The Semiotic Musical Codes of
Two Twentieth Century Composers:

Cowell and Partch

Henry Cowell (1897-1965)

Twentieth-century American composer, pianist and writer Henry Cowell became renown for his coining of the term ‘tone clusters’, which were to be reproduced pianistically by the “forearm, the palm and the fists,” as well as for his innovation of the ‘string piano’ – the idea of “plucking and strumming the strings of the piano.”  These techniques were exhibited in the Aeolian Harp (1923) and The Banshee (1925), and what were the beginnings of prepared piano, in the Piano Piece (1924).

Cowell was born on March 11, 1897 in Menlo Park, California, and initiated his formal music studies at the University of California under the guidance of Charles Seeger.  His first influences came naturally, via Oriental music emanating from San Francisco’s Chinatown, his Celtic heritage and American mid western folk music; and later, through studying non-Western music at the University of Berlin (1932-33) and traveling to India, Japan, Iran and other countries in the East.  “His use of varied sound materials, experimental compositional procedures, and rich palette colored by multiple non-European and folk influences revolutionized American music and popularized, most notably, the tone cluster as an element in compositional design,” sums up the G. Schirmer online biography.

The Tides of Manaunaun (1911), a work inspired by Irish mythology and the god of motion, represents Cowell’s first attempt at utilizing tone clusters as a compositional tool, while other examples of this technique include Advertisements (1914), The Hero Sun (1922), What’s This (1922), the Piano Piece (1924) and Tiger (1928).  “To portray the immense waves set in motion by the Irish god, Cowell played huge clusters in the low register of the piano, first with the right hand, then with the entire forearm.  Above this was a sweeping modal melody.  Without a second thought, he had combined atonal noise elements with a folklike tune,” comments Bruce Saylor in his article Henry Cowell contained within the pages of The New Grove Dictionary of Music and Musicians.

David Cope, in the introduction of New Directions in Music’s chapter on “sound-mass and microtones,” describes the aesthetic implications of the use of clusters thus:

“Sound-mass, in contrast to serialism, minimizes the importance of individual notes and their order, while maximizing the importance of texture, rhythm, dynamics, and/or timbre of broad gestures.  This refocusing is of great significance in the development of the avant-garde movement.  Sound-mass confronts one of the most profound technicalities of the music world – the fine differentiation between sound and noise, a derogatory term applied to sounds antithetical to music.”

Tiger demonstrating Cowell’s method of notating a cluster that involves a performance technique whereby “all of the keys, black and white, between the upper and lower notes are to be played simultaneously using both forearms.”  According to Frederick Koch in Reflections on Composing: Four American Composers, who can legitimately claim a vis-à-vis experience with the composer, “He would eagerly play you some of his famous piano compositions such as The Tides of Manaunaun or the Aeolian Harp and he admitted his Tiger to be one of the wildest in captivity.”

Cowell’s theoretical basis for tone clusters begins with the notion of chord-formation, where he proposes three systems: the first being chord construction based on “fifths and their inversions, fourths, and diminished fifths;” the second, based on “thirds and their inversions, sixths;” while the third, based on “seconds, both major and minor,” which naturally includes their inversions, sevenths.  These three systems theoretically justified by the overtone series, which suggests that the first belongs to the first order or the “common chord of a system of fifths” (the primary partials), with each system thereafter based on the higher overtones of the series.  In New Musical Resources Cowell explicates that from the seventh partial, the series introduces major seconds, and by the fifteenth and sixteenth, minor seconds, pointing out the “sound acoustical foundation” of the whole-tone scale, in view of its natural manifestation between the seventh and fourteenth partials.  He concludes the following:

“The use of chords based on clusters of seconds, built as they are on the next reaches of the overtones after thirds, would seem inevitable in the development of music.  There is no reason to suppose that the progress along the overtones which has been made from early musical times to the present will suddenly stop.”

The overtone series used yet again to point out that from the seventh partial on, “the first dissonance according to the text books”, these so-called dissonances naturally space themselves as seconds, and not as sevenths and ninths.  Cowell’s harmonic theories ultimately promoting the “equal and independent” role of notes within a chord, and the separation of tertian and quartal harmony from secundal, or what he terms as “tone clusters.”

He advocates the same theory for clusters as triadic harmony, which places a minor third above a major third in order to construct a major triad, a major third above a minor third for a minor one, two minor thirds for a diminished, and finally, two major thirds for an augmented.

The same example illustrating how “subtle distinctions between the different placements of major and minor seconds in the inner parts” will ultimately be audible to the trained ear and monotony thus broken, as well as how “in orchestral use we have all the possible variety of large clusters which are neither all chromatic nor diatonic, but constructed from a consistent building up of diversified smaller cluster triads.”  Clusters first appearing in his first orchestral work Some More Music (1916).

One of the important points to consider in cluster harmony according to Cowell is the notion of outer tones forming an either consonant or dissonant interval, with the former aestheticly superior.  It is further suggested to group the tones of the cluster in the same way that tones are grouped in a chord – this theory demonstrated through an example of “a common cluster chord of C, with clusters of a third,” containing three successive clusters: C to E, E to G sharp (in the next octave), and G to B – the lower three tones forming the “common major chord of C.”

Cowell also distinguished between fixed and movable (or additive and subtractive) cluster techniques.  In the fixed, differentiated are the two methods of employing tone clusters for melodic effect, with the first being “to move clusters of the same interval up and down the scale,” while the second, “to shift the size of the interval as the cluster moves.”  The additive cluster technique is illustrated in Ex. 6, which shows how (a) may be replaced by the (b) notation, and (b), (c) and (d) further demonstrating how the cluster may either rise in pitch, begun on a low pitch; may fall in pitch, begun on a high pitch; or expand outwards, begun in a middle pitch.

Cowell’s contribution to twentieth-century art music (an output of over 950 works) was acknowledged during his lifetime with many awards, grants and honorary degrees, and his legacy expounded through his writings, namely his book New Musical Resources (1930) and his series of 40 reviews of contemporary music for Music Quarterly (1947-58); as well as through his far-reaching students John Cage, Lou Harrison and George Gershwin.  His individual nature well framed in his response to the question of “the personal unified style of a composer,” where he declares: “If a man has a distinctive personality of his own, I don’t see how he can keep it out of his music.  And if he hasn’t how can he put it in.”

Harry Partch (1901-1974)

In the 1920s Harry Partch set on his artistic quest of establishing an alternative “monophonic and corporeal music that returned to the primal, ritualistic, corporeal state that music had long ago abandoned,” and what Thomas Mc Geary describes in Bitter Music: Collected Journals, Essays, Introductions, and Librettos as: “a music arising from human speech and the natural acoustical musical intervals generated by sounding bodies; a music no longer estranged from the physical production of sound; a music where the audience experiences an integration of drama, dancers, and performing musicians.” – by the 1930s, he had achieved a total cessation with European tradition.  “Partch, the musical apostate, called all aspects of European music into question: its concert traditions and the specialized role of the composer and performer, its forms and abstract music, its instruments and equal temperament, and its purity of music, dance, and theater,” notes Mc Geary.

Partch was born on June 24, 1901 in Oakland, California, and was essentially an autodidact, refusing to partake in institutionalized education throughout his creative life.  His resume contained in American Composers Forum’s Harry Partch listing his education as “Albuquerque High School, 1919; public libraries,” while his degrees as “none,” categorizing his occupation as “musician, among other things: composer, instrument-builder, theorist, writer, visual artist, proofreader, show-wright, hobo.”

He discarded equal temperament or the division of the octave into twelve equal intervals, subscribing to just intonation, and in doing so adopted a scale of forty-three notes in the octave, creating the appropriate instruments that would enable its full realization.  It is worthy to note that Partch’s main impact on twentieth-century music has not been through his compositional output, but rather through his writings, which promote the notion of “music and its place in human culture” or the “artist’s relation and responsibility to society.”

In order to understand Partch’s philosophy behind the forty-three-note division of the octave, the mere basics must firstly be established.  “In dealing with musical resources and in the building of instruments of fixed intonation,” Western theory excludes any prime number above the 5-limit, and subscribes to Equal Temperament, which is theoretically bounded within seven 5-limit ratios: 1/1, 6/5, 5/4, 4/3, 3/2, 8/5, 5/3 and 2/1.  The further expansion of the system achieve through the creation of triads (“a scale of thirteen degrees tuned correctly on 1/1”) producing fourteen tonalities; seven Otonalities (major tonality or “a tonality expressed by the over numbers of ratios having a Numerary Nexus”) and seven Utonalities (minor tonality or “a tonality expressed by the under numbers of ratios having a Numerary Nexus”), with a total of 144 senses or harmonic functions (theoretically being “the chromatic maximum of Equal Temperament”).  The Incipient Tonality Diamond diagram graphically illustrating how in the 5-limit system each “succession of ratios between the solid and dotted lines is a triad.”

Partch’s justification for the expansion of this system directed towards “harmonic, psycho-physiological, and historical considerations,” stating that the 3-limit legitimately serves “intervals of the most perfect consonance,” while the 5-limit, “intervals of the simplest ‘diatonic’ scales, in the process of evolution since Pythagoras;” then marking the fact that although expansion to the 11-limit had in terms of Western musical evolution always been the next logical step, the 5-limit system had preponderated simply “because it was expedient in the building and tuning of fretted and keyboard instruments and because its demands on notation were less complex.”  His philosophical reasons depicted in the following passage from his monumental work Genesis of a Music: An Account of a Creative Work, its Roots and its Fulfillments:

“The men whose work is widely recognized as the heart of the ‘Western Golden Age of music’ – Bach, Mozart, Haydn, Beethoven, and many more – were daring men, who simply appropriated as a medium of expression whatever was at hand, which happened to be instruments and notation based on the 5 limit.  In the wake of the golden-age masters came a second series of men whom we cannot call daring.  These were the devoted admirers of the masters, whom implemented their admiration with textbooks in which works of the masters were analyzed in the most scholarly fashion and rules laid down stemming from such analyses, who noted, in countless pages, each and every exception to these rules as found in the works of the masters, and who fervently devoted themselves to tying music to the age of the masters – and incidentally to the number 5 – for ever and ever and ever.”

The harmonic reasons that Partch gives for advocating an 11-limit system being that it introduces a wealth of new harmonic material – twenty triads, fifteen quadrads and six quintads for the “six identities of a single Otonality or a single Utonality,” excluding chord inversion and expansion possibilities.  The historical reasons on the other hand directed towards the fact that in “the theoretical expositions of Ptolemy, Alexandrian scientists of the second century, the ratios within the 11 limit are either given or implied.”  The ratios of the 11-limit produce an initial twenty-nine pitches, and through a process of subdivision arrive finally at The Forty-Three-Tone Scale.

This in effect being the identical method applied in North Indian Hindustani art music to arrive to its theoretical scale of The Sixty-Six Srutis (The Scale of Proportions as opposed to The Scale of Fifths) – a division of the octave into 53 distinct intervals, with its additional quarter-tones a result of the further division of the disjunctions of this scale giving a total of 66 intervals.

In view of his complex tuning schemes (which were incidentally complete systems in their own right, based on specific harmonic principles, and therefore adhering to their own laws on resolution, etcetera), Harry Partch, dissimilarly to Cowell and Cage who merely modified existing instruments, created entirely new material forms of expression, and apart from the human voice, his music utilized all newly invented instruments.  Some of these include the Adapted Viola (1930), Adapted Guitar I and II (134-145), Chromelodeon I and II (1942-1950), Kithara I (1938-1959) and the Harmonic Canon I, II and III (1945-1965).

The Chromelodeon I was adapted from a six-octave double-reed harmonium at the University of Wisconsin in 1945.  The two cell-boards, each containing 73 reeds were tuned to the 43-degree Monophonic system, attaining a range of 1,982.5 cents or in Equal Temperament terms, a range just under a flat thirteenth.  Each set of reeds tuned an octave apart, therefore providing a total available range of about three and a half octaves.  The Old Chromelodeon II was an adapted double-reed chapel organ (fitted with an additional 13 sub-bass reeds) with a five-octave keyboard; while the New Chromelodeon II, an 88-key reed organ with a total of 244 reeds.

The 1931 work By the Rivers of Babylon (137th Psalm) presents one of the many avenues that Partch explored with regards to microtonal notation.  In this case, within the context of a musical setting of a sacred text for intoning voice and Monophone (an instrument later renamed Adapted Viola), where the voice must tune to the Adapted Viola’s pitches by ear.

“The ratio notation, one of several he experimented with, gives no visual indication of melodic direction – a shortcoming he tried to address in his other notations,” notes Philip Blackburn in Harry Partch.

The “Key to Diacritical Notation of Monophonic Ratios” from the 1933 work By the Great Wall (one of the 17 Lyrics of Li Po) further illustrating Partch’s attempt to create “a notation that would appropriately connect the visual appearance to the act of playing each instrument.”  This system of diacritical noteheads intended to visually enhance “intervallic distance and melodic contour.”

Delusion of the Fury – A Ritual Dream and Delusion, with its plot combining a Japanese and an African tale represents “a total Partch statement, incorporating voices, mime, his celebrated instruments, dance, lighting and staging, all working to express this philosophical concept.”  The work, which runs for a total duration of between seventy-five and eighty minutes has no libretto, with all the action being either danced or mimed, and its two acts presented as one continuous event.  The set is made up of twenty-five instruments, and there are eighteen to twenty musicians required for its performance (including the conductor).

The liner notes from The World of Harry Partch, which refer to a 1966 live recording of Daphne of the Dunes, originally the sound track for Madeline Tourtelot's film Windsong (based on the ancient myth of Daphne and Apollo) providing a good example of Partch’s also complex rhythmic structures:

“Melodic material is short, haunting, and reoccurs motivically.  Arpeggiated harmonic texture contrasts melodic sections.  Meter is ever changing, almost measure for measure, with pulse sub-divisions of five, seven, and nine common.  A trio of the Bass Marimba, Boo, and Diamond Marimba written in 31/16 meter is structured with 5 unequal beats per measure, the beats sub-divided into sixteenths of 5-5-7-9-5.  A duet of the Boo and Harmonic Canon is written in a polymeter of 4/4--7/4 over 4/8-7/8.”

The legacy of Partch’s lifelong dedication to music is perhaps best summed up by Mc Geary who writes, “Like other composers of his generation in America, Partch suffered from two compounded prejudices: one against contemporary, experimental music; and the second in favor of European musicians, repertoire and tradition.”  The international rise of Stravinskian and Schoenbergian models following World War II diminishing the focus on American identity somewhat.  Adding to this dilemma is the fact that “his compositions could only be performed on his own unique instruments.”  It is nevertheless evident that the artistic voice of Harry Partch may be silent, but indirectly, his music lives on through his writings, and the ongoing influence of Genesis of a Music.

Horizontal Marker

Appendix 1

The Harmonic Series

The overtones of a specific pitch are generally referred to as the harmonic series.  The following table presents the fundamental C and its harmonics (overtones) from the first partial, through the 32nd partial.

Relative Pitch: A4 = 440/C4 (Middle C) = 261.63
 

Degree Number Note Interval Ratio Savarts Frequency (Hertz) Cents Tuning
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16

01

C
D flat
D
E flat
E
F
F sharp
F sharp
G
A flat
A
A
B flat
B flat
B
B

C

unison
major half-tone
major tone
trihemitone
major third
small fourth
small augmented fourth
large augmented fourth
fifth
small diminished sixth
small sixth
cyclic sixth
harmonic minor seventh
minor seventh
major seventh
major seventh

octave

1/1
17/16
9/8
19/16
5/4
21/16
11/8
23/16
3/2
25/16
13/8
27/16
7/4
29/16
15/8
31/16

2/1

0
26.33
51.15
74.63
96.91
118.11
38.31
57.61
76.09
193.82
210.85
227.24
243.04
258.27
273
287.24

301.03

261.63
277.98
294.33
310.68
327.03
343.38
359.74
376.09
392.44
408.79
425.14
441.49
457.84
474.2
490.55
506.9

523.25

0
105
204
298
386
471
551
628
702
773
841
906
969
1030
1088
1145

1200

+ 00
+ 05
+ 04
– 02
– 14
– 29
– 49
+ 28
+ 02
– 27
– 59
+ 06
– 31
+ 30
– 12
+ 45

+ 00

Horizontal Marker

Appendix 2

The Natural (Pure) Division of the Octave

The 'Natural (Pure) Division of the Octave' is based on the harmonic series.  It is a scale of 'Just Intonation', where the intervals are called pure (or just), because there are no beats between the notes or their harmonics.

Relative Pitch: A4 = 440/C4 (Middle C) = 261.63
 

Degree Number Note Interval Ratio Savarts Frequency (Hertz) Cents Tuning
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16

01

C
D flat
D
D
E flat
E
F
F sharp
F sharp
G
A flat
A
B flat
B flat
B flat
B

C

unison
major half-tone
minor tone
major tone
minor third
major third
fourth
harmonic tritone
cyclic tritone
fifth
diminished sixth
harmonic sixth
harmonic minor seventh
minor seventh
minor seventh
major seventh

octave

1/1
16/15
10/9
9/8
6/5
5/4
4/3
45/32
64/45
3/2
8/5
5/3
7/4
16/9
9/5
15/8

2/1

0
28.03
45.76
51.15
79.18
96.91
124.94
148.06
152.97
176.09
204.12
221.85
243.04
249.88
255.27
273

301.03

261.63
279.07
290.72
94.33
313.95
327.03
348.83
367.91
372.09
392.44
418.6
436.04
457.84
465.11
470.93
490.55

523.25

0
112
182
204
316
386
498
590
610
702
814
884
969
996
1018
1088

1200

+ 00
+ 12
– 18
+ 04
+ 16
– 14
– 02
– 10
+ 10
+ 02
+ 14
– 16
– 31
– 04
+ 18
– 12

+ 00

Horizontal Marker

Appendix 3

The Forty-Three-Tone Scale

The 'Forty-Three Tone Scale' is based on the harmonic series and monophonic intonation.  The tuning system was devised by Harry Partch in concordance with the ratios of the 11-limit, which total twenty-nine, although through further subdivision produce the forty-three pitches of The Forty-Three-Tone Scale.

Relative Pitch: A4 = 440/C4 (Middle C) = 261.63
 

Degree Number Note Interval Ratio Savarts Frequency (Hertz) Cents Tuning
01
02
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43

01

C
C
C
D flat
D flat
D flat
D
D
D
D
E flat
E flat
E flat
E flat
E
E
E
F
F
F
F
F sharp
F sharp
F sharp
G
G
G
G
A flat
A flat
A
A
A
A
B flat
B flat
B flat
B flat
B flat
B
B
B
C

C

unison
comma
quarter-tone
minor half-tone
major half-tone
three/quarter-tone
small tone
minor tone
major tone
large tone
small minor third
trihemitone
minor third

major third
ditone
large major third
small fourth
fourth
large fourth

(harmonic) tritone
(cyclic) tritone

small fifth
fifth
large fifth

small diminished sixth
diminished sixth
small sixth
harmonic sixth
cyclic sixth
large sixth
small minor seventh
minor seventh
minor seventh
 

major seventh
major seventh

small octave

octave

1/1
81/80
33/32
21/20
16/15
12/11
11/10
10/9
9/8
8/7
7/6
32/27
6/5
11/9
5/4
14/11
9/7
21/16
4/3
27/20
11/8
7/5
10/7
16/11
40/27
3/2
32/21
14/9
11/7
8/5
18/11
5/3
27/16
12/7
7/4
16/9
9/5
20/11
11/6
15/8
40/21
64/33
160/81

2/1

0
5.4
13.36
21.19
28.03
37.79
41.39
45.76
51.15
57.99
66.94
73.79
79.18
87.15
96.91
104.74
109.14
118.1
124.94
130.33
138.3
146.13
154.9
162.73
170.7
176.09
182.93
191.89
196.29
204.12
213.88
221.85
227.24
234.08
243.04
249.88
255.27
259.64
263.24
273
279.84
287.67
295.63

301.03

261.63
264.9
269.8
274.71
279.07
285.41
287.79
290.7
294.33
299
305.23
310.07
313.95
319.95
327.03
332.98
336.38
343.38
348.83
353.19
359.74
366.28
373.75
380.55
387.59
392.44
398.67
406.97
411.13
418.6
428.11
436.04
441.49
448.5
457.84
465.11
470.93
475.68
479.65
490.55
498.33
507.4
516.79

523.25

0
22
53
84
112
151
165
182
204
231
267
294
316
347
386
418
435
471
498
520
551
583
617
649
680
702
729
765
782
814
853
884
906
933
969
996
1018
1035
1049
1088
1116
1147
1178

1200

+ 00
+ 22
+ 53
– 16
+ 12
+ 51
– 35
– 18
+ 04
+ 31
– 33
– 06
+ 16
+ 47
– 14
+ 18
+ 35
– 29
– 02
+ 20
+ 51
– 17
+ 17
+ 49
– 20
+ 02
+ 29
+ 65
– 18
+ 14
– 47
– 16
+ 06
+ 33
– 31
– 04
+ 18
+ 35
+ 49
– 12
+ 16
+ 47
– 22

+ 00

Horizontal Marker

Appendix 4

The Equally Tempered Division of the Octave

The 'Equally Tempered Division of the Octave' is based on the division of the octave into twelve equal intervals.  The frequency ratio of each semitone (or tempered half-tone) is therefore the twelfth root of 2.  The measurement of a cent derived from a hundredth of this measurement, being the twelve-hundredth root of 2.

Relative Pitch: A4 = 440/C4 (Middle C) = 261.63
 

Degree Number Note Interval Ratio Savarts Frequency (Hertz) Cents Tuning
01
02
03
04
05
06
07
08
09
10
11
12

01

C
D flat
D
E flat
E
F
F sharp
G
A flat
A
B flat
B

C

unison
major half-tone
major tone
minor third
major third
fourth
cyclic tritone
fifth
diminished sixth
harmonic sixth
minor seventh
major seventh

octave

1.0
1.05946309
1.1222462
1.18920712
1.25992105
1.33483985
1.41421356
1.49830708
1.58740105
1.68179283
1.78179744
1.88777486

2.0

0
25.09
50.09
75.26
100.34
125.43
150.51
175.6
200.69
225.77
250.86
275.95

301.03

261.63
277.18
293.66
311.13
329.63
349.23
369.99
392
415.3
440
466.16
493.88

523.25

0
100
200
300
400
500
600
700
800
900
1000
1100

1200

+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00
+ 00

+ 00

*Note that the exact frequency of middle C is equal to 261.62556538 hertz, and that the equally tempered semitone (100 cents) ratio of 10594630940/10000000000 can also be expressed as a decimal ratio of 1.059463094

Horizontal Marker

Appendix 5

The Sixty-Six Srutis (The Harmonic Division of the Octave)

The 'Harmonic Division of the Octave' is based on the harmonic series.  It is a division of the octave into 53 distinct intervals.  The quarter-tone is a result of the further division of the disjunctions of this scale giving a total of 66 intervals.  In Indian musical theory this system is known as The Sixty-Six Srutis.

Relative Pitch: A4 = 440/C4 (Middle C) = 261.63
 

Degree Number Note Interval Expression Ratio Frequency (Hertz) Cents Tuning
01
02
03

04
05
06
07

08
09
10
11
12

13
14
15

16
17
18
19
20

21
22
23
24
25

26
27
28
29

30
31
32
33
34

35
36
37

38
39
40
41
42

43
44
45
46

47
48
49
50
51

52
53

01

C
C +
C + +
¼
D flat – –
D flat –
D flat
D flat + 
¾
D – –
D –
D
D +
D + +
¼
E flat –
E flat
E flat +
¾
E – –
E –
E
E +
E + +
¼
F – –
F –
F
F +
F + +
¼
F sharp – –
F sharp –
F sharp
F sharp +
¾
G – –
G –
G
G +
G + +
¼
A flat –
A flat
A flat +
¾
A – – 
A –
A
A +
A + +
¼
B flat – –
B flat –
B flat
B flat +
¾
B – –
B –
B
B +
B + +
¼
C – –
C –

C

unison
syntonic comma
two syntonic commas
quarter-tone
minor half-tone
limma
major half-tone
large half-tone
three/quarter-tone
small tone
minor tone
major tone
large tone
 

small minor third
trihemitone
minor third
 

small major third
major third
ditone
large major third
 

small fourth
fourth
large fourth
 

small augmented fourth
harmonic tritone
cyclic tritone
large augmented fourth
 

small fifth
fifth
large fifth
 

small diminished sixth
diminished sixth
diminished sixth
 

small sixth
harmonic sixth
cyclic sixth
large sixth

small minor seventh
harmonic seventh
minor seventh
minor seventh
 

small seventh
major seventh
cyclic major seventh
large major seventh
 

small octave

octave

(base)
 
 
 

sad, pathetic
tender, at peace
loving, calm

enterprising
anxious, weak
strong, confident
fierce
 

sad
loving
passionate
 
 

calm, pleasing
awake, lively
hard, indifferent

doubt
moonlight, peace
intense
 
 
 

intense, grief
uncertain, doubtful
intense, active

acute, interrogative
inexpressive, self-contradictory
sunlight, joyful
confused, self-contradictory
 

deep sorrow
tender
loving, enterprising
 

uncertainty
soft, calm
restless, playful
hard, active
 

helpless, subdued
beauty, love
desire, anxiety

doubt
anguish, depression
soft, voluptuous
strong, sensuous
selfish, eager
 
 
 

(base)

1/1
81/80
128/125
31/30
25/24
256/243
16/15
27/25
135/124
800/729
10/9
9/8
256/225
59049/51300
93/80
75/64
32/27
6/5
75/62
8000/6561
100/81
5/4
81/64
32/25
31/24
125/96
320/243
4/3
27/20
512/375
62/45
25/18
45/32
64/45
36/25
90/62
375/256
40/27
3/2
243/160
192/125
31/20
25/16
128/81
8/5
50/31
81/50
400/243
5/3
27/16
128/75
31/18
125/72
225/128
16/9
9/5
29/16
4000/2187
50/27
15/8
243/128
48/25
60/31
125/64
160/81

2/1

261.63
264.9
267.9
270.35
272.53
275.62
279.07
282.56
284.83
287.11
290.7
294.33
297.67
301.14
304.14
306.59
310.07
313.95
316.48
319
322.99
327.03
331.12
334.88
337.93
340.66
344.53
348.83
353.19
357.21
360.46
363.37
367.91
372.09
376.74
379.78
383.24
387.59
392.44
397.34
401.86
405.52
408.79
413.43
418.6
421.98
423.83
430.66
436.04
441.49
446.51
450.58
454.21
459.89
465.11
470.93
474.2
478.51
484.49
490.55
496.68
502.32
506.37
510.99
516.79

523.25

0
22
41
57
71
90
112
133
147
161
182
204
223
244
261
275
294
316
330
343
365
386
408
427
443
457
477
498
520
539
555
569
590
610
631
645
661
680
702
723
743
759
773
792
814
828
835
863
884
906
925
941
955
977
996
1018
1030
1045
1067
1088
1110
1129
1143
1159
1178

1200

+ 00
+ 22
+ 41
+ 57
– 29
– 10
+ 12
+ 33
+ 47
– 39
– 18
+ 04
+ 23
+ 44
+ 61
– 25
– 06
+ 16
+ 30
– 57
– 35
– 14
+ 08
+ 27
+ 43
– 43
– 23
– 02
+ 20
+ 39
+ 55
– 31
– 10
+ 10
+ 31
+ 45
– 39
– 20
+ 02
+ 23
+ 43
+ 59
– 27
– 08
+ 14
+ 28
– 65
– 37
– 16
+ 06
+ 25
+ 41
– 45
– 23
– 04
+ 18
+ 30
– 55
– 33
– 12
+ 10
+ 29
+ 43
– 41
– 22

+ 00

Horizontal Marker

Bibliography

Books

Backus, John.  The Acoustical Foundations of Music: Musical Sound; its Properties, Production,  Behavior, and Reproduction.  2nd ed.  New York: W. W. Norton & Co., 1977.

Blackburn, Philip.   Harry Partch. Enclosure 3.  Saint Paul, MN: American Composers Forum, 1997.

Blatter, Alfred.  Instrumentation and Orchestration.  2nd ed.  New York: Schirmer, 1997.

Cope, David.  New Directions in Music. 6th ed.  Sydney: Mc Graw-Hill, 1993.

- - - .  Techniques of the Contemporary Composer.  New York: Schirmer, 1997.

Cowell, Henry.  New Musical Resources. New York: Cambridge U Press, 1996.

Dallin, Leon.  Techniques of Twentieth Century Composition: A Guide to the Materials of Modern Music.  3rd ed.  Dubuque, Iowa: W. C. Brown Co., 1974.

Daniélou, Alain.  Introduction to the Study of Musical Scales.  London: India Society, 1943

Earls, Paul.  “Harry Partch.”  The New Grove Dictionary of Music and Musicians.  Stanley Sadie, ed.  5th ed.  Vol. 14.  London: Macmillan, 1980.  252-253.

Grout, Donald Jay, and Claude V. Palisca. A History of Western Music.  5th ed.  New York: W. W. Norton, 1996.

Koch, Frederick.  Reflections on Composing: Four American Composers.  Pittsburgh, Pa.: Carnegie-Mellon U Press, 1983.

Miller, Leta E., and Fredric Lieberman. Lou Harrison: Composing a World.  New York: Oxford U Press, 1998.

Morris, Mark.  The Pimlico Dictionary of Twentieth Century Composers.  London: Pimlico, 1999.

Olson, Harry F.  Music, Physics and Engineering. 2nd ed.  New York: Dover, 1967.

Partch, Harry.  Bitter Music: Collected Journals, Essays, Introductions, and Librettos.  ThomasMc Geary ed.  Urbana: U of Illinois Press, 1991.

- - - .  Genesis of a Music: An Account of a Creative Work, its Roots and its Fulfillments.  2nd ed.  New York: Da Capo Press, 1974.

Persichetti, Vincent.  Twentieth-Century Harmony: Creative Aspects and Practice.  New York: W. W. Norton & Co, 1961.

Randel, Don Michael, ed.  The New Harvard Dictionary of Music.  Cambridge, Mass.: Belknap Press of Harvard U Press, 1986.

Rossing, Thomas D.  The Science of Sound. 2nd ed.  Reading, MA.: Addison-Wesley, 1990.

Sadie, Stanley, ed.  The Grove Concise Dictionary of Music.  London: Macmillan, 1994.

- - - . The New Grove Dictionary of Music and Musicians.  5th ed.  20 vols.  London: Macmillan, 1980.

Saylor, Bruce.  “Henry Cowell.”  The New Grove Dictionary of Music and Musicians.  Stanley Sadie, ed.  5th ed.  Vol. 5.  London: Macmillan, 1980.  8-12.

Discography

Sound Forms for Piano.  Perf. Robert Miller.  Recorded Anthology of American Music.  New World, 1976.

Internet Resources

“Genesis of a Music: Harry Partch (1901-1974).” Hampshire College Web Site (n.d.): no. pag.  Online.  Internet.  Available HTTP: http://hamp.hampshire.edu/~ngzF92/partch/partch.html  (30 Oct. 2000)

“Harry Partch: An American Original.”  Corporeal Meadows  (3 Sep. 2000): no. pag.  Online.  Internet.  Available HTTP: http://www.corporeal.com/welcome.html  (30 Oct. 2000)

“Henry Cowell.”  G. Schirmer, Inc. and Associated Music Publishers Home Page (19 Oct. 1999): no. pag.  Online.  Internet.  Available HTTP: http://www.schirmer.com/composers/cowell_bio.html  (30 Oct. 2000)

Photographs

Mitchell, Danlee.  “The Adapted Viola.”  Harry Partch.  Genesis of a Music: An Account of a Creative Work, its Roots and its Fulfillments.  2nd ed.  Photograph.  New York: Da Capo Press, 1974.  199.

- - - .  “The Chromelodeon I.”  Harry Partch.  Genesis of a Music: An Account of a Creative Work, its Roots and its Fulfillments.  2nd ed.  Photograph.  New York: Da Capo Press, 1974.  196.

“Harry Partch.”  David Cope.  New Directions in Music.  6th ed.  Photograph.  Sydney: Mc Graw-Hill, 1993.  97.

“Henry Cowell.”  David Cope.  New Directions in Music.  6th ed.  Photograph.  Sydney: Mc Graw-Hill, 1993.  55.

All rights reserved. All text, graphics and sound files on this page are copyrighted.
Unauthorized reproduction and copying of this page is prohibited by law. Copyright © 2001 by Andrián Pertout.

Horizontal Marker

Andrián Pertout's Home Page