.
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