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Andrián Pertout
Folio of Compositions 2003-2007
Volume 2
Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy
Produced on acid-free paper
Faculty of Music
The University of Melbourne
March, 2007
THE UNIVERSITY OF MELBOURNE Faculty of Music
TO WHOM IT MAY CONCERN
This is to certify that
(i) the thesis comprises only my original work towards the PhD except where indicated in the Preface*,
(ii) due acknowledgement has been made in the text to all other material used,
(iii) the thesis is less than 80,000 words in length, exclusive of tables, maps, bibliographies and appendices or the thesis is [number of words] as approved by
the RHD Committee.
Signature:
Name in Full: Andrián Pertout
Date: 2 March, 2007
Table of Contents
Volume 2
Recordings – Folio of Compositions 2003-2007: Volume 2 ........................................................................................................................................................................... vii
1. Àzàdeh for Santär and Tape, no. 389 (2004, Rev. 2005) ........................................................................................................................................................................ 1
2. Exposiciones for Sampled Microtonal Schoenhut Toy Piano, no. 392 (2005) ................................................................................................................................ 47
3. La Homa Kanto for Harmonically Tuned Synthesizer Quartet, no. 393 (2005) ............................................................................................................................... 91
4. Symétrie intégrante for Flute, Organ and Electronics, no. 394 (2005-2006) ..................................................................................................................................... 153
5. Tres Imágenes Norteñas for Shakuhachi and Harpsichord, no. 396 (2006) ..................................................................................................................................... 203
† All items separated by coloured pages
Recordings
Folio of Composition 2003-2007: Volume 2
Compact Disc 1
à Àzàdeh for Santär and Tape, no. 389 13:01
Recorded at Andrián Pertout Studio, Richmond, Melbourne, Australia, 25 September, 2006
Engineered by Andrián Pertout
Mixed and Mastered by Michael Costa at Stream AV Pty. Ltd., Melbourne, Australia, 3 November, 2006
Qmars Piraglu – santär
á Exposiciones for Sampled Microtonal Schoenhut Toy Piano, no. 392 7:00
Recorded at Andrián Pertout Studio, Richmond, Melbourne, Australia, 22 July, 2005
Mastered by Michael Costa at Stream AV Pty. Ltd., Melbourne, Australia, 17 October, 2006
Programming by Andrián Pertout
â La Homa Kanto for Harmonically Tuned Synthesizer Quartet, no. 393 11:50
Recorded at Andrián Pertout Studio, Richmond, Melbourne, Australia, 22 November, 2006
Programming by Andrián Pertout
ã Symétrie intégrante for Flute, Organ and Electronics, no. 394 (2005-2006) ‘MIDI’ 12:31
Recorded at Andrián Pertout Studio, Richmond, Melbourne, Australia
Programming by Andrián Pertout
ä Tres Imágenes Norteñas for Shakuhachi and Harpsichord, no. 396 (2006) 11:26
Performance at the Melbourne Composers’ League ‘From a Silence Well’ Concert
Recorded live at Richmond Town Hall, Richmond, Melbourne, Australia, 10 December, 2006
Anne Norman – shakuhachi; Peter Hagen – harpsichord
å Àzàdeh for Santär and Tape, no. 389 13:18
Performance at the 2007 Asia Pacific Festival (26th Asian Composers League Festival & Conference), 8-16 February, 2007, Wellington, New Zealand
‘Transformations: East South West’ Concert
Recorded live at St Andrews on the Terrace, Wellington, New Zealand, 9 February, 2007
Qmars Piraglu – santñr
æ Tres Imágenes Norteñas for Shakuhachi and Harpsichord, no. 396 (2006) ‘MIDI’ 9:13
Recorded at Andrián Pertout Studio, Richmond, Melbourne, Australia
Programming by Andrián Pertout
÷××× Recordings
Andrián Pertout
Àzàdeh for Santñr and Tape
�
No. 389
Composed between March and August, 2004 (Revised between January and February, 2005) Composed for Qmars Piraglu (formerly Siamak Noory)
Premier: 9 February, 2007 (St Andrews on the Terrace, The Asia Pacific Festival/26th ACL Festival & Conference, Wellington, New Zealand, 8-16 February, 2007)
Duration: 13’01”
Copyright © 2005 Andrián Pertout
PROGRAMME NOTES
At the beginning of the twentieth century during the Pahlavi dynasty (1925-1979) we begin to see the resurgence of theoretical research into the Persian theory of
intervals and scales. This ideological shift in affect being the impetus for three separate theories on intervals and scales of Persian music proposed in the twentieth
century: the twenty-four quarter-tone (equally-tempered) scale proposed by Ali Naqi Vaziri in the 1920s, the alternative twenty-two-note scale proposed by
Mehdi Barkešli in the 1940s based on Pythagorean principles, as well as the theory of the five primary intervals of performance practice presented by Hormoz Farhat
in his 1990 publication The Dastgàh Concept in Persian Music.
‘Àzàdeh’ for Santñr and Tape – composed for Iranian santñrist Qmars Piraglu (formerly Siamak Noory) – features the Persian santär (72-string box zither), and serves
as a practical study of Persian tuning systems, with its presentation of both ‘theoretical’ and ‘performance practice’ tunings. Within the context of an analysis of the
tuning methodology of performer Qmars Piraglu, an attempt is made to make comparisons not just with the three propositions outlined previously, but also with
other existing alternative tuning systems. This discussion presented in order to generate a greater understanding of the musical processes that govern the theory of
Persian intervals, at the same time disclosing some of the strategies employed in the general contemporary ‘cross-cultural’ compositional process.
The work incorporates six of the most prominent elements of the radif of the dastgàh-e Segàh belonging to the school of Musa Maaroufi. Pitch material from the
main gušes, which include guše-ye Zàbol, Mñye, Moxàlef and Maqlub, as well as the daràmad and forñd have been accessed and catagorized (according to Qmars
Piraglu) to then be utilized in adherence to Western contemporary compositional practices, and therefore resulting in a work that has no intention in representing
Persian classical music tradition. The juxtaposition of notated improvisation along with corresponding Taknavåzi-e Santñr (Santär ad-lib solo) sections for each of the
gušes a representation of the composer/performer culturally distinct artistic perspective.
A structural scheme based on ‘golden mean’ or ‘golden section’ proportions has been incorporated in the linear plan. The aesthetic notion of these proportions
being a technique directly borrowed from art and architecture, with its conceptual basis stating that “if the proportion of ‘ab’ to ‘bc’ is the same as the proportion
of ‘bc’ to the whole line, then ‘ac’ is segmented according to the golden mean.” The fraction represented by this ideology is .618, and manifests itself in the work
at guêe-ye Moxàlef with its introduction of melodic material based on the second tetrachord of dastgàh-e Segàh.
The tape element of ‘Àzàdeh’ includes sampled santär (tuned to Barkešli’s ‘Twenty-Two-Note Division of the Octave’) and sampled vocals – combining an F pedal
point or drone (with a 500ms and 250ms rhythmic pulse), structural markers, and the recitation of poetry by Qmars Piraglu.
4 Œzœdeh
The Artist
Iranian artist Qmars Piraglu (formerly Siamak Noory) was born in Tehran in 1961, and initiated his musical
education at the age of five via Orff instruments (children’s instruments designed by Carl Orff [1895-1982]
such as the xilophon, metalophon and vibraphon). Following a seven-year period, he then adopted the
Persian santär (a 72-string [or 18 quadruple-stringed] box zither), initially learning the instrument under the
guidance of Ms Farzaneh Noshad (a student at the Persian Traditional Music Conservatory in Tehran).
Three years later, he is accepted as a student of “one of Iran’s greatest contemporary composers and
master santärists,” Faramarz Payvar. For the next eight years Qmars develops his knowledge and
understanding of the complete Persian classical music repertoire. As well as this, he synchronically
studies Western music – the pianoforte with Taher Djalili (a pianist from the Music Conservatory), and for a
year, the bassoon with Khosrow Soltani. Qmars ultimately escaped from Iran in 1986 (during the Iran-Iraq
war of the eighties), arriving in Turkey as a refugee, to then temporarily settle in Belgium, where he studied
the piano at the Music Academy in Antwerp with Hedvig Vanvarenberg, before establishing a permanent
base in Sweden in 1989. Here he studied the piano for two years at the Birkagårdens Folkhögskolan in Stockholm with Stella Tchaikowsky, and went on to graduate
from the University of Göteborg with a Bachelor of Science in Musicology. Since 2001, Qmars has been living in Melbourne, Australia. In 2003, he completed a
Master of Music (MMus) degree at the University of Melbourne, and is currently undertaking a Doctor of Philosophy (PhD) degree at Monash University.
The Instrument
The Persian or Iranian santär is an integral part of the traditional orchestra, sharing the lute repertoire of the tàr and setàr. It is also utilized in the motrebi
‘entertainment music’ genre, but folk styles are excluded. An article by Jean During, Scheherazade Q. Hassan and Alastair Dick describes the santär’s constructing
thus: “The santär consists of a trapeziform case made of walnut wood, approximately 90cm wide at the broad end, 35cm wide at the narrow end and 6cm deep.
The sides form an angle of 45 degrees to the wider end. The strings are fixed to hitch-pins along the left-hand side and wound round metal wrest-pins on the right
by means of which they are tuned with a tuning-key. Each quadruple set of strings rests on a movable bridge of hardwood (kharak). These bridges are aligned
almost parallel with the sides of the case. The right-hand rank corresponds to the bass strings and that on the left to the treble strings. In the centre of the santär the
low-pitched strings on the right cross the high-pitched strings on the left.” Adding to this, the instrument features three courses of strings (the bass strings, made of
brass, while the treble ones, steel), with a total of 72 strings, or 18 groups of strings, capable of producing 27 different pitches, and is played “by striking the strings
with two hammers (mezràb) held in three fingers of each hand.”
Œzœdeh 5
The Text
“Kas nadànad darde bi darmàne mà,
Jore Leili dar dele por êñre mà.
Hazar kardim ze haráe xalgo donyà
Kajàst Àzàdeh in mahpeykare mà?”
Àzàdeh, Qmars Piraglu.
“Nobody knows the pain inside me,
The pain that emanates, being away from my beloved Àzàdeh.
Because my soul is with her, I am oblivious to everybody and everything
Where is my beloved Àzàdeh, who reflects the beauty of moonlight?”
Àzàdeh, Qmars Piraglu.
6 Œzœdeh
The Harmonic Characteristics of ‘Dastgàh-e Segàh’
Dastgàh-e Segàh in the Key of F
First Tetrachord
1. daràmad-e Segàh
2. guêe-ye Zabçl
Œzœdeh 7
3. guêe-ye Mñye
Second Tetrachord
4. guêe-ye Moxàlef
5. guêe-ye Maqlub
6. forñd-e Segàh
dastgàh = (organization, system); guêe = (corner, section, piece); daràmad = (opening, introduction); finalis “F” = note of repose and conclusion; ist “I” = (stop), ending note for phrases;
êahed “Š” = (witness), prominent note; forñd = (descent, cadence)
(Hormoz Farhat, The Dastgàh Concept in Persian Music, New York: Cambridge U. Press, 1990.)
8 Œzœdeh
INSTRUMENTATION
Santñr
Persian 72-string (or 18 quadruple-stringed) box zither
Tuning of the Santñr for Dastgàh-e Segàh (on F)
Tape – Sampled Santñr and Vocals (CD player) Transposed score
Œzœdeh 9
PERFORMANCE NOTES
In this score, accidentals apply throughout the bar (a bar in this particular case representing a unit of time equal to one-sixtieth of a minute, or two beats of a 2/4 bar
at Ê=120, marked numerically in the score in five-second increments).
Two tuning systems are proposed: The theoretical 'Twenty-Two Note Division of the Octave' of Persian scholar Mehdi Barkešli based on the cycle of fifths and the
‘performance practice’ dastgàh-e Segàh santär tuning obtained via the intervallic analysis of Persian performer Qmars Piraglu’s instrument.
The Ali Naqi Vaziri Notation System (The Accidentals of Persian Music) is utilized in the score, which is fully disclosed in the section following.
The Ali Naqi Vaziri Notation System (The Accidentals of Persian Music)
sori – raised by one Pythagorean limma (90.225 cents)
sharp – raised by one limma and one Pythagorean comma (113.685 cents)
koron – lowered by one Pythagorean limma (90.225 cents)
flat – lowered by one limma and one Pythagorean comma (113.685 cents)
Santär
muffle string/s with fingers
mano destra (left-hand)
10 Œzœdeh
mano sinistra (right-hand)
9th bridge
roll note
unmeasured tremolo (rapid alternations between the two notes)
strike both pitches simultaneously, and then execute an unmeasured tremolo
strike the lower pitch, and then execute an unmeasured tremolo
strike pitch (or pitches, if more than one) singularly
mordent (rapid alternation between the principal note and its lower neighbour)
inverted or upper mordent (rapid alternation of the principal note with its upper neighbour)
turn (stepwise descent of three notes beginning with the upper neighbour, followed by a return to the principal note)
rapid alternations between the principal note and its upper neighbour, beginning with the latter
rapid alternations between the principal note and its lower neighbour, beginning with the latter
rapid alternations between the principal note and its upper neighbour, beginning with the latter and featuring termination (a turned ending)
rapid alternations between the principal note and its upper neighbour chromatically altered
Taknavàzi-e Santär Santär ad-lib solo
Œzœdeh 11
Mehdi Barkešli’s Twenty-Two-Note Division of the Octave Relative Pitch: A4=440Hz / C4 (middle C)=261.6255654Hz
DEGREE
NUMBER
NOTE INTERVAL RATIO
(FRACTION)
RATIO
(DECIMAL)
FREQUENCY
(HERTZ)
CENTS TUNING
ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ ÑÙ ÒÐ ÒÑ ÒÒ
ÐÑ
CCÎ CÚ Dî D
DÎ DÚ Eî E F
FÎ FÚ Gî G
GÎ GÚ Aî A BÝ AÚ Bî B
C
unison
superoctave [6] (D) V
Pythagorean apotome, or chromatic semitone [7] (A) VII
neutral second [8] (D) X
just major tone (A) II (9th harmonic)
supermajor second [9] (D) III
Pythagorean augmented second [10] (A) IX
neutral third [11] (D) VIII
Pythagorean major third, or ditone (A) IV (81st harmonic)
just and Pythagorean perfect fourth (D) I
superfourth [12] (D) VI
Pythagorean tritone, or augmented fourth [13] (A) VI
subfifth [14] (D) XI
just and Pythagorean perfect fifth (A) I (3rd harmonic)
superfifth [1] (D) IV
Pythagorean augmented fifth [2] (A) VIII
neutral sixth [3] (D) IX
Pythagorean major sixth (A) III (27th harmonic)
Pythagorean minor seventh (D) II
Pythagorean augmented sixth [4] (A) X
neutral seventh [5] (D) VII
Pythagorean major seventh (A) V
octave
1/1
256/243
2187/2048
65536/59049
9/8
32/27
19683/16384
8192/6561
81/64
4/3
1024/729
729/512
262144/177147
3/2
128/81
6561/4096
32768/19683
27/16
16/9
59049/32768
4096/2187
243/128
2/1
1.000000
1.053498
1.067871
1.109858
1.125000
1.185185
1.201355
1.248590
1.265625
1.333333
1.404664
1.423828
1.479811
1.500000
1.580247
1.601807
1.664787
1.687500
1.777778
1.802032
1.872885
1.898438
2.000000
261.626
275.622
279.382
290.367
294.329
310.075
314.305
326.663
331.120
348.834
367.496
372.510
387.156
392.438
413.433
419.074
435.551
441.493
465.112
471.458
489.995
496.680
523.251
0.000
90.225
113.685
180.450
203.910
294.135
317.595
384.360
407.820
498.045
588.270
611.730
678.495
701.955
792.180
815.640
882.405
905.865
996.090
1019.550
1086.315
1109.775
1200.000
+00
ß10
+14
ß20
+04
ß06
+18
ß16
+08
ß02
ß12
+12
ß22
+02
ß08
+16
ß18
+06
ß04
+20
ß14
+10
+00
12 Œzœdeh
Tuning of the Santñr
The tuning of the santñr for dastgàh-e segàh (on F) presents the following series of pitches: C3, F3, G3, Aù3, B"3, C4, Dù4, E"4, F4 (first position); Eù4, F4, G4, Aù4, B"4,
C5, Dù5, E"5, F5 (second position); and Eù5, F5, G5, A"5, B"5, C6, Dù6, E6, F6 (third position). The ‘position’ is in reference to each of the instrument’s three courses of
strings. The instrument’s design consisting of eighteen quadruple set of strings, with the division via movable bridges of the second set of nine strings generating the
second and third courses (two individual pitches generally tuned octaves apart), to produce twenty-seven pitches in total. The santñrist generally commencing with
the tuning of the first front string, which then becomes the basis for the generation of unison intervallic relationships (removing beating as much as possible) with the
other three strings of each set. An interesting point of note is that although the primary structure of dastgàh-e segàh can be essentially stated to be heptatonic, in
performance practice the scale is expanded into a three-octave scale with dissimilar tetrachords. Some points of interest include the low brass string tuned to C'; the A’s in the first two octaves tuned to Aù, while in the third, tuned to A"; E" and Eù alternatives provided in two octaves; and the duplication of F pitches in the
second and third octaves. The design of the instrument – providing a total of nine strings per octave, with two strings, E and F, tunable to either E', E" or Eù; and F' or F! respectively – allowing for the performance of heptatonic scales (inclusive of their auxiliary pitches) from the complete Persian modal system.
Spectrum Analysis Results
The following three tables (tuning no. 1, 2, and 3 of the santñr for dastgàh-e segàh [on F]) present the spectrum analysis results collected on three separate
occasions (with a periodicity of 3-6 months) for each of the twenty-seven sets of strings, and therefore denotes all data for string set, pitch, order, frequency (Hz),
ratio (decimal), and cents. The calculation of frequency represents prime (not normalized) data, and therefore ratio and cents are the only two comparative frames
of reference. Ratios have been calculated from the relationship of frequencies to the base pitch of the second position C5 (526.350Hz, 526.400Hz, and
523.730Hz respectively for each of the three tunings), while cents are a derivative of ratio data. An analysis of simultaneous sonorities based on the tuning process
for the three tunings reveal octaves with a mean value of 1201.019 cents, a range between 1181.941 and 1218.810 cents, and a standard deviation of 7.771183;
perfect fifths with a mean value of 706.894 cents, a range between 694.718 and 716.381 cents, and a standard deviation of 6.537279; perfect fourths with a mean
value of 497.436 cents, a range between 483.049 and 514.208 cents, and a standard deviation of 7.640715; tempered perfect fourths with a mean value of
501.373 cents, a range between 488.349 and 518.700 cents, and a standard deviation of 8.744854; and neutral thirds with a mean value of 350.057 cents, a
range between 338.758 and 355.954 cents, and a standard deviation of 6.396299. The fourth table presents an ‘analysis of variance’ with regards to the three
tunings, and therefore provides a platform for the evaluation of the tuning of the seventy-two strings of the santñr for dastgàh-e segàh (on F) utilizing average and
standard deviation criterion. In this case standard deviation has been derived from cents data, and frequencies normalized to A=440Hz, although in direct relation
to ratio data, which has been obtained via the mathematical equation of 1200ïcentsÏ 24 2 =ratio.
Œzœdeh 13
Tuning of the Santñr for Dastgàh-e Segàh (on F) – Tuning no. 1
1st position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
C3 F3 G3 Aî3 BÝ3 C4 Dî4 EÝ4 F4
3 (I-iii)6 (II-ii)
12 (III-ii) 18 (V-ii) 15 (IV-ii)
2 (I-ii) 20 (VI-ii) 23 (VII-ii) 10 (II-vi)
130.830174.990 196.480 213.800 232.060 261.390 286.780 310.080 351.200
1.9884871.329838 1.493151 1.624774 1.763541 1.986435 1.089693 1.178227 1.334473
1190.005 493.500 694.032 840.287 982.171
1188.218 148.706 283.942 499.524
2nd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ
Eî4 F4 G4 Aî4 BÝ4 C5 Dî5 EÝ5 F5
25 (VIII-i)5 (II-i)
11 (III-i) 17 (V-i) 14 (IV-i)
1 (I-i) 19 (VI-i) 22 (VII-i) 8 (II-iv)
322.540350.090 394.970 429.610 465.950 526.350 578.200 620.720 703.100
1.2255721.330256 1.500788 1.632412 1.770495 1.000000 1.098509 1.179291 1.335803
352.147 494.044 702.865 848.406 988.983 0.000
162.655 285.504 501.249
3rd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÙ ÒÐ ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ ÒÖ Ò×
Eî5 F5 G5 AÝ5 BÝ5 C6 Dî6 EÝ6 F6
26 (VIII-ii)7 (II-iii)
13 (III-iii) 27 (IX-i) 16 (IV-iii) 4 (I-iv)
21 (VI-iii) 24 (VII-iii)
9 (II-v)
645.220697.240 788.260 827.400 930.310 1049.300 1144.400 1246.000 1406.200
1.2258381.324670 1.497597 1.571958 1.767474 1.993540 1.087109 1.183623 1.335803
352.522 486.759 699.179 783.075 986.027
1194.399 144.596 291.852 501.249
14 Œzœdeh
Tuning of the Santñr for Dastgàh-e Segàh (on F) – Tuning no. 2
1st position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
C3 F3 G3 Aî3 BÝ3 C4 Dî4 EÝ4 F4
3 (I-iii)6 (II-ii)
12 (III-ii) 18 (V-ii) 15 (IV-ii)
2 (I-ii) 20 (VI-ii) 23 (VII-ii) 10 (II-vi)
130.790174.260 197.400 213.740 231.990 260.930 286.690 310.050 351.170
1.9876901.324164 1.500000 1.624164 1.762842 1.982751 1.089248 1.178002 1.334233
1189.311 486.098 701.955 839.637 981.484
1185.004 147.999 283.610 499.212
2nd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ
Eî4 F4 G4 Aî4 BÝ4 C5 Dî5 EÝ5 F5
25 (VIII-i)5 (II-i)
11 (III-i) 17 (V-i) 14 (IV-i)
1 (I-i) 19 (VI-i) 22 (VII-i) 8 (II-iv)
322.490348.840 394.670 428.470 465.940 526.400 578.150 620.620 703.090
1.2252661.325380 1.499506 1.627926 1.770289 1.000000 1.098309 1.178989 1.335657
351.714 487.687 701.385 843.642 988.782 0.000
162.341 285.061 501.060
3rd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÙ ÒÐ ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ ÒÖ Ò×
Eî5 F5 G5 AÝ5 BÝ5 C6 Dî6 EÝ6 F6
26 (VIII-ii)7 (II-iii)
13 (III-iii) 27 (IX-i) 16 (IV-iii) 4 (I-iv)
21 (VI-iii) 24 (VII-iii)
9 (II-v)
645.160697.280 788.220 829.380 930.230 1048.700 1144.200 1254.800 1406.000
1.2256081.324620 1.497378 1.575570 1.767154 1.992211 1.086816 1.191869 1.335486
352.197 486.694 698.927 787.049 985.714
1193.245 144.129 303.871 500.838
Œzœdeh 15
Tuning of the Santñr for Dastgàh-e Segàh (on F) – Tuning no. 3
1st position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
C3 F3 G3 Aî3 BÝ3 C4 Dî4 EÝ4 F4
3 (I-iii)6 (II-ii)
12 (III-ii) 18 (V-ii) 15 (IV-ii)
2 (I-ii) 20 (VI-ii) 23 (VII-ii) 10 (II-vi)
131.160174.570 197.130 212.300 231.460 262.250 285.400 311.140 346.900
1.0017381.333282 1.505585 1.621446 1.767781 1.001470 1.089875 1.188169 1.336185
3.005 497.979 708.389 836.737 986.328 2.543
148.995 298.489 501.743
2nd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ
Eî4 F4 G4 Aî4 BÝ4 C5 Dî5 EÝ5 F5
25 (VIII-i)5 (II-i)
11 (III-i) 17 (V-i) 14 (IV-i)
1 (I-i) 19 (VI-i) 22 (VII-i) 8 (II-iv)
320.500348.970 394.930 427.390 462.800 523.730 569.000 617.650 698.550
1.2239131.332633 1.508144 1.632101 1.767323 1.000000 1.086438 1.179329 1.333798
349.801 497.136 711.328 848.076 985.879 0.000
143.526 285.560 498.648
3rd position
STRING SET NOTE ORDER FREQUENCY (HERTZ) RATIO (DECIMAL) CENTS ÑÙ ÒÐ ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ ÒÖ Ò×
Eî5 F5 G5 AÝ5 BÝ5 C6 Dî6 EÝ6 F6
26 (VIII-ii)7 (II-iii)
13 (III-iii) 27 (IX-i) 16 (IV-iii) 4 (I-iv)
21 (VI-iii) 24 (VII-iii)
9 (II-v)
638.520695.250 791.640 824.560 925.770 1051.000 1141.700 1242.500 1396.800
1.2191781.327497 1.511542 1.574399 1.767647 1.003380 1.089970 1.186203 1.333512
343.090 490.450 715.226 785.761 986.197 5.84102 149.146 295.621 498.276
16 Œzœdeh
Tuning of the Santñr for Dastgàh-e Segàh (on F) – Analysis of Variance
1st position
STRING SET NOTE FREQUENCY (HERTZ) RATIO (DECIMAL) AVERAGE (CENTS) STANDARD DEVIATION ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
C3 F3 G3 Aî3 BÝ3 C4 Dî4 EÝ4 F4
130.368173.862 196.163 212.369 230.848 260.408 285.069 309.099 349.261
1.9932041.329089 1.499570 1.623461 1.764720 1.990689 1.089605 1.181457 1.334963
1194.107492.526 701.459 838.887 983.327
1191.922 148.566 288.680 500.160
7.7138465.999891 7.191309 1.889998 2.620925 9.337949 0.512523 8.496235 1.380069
2nd position
STRING SET NOTE FREQUENCY (HERTZ) RATIO (DECIMAL) AVERAGE (CENTS) STANDARD DEVIATION ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ
Eî4 F4 G4 Aî4 BÝ4 C5 Dî5 EÝ5 F5
320.470347.810 393.173 426.662 462.912 523.251 572.642 617.019 698.585
1.2249171.329419 1.502808 1.630811 1.769368 1.000000 1.094404 1.179203 1.335086
351.221492.956 705.193 846.708 987.881 0.000
156.174 285.375 500.319
1.2480944.817387 5.365009 2.660578 1.737114 0.000000
10.954514 0.273364 1.450061
3rd position
STRING SET NOTE FREQUENCY (HERTZ) RATIO (DECIMAL) AVERAGE (CENTS) STANDARD DEVIATION ÑÙ ÒÐ ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ ÒÖ Ò×
Eî5 F5 G5 AÝ5 BÝ5 C6 Dî6 EÝ6 F6
640.217693.619 786.006 823.584 924.807 1048.400 1138.557 1242.435 1397.011
1.2235371.325595 1.502158 1.573975 1.767425 1.001813 1.087964 1.187227 1.334933
349.270487.968 704.444 785.295 985.979
1197.828 145.957 297.115 500.121
5.3541952.149959 9.338180 2.027411 0.245081 6.963106 2.771441 6.147445 1.610794
Œzœdeh 17
Utilizing the mean ratios from the ‘analysis of variance’ data, and considering solely the base pitch of second position C5, as well as all primary derivative pitches
(second position F4, G4, B"4, Aù4, Dù5, E"5, Eù4, and third position A"5), it is possible to arrive at the ‘tuning characteristics’ personified by the three tunings, and therefore what may be stated as being a ‘performance practice’ tuning obtained via the intervallic analysis of Persian performer Qmars Piraglu’s
instrument, which was tuned to dastgàh-e segàh by ear, and therefore not artificially influenced by tuning devices in order to adhere to strict theoretical schemes.
Piraglu’s tuning methodology involving the obtaining of a fundamental C note calibrated approximately to A=440Hz, which would then serve as the reference for
the generation of all required perfect fifths and fourths, as well as tempered fourths, with problem intervals such as A koron and A flat left to the discretion of the ear
and the perceived musicality of performed extracts from associated gušes (individual pieces which make up the repertoire of a particular dastgàh).
Dastgàh-e Segàh (on F) – Tuning Characteristics
Relative Pitch: A4 = 440Hz/C4 (Middle C) = 261.6255654Hz
DEGREE NUMBER
NOTE APPROXIMATE INTERVAL FREQUENCY (HERTZ)
RATIO (DECIMAL)
AVERAGE (CENTS)
ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
ÐÑ
C4 D4 EÝ4 Eî4 F4 G4 Aî4 BÝ4 Bî4
C5
unison just major tone (9th harmonic)
Pythagorean minor third, or trihemitone neutral third
just and Pythagorean perfect fourth just and Pythagorean perfect fifth (3rd harmonic)
grave or small major sixth Pythagorean minor seventh
grave or small major seventh
octave
261.626 295.748 309.753 320.939 348.206 393.594 430.750 464.127 482.120
523.251
1.000000 1.130424 1.183957 1.226709 1.330933 1.504416 1.646439 1.774012 1.842785
2.000000
0.000 212.237 292.339 353.752 494.926 707.044 863.219 992.419
1058.265
1200.000
The abovementioned process consequentially producing intervals approximating the just major tone (9/8), Pythagorean minor third, or trihemitone (32/27), neutral
third (11/9), just perfect fourth (4/3), just perfect fifth (3/2), grave or small major sixth (400/243), Pythagorean minor seventh (16/9), and grave or small major seventh
(50/27). The findings proclaiming the obvious Pythagorean connection with the resulting ‘mean’ measurements for the major second (equal to 212.237 cents, with
a range between and 208.821 and 214.193 cents, and a standard deviation of 2.968984); minor third (equal to 292.339 cents, with a range between 288.626
18 Œzœdeh
and 299.361 cents, and a standard deviation of 6.084603); perfect fourth (equal to 494.926 cents, with a range between 488.743 and 501.094 cents, and a
standard deviation of 6.175730); perfect fifth (equal to 707.044 cents, with a range between 702.864 and 712.313 cents, and a standard deviation of 4.817387);
and minor seventh (equal to 992.419 cents, with a range between 988.424 and 997.374 cents, and a standard deviation of 4.551339). The research interestingly
also suggesting a distinction between the neutral orientation of microtonal inflections such as Eù4 (equal to 353.752 cents, with a range between 350.940 and 355.954 cents, and a standard deviation of 2.562172); Aù5 (equal to 863.219 cents, with a range between 846.391 and 874.654 cents, and a standard deviation of 14.883326); and Bù4 (equal to 1058.265 cents, with a range between 1052.666 and 1064.027 cents, and a standard deviation of 5.682304); which reveal a ‘grave or small major’ intervallic orientation. A tuning system comparison table incorporating data from the twenty-four equally-tempered quarter-tone scale of Vaziri, twenty-two-note scale of Barkešli,
and the theory of flexible intervals, or of the five primary intervals of performance practice of Farhat, as well as the performance practice tuning of Piraglu reveals a
close link between the latter two. Farhat and Piraglu sharing similarities with all intervals (a falsity of +8.237, ß1.661, ß10.248, ß3.074, +5.044, +1.219, ß3.581,
and ß7.735 on each count) but for the neutral third (Eî4), which has a closer association with the equally-tempered quarter-tone of Vaziri (a falsity of +3.752, as
opposed to ß10.248).
Dastgàh-e Segàh (on F) – Tuning System Comparison
DEGREE NUMBER
NOTE ALI NAQI VAZIRI (CENTS)
MEHDI BARKEÊLI
(CENTS) HORMOZ FARHAT
(CENTS) QMARS PIRAGLU
(CENTS)
ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ
ÐÑ
C4 D4 EÝ4 Eî4 F4 G4 Aî4 BÝ4 Bî4
C5
0.000 200.000 300.000 350.000 500.000 700.000 850.000 1000.000 1050.000
1200.000
0.000 203.910 294.135 384.360 498.045 701.955 882.405 996.090 1086.315
1200.000
0.000 204.000 294.000 364.000 498.000 702.000 862.000 996.000
1066.000
1200.000
0.000 212.237 292.339 353.752 494.926 707.044 863.219 992.419 1058.265
1200.000
Œzœdeh 19
Utilizing Farhat’s theory of the division of the whole-tone and nomenclature for Persian intervals, it is then possible to conduct an analysis of all minor second (D and
E"), small neutral tone (Eù and F, Bù and C), large neutral tone (D and Eù, G and Aù), and major second (C and D, E" and F, F and G, B" and C) intervals encountered
within the framework established via the base and primary derivative pitches in the performance practice tuning of Qmars Piraglu, and consequently produce a
comparison table outlining range, as well as the average for each interval in the two supportive propositions.
Dastgàh-e Segàh (on F) – Hormoz Farhat’s and Qmars Piraglu’s Division of the Whole-Tone
DEGREE NUMBER
INTERVAL HORMOZ FARHAT RANGE (CENTS)
HORMOZ FARHAT AVERAGE (CENTS)
QMARS PIRAGLU RANGE (CENTS)
QMARS PIRAGLU AVERAGE (CENTS)
ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ
unison minor second
small neutral tone large neutral tone
major second
0.000 90.000
125.000 � 145.000 150.000 � 170.000
204.000
0.000 90.000
135.000 160.000 204.000
0.000 74.433 � 85.664
135.973 � 147.334 136.747 � 162.655 200.117 � 214.193
0.000 80.102
141.454 148.845 208.631
In conclusion, it must be stated that Farhat’s theory of flexible intervals or of the five primary intervals of performance practice certainly holds true in the final analysis,
and especially in view of the fact that although general assumptions may be reached with regards to tuning practice, there is no doubt that standard deviation data
is so conflicting in some instances (the three tunings producing an overall standard deviation average of 3.258156, with a range between 0.245081 and 10.954514,
while octaves between 0.187035 and 13.715187, perfect fifths between 3.980471 and 9.338180, perfect fourths between 1.450061 and 7.960749, tempered
fourths between 1.897984 and 12.340378, and neutral thirds between 2.562172 and 7.399249) that the results cannot be stated as being the axiom.
In support of these findings, in Intervals, Scales and Temperaments: An Introduction to the Study of Musical Intonation Boyle makes the appropriate observation that
“sounds should be pitched according to the dictates of the ear. For this certain notes in the scale must be free to move about a comma (approximately 21.506
cents), which is perfectly possible on all but keyboard instruments.” It is further relevant to note that according to foreword contributor Kenneth Van Barthold, in the
piano tuning practice of the latter part of the twentieth century, octaves began to be often “stretched for added brilliance,” and therefore “theoretically accurate
equal temperament” has never existed in piano tuning, with stretched octaves often induced in the highest and lowest octaves. Theoretically accurate octaves or
the ratio 2/1 defined in musical acoustics by a “beat-free condition between all the partials of the upper musical tone and the even-numbered partials of the lower
tone.” Stretched, as well as compressed octaves a common occurrence in Piraglu’s tuning of the santñr.
20 Œzœdeh
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46 Œzœdeh
Andrián Pertout
Exposiciones for Sampled Microtonal Schoenhut Toy Piano
No. 392
Composed between February and July, 2005
Composed for the Extensible Toy Piano Project (Clark University, Department of Visual and Performing Arts, 4-5 November, 2005, Worcester, MA, USA) Hommage à Frank Zappa (1940-1993)
World Premier: 5 November, 2005 (Razzo Recital Hall, Traina Center for the Arts, Clark University, Worcester, MA, USA) Latin American Premier: 10 March, 2006 (Museo de Ron, International Electroacoustic Music Festival ‘Spring in Havana’ 2006, 6-12 March, 2006, Havana, Cuba)
European Premier: 24 October, 2006, Logos Tetrahedron, Ghent, Belgium Australian Premier: 11 July, 2006 (Scott Theatre, Elder Conservatorium of Music, University of Adelaide, Medi(t)ations: Computers, Music and Intermedia, Australasian
Computer Music Association Conference 2006, 11-13 July, 2006, Adelaide, Australia) Duration: 7’00”
Copyright © 2005 Andrián Pertout
PROGRAMME NOTES
“It has a deceptively simple mechanism – plastic hammers hitting steel rods. Yet, the toy piano produces a rich and quirky sound palette. John Cage brought the
instrument from a treasured plaything to a bona fide musical instrument with his Suite for Toy Piano (1948). Our aim is to bring the instrument into the 21st Century.”
The Extensible Toy Piano Project, Clark University, Department of Visual and Performing Arts, Worcester, MA, USA
The history of the toy piano (Fr. piano jouet; Ger. Spielzeugklavier; It. pianino-giocattolo) begins as Troiger’s ‘Stahlklavier’ (Dessau, 1792) and Franz Schuster’s
‘Adiaphonon’ (Vienna, c. 1818), to be later developed in Philadelphia, USA, in 1872, where German immigrant Albert Schoenhut ultimately conceives the child’s toy
that in time will also capture the imagination of the contemporary composer. The instrument is usually made out of wood or plastic, and is dimensionally less than
fifty centimetres in width, with a range between two diatonic and three chromatic octaves. It has a simple sounding mechanism (similar to that of the full-sized
keyboard glockenspiel) consisting of plastic hammers operated via a keyboard, which strike fixed metal plates or steel rods. Traditionally, toy pianos were modelled
on uprights, but following the 1950s grand piano varieties were commonplace.
Contemporary works that have incorporated the toy piano include John Cage’s Suite for Toy Piano (1948) and George Crumb’s Ancient Voices of Children (1970),
as well as other works by Renaud Gagneux, Mauricio Kagel, Louis Roquin, Zygmunt Krauze, and Leonid Aleksandrovich, among many. Internationally acclaimed
concert pianist Margaret Leng Tan made her debut on the toy piano in 1993 at New York’s Lincoln Centre, and went on to introduce the model 6625, 25-key
Schoenhut Traditional Spinet to Carnegie Hall in 1997; also releasing ‘The Art of the Toy Piano’ in that same year – a collection of works by Stephen Montague, John
Lennon and Paul McCartney, Toby Twining, Jed Distler, Philip Glass, David Lang, Julia Wolfe, Ludwig van Beethoven, Guy Klucevsek, Raphael Mostel, and Erik Satie.
‘Exposiciones’ for Sampled Microtonal Schoenhut Toy Piano is an ‘acousmatic’ work that attempts to explore the equally-tempered sound world within the context
of a sampled microtonal Schoenhut model 6625, 25-key toy piano and a complex polyrhythmic scheme. All equal temperaments between 1 and 24 – essentially
functioning as tuning modulations – as well as all polyrhythms (divisible only by 1 and including their inversions) between the ranges of 2 and 15 are presented. In
other words, polyrhythmic ratios 3:2Ê (2:3Ê�), 5ç:2Ê (2É:5Ê�), 4:3Ê (3:4�), 5:3Ê (3:5�), and so on – 57 polyrhythmic sets in total, with the last set represented by 15:14Ê (14:15Ê) – alongside two complementary scales (Indonesian Pélog and Sléndro forms with primary and secondary scale tones, as well as primary and secondary
auxiliary tones) shaped via microtonal inflections produced by sequential tuning modulations featuring the first 24 equally-tempered divisions of the octave.
50 Exposiciones
The intervallic structure of the pentatonic scales defined by the ratios of just intonation, or the ‘Scale of Proportions’ (The Harmonic Division of the Octave) as
presented by Alain Daniélou in Music and the Power of Sound: The Influence of Tuning and Interval on Consciousness (1995) – the current edition of his 1943
monumental work Introduction to the Study of Musical Scales. The ‘Scale of Proportions’ is based on the harmonic series. It is a division of the octave into fifty-
three distinct intervals, and 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. The quarter-tone (three-quarter-tone), a result of the further division of the disjunctions of this scale (major half-tone, or just diatonic semitone), giving a
total of sixty-six unique intervals (the octave included). In Indian musical theory this system referred to as ‘The Sixty-Six Ærutis’. The notation (inspired by Alain
Daniélou’s work and highly illustrative of the effect of each equal temperament on the two scales and their consequential intervallic deviation from just intonation),
based on approximate syntonic comma (81/80, or 21.506 cents) subdivisions of the just major tone (9/8, or 203.91 cents) and resulting in the following scheme:
Note C C¢ C£ CË / Dì CÚ D¹ D¸ DÝ CÍ / Dí D³ D² D
Interval unison syntonic comma great diesis Greek enharmonic or septimal quarter-tone small just chromatic semitone Pythagorean limma just diatonic semitone great limma three-quarter-tone small tone just minor tone just major tone (9th harmonic)
Ratio 1/1 81/80 128/125 31/30 25/24 256/243 16/15 27/25 135/124 800/729 10/9 9/8
Cents 0.000 21.506 41.059 56.767 70.672 90.225 111.731 133.238 147.143 160.897 182.404 203.91
The Schoenhut model 6625, 25-key toy piano samples (recorded in dead studio space [96kHz/24bit] by engineer John Shirley at Clark University, Department of
Visual and Performing Arts, Worcester, MA, USA, utilizing two Neumann TLM 103s [positioned front-L and back-R] and a Nuendo recorder) include three sets of
twenty-five (two-octave chromatic span) forte ( � ), mezzo forte ( � ), and piano ( � ) samples, as well as one corresponding set of keyboard release clicks. All
these sounds multi-sampled on an Akai S3000XL Midi Stereo Digital Sampler – tuned firstly to standard A=440 Hz twelve-tone equal temperament, modified within
thirty velocity cross-faded patches, and then operated via a midi sequencer; a gong-like detuned middle C (octave down) sounding the tonal centre, as well as
marking the downbeat, while another severely gated alternative providing the rhythmic pulse (downbeats and upbeats).
Exposiciones 51
Polyrhythm 1-16 Set
1-et
2-et
3-et
4-et
5-et
6-et
7-et
8-et
9-et
10-et
11-et
12-et
13-et
14-et
15-et
16-et
17-et
18-et
19-et
20-et
21-et
22-et
23-et
24-et
3:2Ê 5ç:2Ê 4:3Ê 5:3Ê 7ç:2Ê 7ç:3Ê 8ç:3Ê 6:5Ê 11è:2Ê 8:5Ê 9:5Ê 8:7Ê 9:7Ê 12ç:5Ê 13ç:5Ê 13ç:6Ê 13:7Ê 11:10Ê 15:8Ê 12:11Ê 14:11Ê 15:11Ê 15:13Ê 15:14Ê
(2:3Ê ) (2É:5Ê ) (3:4�) (3:5�) (2É :7Ê ) (3É :7Ê ) (3É:8Ê ) (5:6Ê ) (2È:11Ê) (5:8Ê) (5:9Ê) (7:8Ê) (7:9Ê) (5É:12Ê) (5É:13Ê) (6É:13Ê) (7:13Ê) (10:11Ê) (8:15Ê) (11:12Ê) (11:14Ê) (11:15Ê) (13:15Ê) (14:15Ê)
5:4Ê 9è:2Ê 7:4Ê 7:5Ê 10ç:3Ê 7:6Ê 13è:2Ê 13è:3Ê 15è:2Ê 11:6Ê 11:7Ê 12:7Ê 11:9Ê 15ç:7Ê 14:9Ê 13:11Ê 13:12Ê 14:13Ê
(4:5Ê ) (2È:9Ê ) (4:7Ê ) (5:7Ê ) (3É:10Ê) (6:7Ê) (2È:13Ê) (3È:13Ê) (2È:15Ê) (6:11Ê) (7:11Ê) (7:12Ê) (9:11Ê) (7É:15Ê) (9:14Ê) (11:13Ê) (12:13Ê) (13:14Ê)
9ç:4Ê 11ç:3Ê 11ç:4Ê 11ç:5Ê 14è:3Ê 10:7Ê 15ç:4Ê 11:8Ê 13:8Ê 13:9Ê 13:10Ê
(4É:9Ê) (3É:11Ê) (4É:11Ê) (5É:11Ê) (3È:14Ê) (7:10Ê) (4É:15Ê) (8:11Ê) (8:13Ê) (9:13Ê) (10:13Ê)
13ç:4Ê 9:8Ê 14ç:5Ê 10:9Ê
(4É:13Ê) (8:9Ê) (5É:14Ê) (9:10Ê)
Exposiciones 65
INSTRUMENTATION
PLAYER 1 Sampled Microtonal Schoenhut Toy Piano (Akai S3000XL Midi Stereo Digital Sampler)
Schoenhut Traditional Spinet (Model 6625, 25-key)
Piano features: 25-key two-octave designer spinet Age range: 3 and up Chromatically tuned with lovely chime like notes produced by little hammers striking precision ground, German steel music rods Play-by-colour teaching method makes playing simple and fun Removable colour strip fits behind the keys to guide small fingers from chord to chord Helps to build your child's confidence and develop basic playing skills Comes with a songbook which contains a collection of familiar tunes Available in mahogany, white, or red finish Dimensions: 19¾" high Ï 10¼" deep Ï 17" wide Matching bench: 9¼" high Ï 6" deep Ï 10" wide Weighs 17 lbs
66 Exposiciones
PERFORMANCE NOTES
In this score, accidentals apply throughout the bar.
The notation utilized in the score is based on Alain Daniélou’s ‘Scale of Proportions’ (The Harmonic Division of the Octave). It contains 23 unique symbols – 3
identical to conventional sharp (Ú), flat (Û), and natural (Ö) accidentals (raising, lowering or neutralizing a tone by 25/24, or 70.672 cents), with an additional 4
derived from standard quarter-tone notation in twentieth century contemporary music practice; the latter representative of the division of the ‘unequal’ major half-
tone, or just diatonic semitone (16/15), and not of the ‘equal’ quarter-tone (1:1.029302237, or 50.000 cents) derived from twenty-four-tone equal temperament
( 24 2 ). The quarter-tone symbols include (Ë) and (í), raising or lowering a tone by 31/30 (Greek enharmonic or septimal quarter-tone), or 56.767 cents; and (Í)
and (ì), raising or lowering a tone by 135/124 (three-quarter-tone), or 147.143 cents. Additional symbols include (¢, ¦, ¤, ¨) and (², ¶, ´, ¸), raising or lowering an
unaltered, naturalized, sharpened, or flattened tone by 81/80 (one syntonic comma), or 21.506 cents; and (£, §, ¥, ©) and (³, ·, μ, ¹), raising or lowering an
unaltered, naturalized, sharpened, or flattened tone by 128/125 (approximately two syntonic commas, or one great diesis), or 41.059 cents.
raised by one comma (81/80, or 21.506 cents)
raised by approximately two commas, or one great diesis (128/125, or 41.059 cents)
natural raised by one comma (81/80, or 21.506 cents)
natural raised by approximately two commas, or one great diesis (128/125, or 41.059 cents)
raised by one Greek enharmonic or septimal quarter-tone (31/30, or 56.767 cents)
raised by one small just chromatic semitone, or sharp (25/24, or 70.672 cents)
sharp raised by one comma (81/80, or 21.506 cents)
Exposiciones 67
sharp raised by approximately two commas, or one great diesis (128/125, or 41.059 cents)
sharp lowered by one comma (81/80, or 21.506 cents)
sharp lowered by approximately two commas, or one great diesis (128/125, or 41.059 cents)
raised by one three-quarter-tone (135/124, or 147.143 cents)
raised or lowered to natural tone
lowered by one comma (81/80, or 21.506 cents)
lowered by approximately two commas, or one great diesis (128/125, or 41.059 cents)
natural lowered by one comma (81/80, or 21.506 cents)
natural lowered by approximately two commas, or one great diesis (128/125, or 41.059 cents)
lowered by one Greek enharmonic or septimal quarter-tone (31/30, or 56.767 cents)
lowered by one small just chromatic semitone, or flat (25/24, or 70.672 cents)
flat lowered by one comma (81/80, or 21.506 cents)
flat lowered by approximately two commas, or one great diesis (128/125, or 41.059 cents)
flat raised by one comma (81/80, or 21.506 cents)
flat raised by approximately two commas, or one great diesis (128/125, or 41.059 cents)
lowered by one three-quarter-tone (135/124, or 147.143 cents)
68 Exposiciones
Sound Diffusion Matrix Razzo Recital Hall, Clark University, Department of Visual and Performing Arts
Worcester, MA, USA
The optimum method of performance for ‘Exposiciones’ for Sampled
Microtonal Schoenhut Toy Piano is 7-channel sound diffusion, with a scheme
designed around the speaker system available in the performance space of the
Razzo Recital Hall at Clark University, Department of Visual and Performing Arts,
in Worcester, MA, USA, although the work may be performed utilizing a simple
two-channel system (CD player).
The system incorporates seven EAW speakers in various dimensions: three on-
stage large soffit-mounted speakers (left front = 1, centre front = 2, right front
= 3); plus four other smaller ‘left and right side sets’ soffit-mounted speakers
(right side = 4, left side = 7); as well as left and right rear sets (left rear = 6,
right rear = 5).
Sound diffusion organized in such a manner as to sonically delineate the
various elements of the toy piano samples: toy piano (1 = 75.0%, 3 =
100.0%, 4 = 12.5%, 7 = 50.0%); key clicks (1 = 100.0%, 3 = 75.0%, 4 =
50.0%, 7 = 12.5%); gong (2 = 100.0%); downbeat counter (4 = 50.0%, 5
= 100.0%, 6 = 100.0%, 7 = 50.0%); and upbeat counter (1 = 50.0%, 3 =
50.0%, 4 = 100.0%, 5 = 50.0%, 6 = 50.0%, 7 = 100.0%).
Exposiciones 69
Alain Daniélou’s Scale of Proportions (The Harmonic Division of the Octave) Relative Pitch: A4=440Hz / C4 (middle C)=261.6255654Hz
DEGREE NUMBER
NOTE INTERVAL RATIO(FRACTION)
RATIO(DECIMAL)
FREQUENCY(HERTZ)
CENTS TUNING
ÐÑ ÐÒ ÐÓ
ÐÔ ÐÕ ÐÖ Ð×
ÐØ ÐÙ ÑÐ ÑÑ ÑÒ
ÑÓ ÑÔ ÑÕ
ÑÖ Ñ× ÑØ ÑÙ ÒÐ
ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ
ÒÖ
CC¢ C£
CË / Dì CÚ D¹ D¸ DÝ
CÍ / Dí D³ D² D D¢ D£
DË / Eì DÚ E¸ EÝ
DÍ / Eí E³ E² E E¢ E£
EË / Fí F³ F² F F¢ F£
FË / Gì FÚ
unisonsyntonic comma
great diesis Greek enharmonic or septimal quarter-tone
grave or small just chromatic semitone, or minor half-tone Pythagorean limma
just diatonic semitone, or major half-tone great limma, acute or large half-tone
three-quarter-tone grave or small tone
just minor tone just major tone (9th harmonic)
acute or large tone supermajor second five quarter-tones
augmented second (75th harmonic) Pythagorean minor third, or trihemitone
just minor third seven quarter-tones
neutral third grave or small major third
just major third (5th harmonic) Pythagorean major third, or ditone (81st harmonic)
acute or large major third nine quarter-tones
subfourth grave or small fourth
just and Pythagorean perfect fourth acute or large fourth
superfourth eleven quarter-tones
grave or small augmented fourth
1/181/80
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
1.0000001.012500 1.024000 1.033333 1.041667 1.053498 1.066667 1.080000 1.088710 1.097394 1.111111 1.125000 1.137778 1.151053 1.162500 1.171875 1.185185 1.200000 1.209677 1.219326 1.234568 1.250000 1.265625 1.280000 1.291667 1.302083 1.316872 1.333333 1.350000 1.365333 1.377778 1.388889
261.626264.896 267.905 270.346 272.527 275.622 279.067 282.556 284.834 287.106 290.695 294.329 297.672 301.145 304.140 306.592 310.075 313.951 316.483 319.007 322.995 327.032 331.120 334.881 337.933 340.658 344.527 348.834 353.195 357.206 360.462 363.369
0.00021.506 41.059 56.767 70.672 90.225
111.731 133.238 147.143 160.897 182.404 203.910 223.463 243.545 260.677 274.582 294.135 315.641 329.547 343.301 364.807 386.314 407.820 427.373 443.081 456.986 476.539 498.045 519.551 539.104 554.812 568.717
+00 +22 +41 +57 ß29 ß10 +12 +33 +47 ß39 ß18 +04 +23 +44 +61 ß25 ß06 +16 +30 ß57 ß35 ß14 +08 +27 +43 ß43 ß23 ß02 +20 +39 +55 ß31
70 Exposiciones
DEGREE NUMBER
NOTE INTERVAL RATIO (FRACTION)
RATIO (DECIMAL)
FREQUENCY (HERTZ)
CENTS TUNING
Ò× ÒØ ÒÙ
ÓÐ ÓÑ ÓÒ ÓÓ ÓÔ
ÓÕ ÓÖ Ó×
ÓØ ÓÙ ÔÐ ÔÑ ÔÒ
ÔÓ ÔÔ ÔÕ ÔÖ
Ô× ÔØ ÔÙ ÕÐ ÕÑ
ÕÒ ÕÓ
ÐÑ
F¤F¥ GÝ
FÍ / Gí G³ G² G G¢ G£
GË / Aì GÚ A¸ AÝ
GÍ / Aí A³ A² A A¢ A£
AË / Bì AÚ B¹ B¸ BÝ
AÍ / Bí B³ B² B B¢ B£
BË / Cí C³ C²
C
just tritone, or augmented fourth (45th harmonic) acute or large tritone, or augmented fourth
acute or large diminished fifth thirteen quarter-tones
subfifth grave or small fifth
just and Pythagorean perfect fifth (3rd harmonic) acute or large fifth
superfifth fifteen quarter-tones
augmented fifth (25th harmonic) Pythagorean minor sixth
just minor sixth seventeen quarter-tones
neutral sixth grave or small major sixth
just major sixth Pythagorean major sixth (27th harmonic)
acute or large major sixth nineteen quarter-tones
augmented sixth grave or small minor seventh Pythagorean minor seventh
acute or large minor seventh twenty-one quarter-tones (29th harmonic)
neutral seventh grave or small major seventh
just diatonic major seventh (15th harmonic) Pythagorean major seventh
acute or large major seventh twenty-three quarter-tones
suboctave (125th harmonic) grave or small octave
octave
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
1.406250 1.422222 1.440000 1.451613 1.464844 1.481481 1.500000 1.518750 1.536000 1.550000 1.562500 1.580247 1.600000 1.612903 1.620000 1.646091 1.666667 1.687500 1.706667 1.722222 1.736111 1.757813 1.777778 1.800000 1.812500 1.828989 1.851852 1.875000 1.898438 1.920000 1.935484 1.953125 1.975309
2.000000
367.911 372.090 376.741 379.779 383.241 387.593 392.438 397.344 401.857 405.520 408.790 413.433 418.601 421.977 423.833 430.659 436.043 441.493 446.508 450.577 454.211 459.889 465.112 470.926 474.196 478.510 484.492 490.548 496.680 502.321 506.372 510.987 516.791
523.251
590.224 609.776 631.283 645.188 660.896 680.449 701.955 723.014 743.014 758.722 772.627 792.180 813.686 827.592 835.193 862.852 884.359 905.865 925.418 941.126 955.031 976.537 996.090 1017.596 1029.577 1045.256 1066.762 1088.269 1109.775 1129.328 1143.233 1158.941 1178.494
1200.000
ß10 +10 +31 +45 ß39 ß20 +02 +23 +43 +59 ß27 ß08 +14 +28 ß75 ß37 ß16 +06 +25 +41 ß45 ß23 ß04 +18 +30 ß55 ß33 ß12 +10 +29 +43 ß41 ß22
+00
Exposiciones 71
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4-tone equal temperament
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5:3�
3:2� 3:2�
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ExposicionesAndrián Pertout, No. 392
2005
Exposiciones Copyright © 2005 Andrián Pertoutwww.pertout.com • PO Box 4172 • Richmond East • Victoria 3121 • Australia
Made in Australia International Copyright Secured
for Sampled Microtonal Schoenhut Toy Piano
Toy Piano
Hommage à Frank Zappa (1940-1993)
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AP • 392
74 Exposiciones
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VIII 8-tone equal temperament
3+2
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�� �“ IX 9-tone equal temperament
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AP • 392
Exposiciones 75
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AP • 392
76 Exposiciones
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AP • 392
Exposiciones 77
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AP • 392
78 Exposiciones
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57
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XIV 14-tone equal temperament
3+2
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AP • 392
Exposiciones 79
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66 ����‚àXV
3+2
15-tone equal temperament
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13��:5�
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8+5
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3:2�� 3:2�� 3:2�� 3:2�� 3:2���� � � � � � � � �� � � � � � �
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AP • 392
80 Exposiciones
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69
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Exposiciones 81
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81 ���’�5+5
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82 �XVII 17-tone equal temperament
2+3+2
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AP • 392
82 Exposiciones
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84
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85 ���’�
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Exposiciones 83
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88
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XVIII 18-tone equal temperament
5+5
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4:3��
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91 �5+5+5
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13:9��
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�‡ �ä �À � �ƒ �À � � �˜ �˜ �“ � � � �… �‡ �äz���z
9:13��#
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94
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XIX 19-tone equal temperament
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15:8��
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14:9��
�� � � �� � � �� � ��� �� ��
AP • 392
84 Exposiciones
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97 �7+7
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9:14��#
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�’ �à �å �à �à � � � � � �À �˜ � � � � �À � �à �à �à � � � �z���z
13:10��
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99 �8+5�à �à � �’ � � � � �à �˜ � �– �à �å � �– �à � �z���z
10:13��#
�� � � � � � � � �� � � � �� �� ��
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6+5
XX 20-tone equal temperament
� � � �‚� � � � �“� � � � ��‚˜ � � � ��� � � ��“� � � ��� � ����
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101
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� �à � �� � � � �à � �� ��z���z
13:11��#
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11:13��
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AP • 392
Exposiciones 85
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104
��
XXI 21-tone equal temperament
6+5
� � �‚ � �˜ � �“ � � � �† � �‚ � �“ � � � �’ � �˜ � �ƒ � � � �– � �å � �‚ � � � � � �‚ � � � � � �˜ � �† � �˜ � �† � �‚�z���z
14:11��
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105 �’�7+7
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6:5��#
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13:12��
4:5��
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107 �8+5
�à � �å �™ �˜ �ƒ �’ �à �À �† �“ �˜ �˜ �ä � �à � �å �™ �˜ �ƒ �’ �à z���z
12:13��#
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AP • 392
86 Exposiciones
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108
��…XXII
6+5
22-tone equal temperament
�� �� ��… �� ���à ��� ��� ��� ����å ���� �����˜ ����� �����Âå ��������15:11��
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109 ����À�5+5+5
�˜ �˜ � � �À �À �˜ �˜ �Å �Å �˜ �˜ � � �Å �Å �ƒ �ƒ � � �“ �“ �… �… � � � � �ä �ä � � �à �à � � �™ �™ � �z���z
11:15��
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110
��8+5
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�� � � � � � � � �� � � � �� �� ��
AP • 392
Exposiciones 87
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111 ��å7+7
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112 �XXIII 23-tone equal temperament
8+5
�˜ �˜ � �à � � � �“ �˜ ��– �‚ �‚
� � � � � �“ z���z15:13��
3:2��#3:2��#
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113 �5+5+5
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13:15��#
3:2��#3:2��# 3:2��#
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AP • 392
88 Exposiciones
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114 ��XXIV 24-tone equal temperament(7+7)
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�˜ �˜ � �† �˜ � � �… �— �˜ � �ƒ �à � � � �… � �À �˜ �ƒ �à �å � � �… � �˜15:14��
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115 ��
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cresc.
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15:14��##
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116 *5+5+5
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AP • 392
Exposiciones 89
Andrián Pertout
La Homa Kanto for Harmonically Tuned Synthesizer Quartet
No. 393
Composed between August and October, 2005
Hommage à Lou Harrison (1917-2003)
‘Acousmatic’ Premier: 27 April, 2007 (St. Neighborhood Unaitarian Church, Los Angeles Sonic Odyssey: Electronic and
Computer Music Concert Series 2007, 26-28 April, 2007, Pasadena, California, USA)
Duration: 11’50”
Copyright © 2005 Andrián Pertout
PROGRAMME NOTES
In order to understand the basic concept of just intonation, one must refer to the natural acoustic phenomenon known as the ‘harmonic series’. The overtones of a
specific pitch are generally referred to as the ‘harmonic series’, and the musical scale derived from this series is constructed around pure (or just) intervals. This
system of just intonation is strikingly dissimilar to the 'twelve-tone equally-tempered division of the octave', which is based on the division of the octave into twelve
equal intervals – the frequency ratio of each semitone (or tempered half-tone) being the twelfth root of 2. In Lou Harrison: Composing a World Leta E. Miller and
Fredric Lieberman describes just intonation thus: “Pure intervals arise when the frequencies of the individual tones reflect the precise mathematical proportions that
occur in the series: 3/2 for the fifth, 4/3 for the fourth, etc.” Intervals manifested naturally within the harmonic series are particularly favourable in just intonation, and
certainly ones with “superparticular vibration ratios”, where the “numerator exceeds the denominator by one” such as the just perfect fifth (3/2), perfect fourth (4/3),
major third (5/4) and minor third (6/5).
‘La Homa Kanto’ or ‘The Human Song’ in Esperanto is a dedication to the late American composer Lou Harrison (1917-2003), and its pitch material has been derived
directly from Harrison’s five-tone scales, presented in Lou Harrison’s Music Primer: Various Items About Music to 1970. Included are the first five in the series, with
the first – the diatonic or major pentatonic scale – acknowledged by Harrison as the “prime pentatonic”, and “practically the Human Song.” According to Harrison,
“These first five are the most widespread, the core, the principal modes of ‘Human Music’. They also constitute the bone-work, the firmest compositional basis for
seven-tone music.” Modes one, two and five may be considered to be anhemitonic pentatonic forms (scales incorporating half steps, or semitones), while three
and four, hemitonic pentatonic forms (scales not incorporating half steps, or semitones). Harrison’s five pentatonic scales include the diatonic or major pentatonic,
minor pentatonic (or fifth mode major pentatonic), Japanese Hirajoshi, fifth mode Indonesian Pélog, as well as the Indonesian Sléndro (or second mode major
pentatonic). The consideration of their complements presents the third mode major pentatonic, fourth mode major pentatonic, third mode Indonesian Pélog,
fourth mode Japanese Hirajoshi, as well as the Indonesian Sléndro (or second mode major pentatonic).
Major Pentatonic Scale “The Human Song”
94 La Homa Kanto
The compositional strategy for the work involves the creation of two complimentary sets of melodic material, consisting of what is essentially a four-bar melodic
sentence based on Harrison’s first pentatonic (or major pentatonic), with an additional four-bar variant based on its complement (or third mode major pentatonic).
In some aspects, this second sentence could be considered an almost comparable inversion, although it does not represent an ‘authentic’ inversion in the serial
sense of the word, but rather an inversion of contour utilizing the inverted pitch material of the original major pentatonic. The third bar of both versions represents
the only literal inversion of intervals. A further observation reveals the respective major and minor tonalities of the two four-bar melodic sentences.
Four-bar melodic sentence
Complimentary sentence
The work also features ten distinct tuning modulations: three-limit, five-limit, seven-limit, eleven-limit, thirteen-limit, seventeen-limit, nineteen-limit, twenty-three-limit, twenty-nine-
limit, and thirty-one-limit just intonation systems, based on the third, fifth, seventh, eleventh, thirteenth, seventeenth, nineteenth, twenty-third, twenty-ninth, and thirty-first partials of
the harmonic series – each system adding its own microtonal nuances to the recurring melodic material, which is further transformed via the introduction of alternative scalar
material, as well as via harmonic development pertinent to each individual just intonation system. The structural framework of the composition is directly related to the primary
motive of the four-bar melodic sentence. In five-limit terms, the primary motive denotes the following intervals: 5/4, 3/2, and 9/8, and 5/4, and 3/2; and is expressed in the
score as section one (rehearsal letters A and B – incorporating Lou Harrison Pentatonic #1, and both three-limit and five-limit just intonation), which is designated a 5/4 metrical
structure; section 2 (rehearsal letters C and D – incorporating Lou Harrison Pentatonic #2, and both seven-limit and eleven-limit just intonation), a 3/2 metrical structure; section 3
(rehearsal letters E and F – incorporating Lou Harrison Pentatonic #3, and both thirteen-limit and seventeen-limit just intonation), a 9/8 metrical structure; section 4 (rehearsal
letters G and H – incorporating Lou Harrison Pentatonic #4, and both nineteen-limit and twenty-three-limit just intonation), a 5/4 metrical structure; and section 5 (rehearsal
letters I and J – incorporating Lou Harrison Pentatonic #5, and both twenty-nine-limit and thirty-one-limit just intonation), a 12/8 metrical structure (equal to 3/2). A sequential
series of metrical structures is therefore utilized in the work to reflect the primary motive and its frequency ratios of 5/4, 3/2, 9/8, 5/4, and 3/2.
La Homa Kanto 95
Saturday, 3 February, 2001 (Our Colleague Lou Harrison)
Dear Fellow SCI Members:
“I just received very sad news from my colleague and fellow SCI member Donald Harris. He reports that Lou Harrison, noted American composer, passed away last
night.
“Lou Harrison had appeared at several of our National Conferences. His cheerful, luminous personality endeared him to and will be remembered by all who knew
him. Lou was en route to Ohio State for our annual New Music Festival which honours him and features his music.
“I include the message I received from Don Harris, who related the sad news to our faculty.”
Thomas Wells (President, Society of Composers, Inc.), Professor of Music, Director, Sound Synthesis Studios, Ohio State University, Columbus, Ohio, USA
96 La Homa Kanto
Saturday, 3 February, 2001 (Our Colleague Lou Harrison)
“Last night, while travelling from Chicago to Columbus, Lou Harrison passed away. We had sent Adam Schweigert and Joe Panzner, two students in Composition
and Theory, to Chicago with a University van to greet Lou and his travelling companion, Todd Burlingame, and drive them back to campus for the Festival. Lou does
not like to fly and took the train, the California Zephyr, from near San Francisco to Chicago. The train arrived at about 5:15 PM. While en route to Indianapolis, their
overnight destination, Adam, Joe, Lou and Todd decided to stop at a Denny's restaurant in Lafayette, Indiana, for some dinner. Lou stumbled and fell upon getting
out of the vehicle and apparently suffered a heart attack. He had great difficulty breathing. Paramedics were called and they arrived within minutes. Lou was
transported to the hospital but was unable to be revived. He passed away around 9 or 9:30 PM.
“This is a great tragedy for the entire world of music. Lou was as excited about the Festival as we were. Our sympathies go out to all in the world of music and
dance who treasured his great gift. I will always remember the joy in his voice when we spoke over the telephone about the Festival. He was an active participant
in planning the concerts. He had also prepared a special seminar for OSU students in composition. He was very much looking forward to the CSO performances
of his Third Symphony in a final revision that he had just completed. He told me how honoured he felt to have so many of his compositions performed on the
Festival. Let everyone know that the Festival performances will go on as planned as a tribute to this legendary American musician.
“I must also at this time offer our sincere thanks to Adam and Joe. As you might imagine, they were devastated by what took place. Yet they remained calm at all
times, stayed in close touch with me, and were of great comfort to Todd Burlingame. We can be proud of the way they represented Ohio State and the School of
Music. Adam and Joe will return to Columbus today. When you see them, please thank them for their calm and measured reactions under such tragic
circumstances.
“Lou Harrison will be cremated today; his remains shipped back to California. He was eighty-five years old.”
Donald Harris, Professor of Composition and Theory, School of Music, Ohio State University, Columbus, Ohio, USA
La Homa Kanto 97
Thursday, 6 February, 2003 (Death of Lou Harrison)
Dear Thomas Wells,
“Thank you very much for sharing the sad information about Lou Harrison. And what a beautiful tribute by long-time SCI member, Donald Harris. Lou attended
symposia in his honour many times here in Portland, Oregon, Lou's place of birth. Two recent ones in particular stand out when Lou was aged 79 and 82. The first
was at Lewis & Clark College in Portland with Bill Colvig, his late partner. Lou gave numerous inspiring lecture presentations that took your breath away, and when his
music was performed by L&C students to a large public audience, Lou signed CD's late into the night despite his need to get up early the next morning to present
again and again for several days. His music was, and continues to be, performed often in Portland on many of the instruments Lou invented with Bill Colvig.
“Do you remember how Lou would title many of his musical compositions in Esperanto?! Lou was passionate about keeping this rarely used universal language alive.
Lou also designed numerous letter fonts, many of which we now select on the internet when writing our documents. Remember his beautiful calligraphic
handwriting and the painstaking care with which he wrote each letter?
“At aged 82, Lou again came to Oregon and was honoured in a Symposium at the University of Oregon in Eugene where he taught a roomful of young composers
for several days. Lou was a lively and brilliant presenter at these events. His eyes and whole body lit up when he spoke, and his ideas were often more
controversial than those of students 60 years younger! Despite his exceptional brilliance, he never boasted of his intelligence or of anything else, instead inspiring
the listener to invent and create as he did, living life to the fullest. Even into his 80's, the cogency of his ideas, his wit, passion, and joy of learning were as strong as
that of a young person. Your choice of the word ‘luminous’ to describe Lou is perfect. He was a wonderful, brilliant human being, and we will all miss him greatly. I
can only imagine what your New Music Festival is like with the aura of Lou Harrison hovering in the room. The music must be exceptional and every word spoken
charged with power. I'm sure Lou is there with you and I wish I could be there too.
“Warm remembrances, and thank you for writing.”
Linda Hathaway Bunza, Director, Columbia Research Institute for the Arts and Humanities, Portland, Oregon, USA.
98 La Homa Kanto
Lou Harrison, Beloved Icon and Pioneer By Fredric Lieberman
The musical world was stunned by the death, on Sunday, February 2, of Lou Harrison, the distinguished and much beloved composer and humanitarian. In his
delightful Music Primer (1971) Lou wrote, ‘Someone has said that music is to be recommended because the Angels practice it.’ Self-proclaimed a ‘glandular
optimist,’ certainly Lou is now cherishing the songs of that Angelic choir, and I imagine he’s already started teaching them to sing in Just Intonation.
Harrison, who celebrated his 85th birthday this year, was on his way to a week-long festival of his music in Columbus, Ohio, when an accidental fall apparently
brought on a heart attack. The performances will go on as a memorial tribute. Lou had recently completed revisions to his Third Symphony – he continually revised
works until they ‘stopped itching’ – and was enthusiastically looking forward to the premiere of the new version next Friday. (The Third Symphony was first
performed in 1982, though its diverse movements include material from as early as 1937.)
Lou met his life-partner, William Colvig, in 1967; they lived and worked together until Bill’s death in 2000. Lou’s younger brother Bill also predeceased him. He is
survived by his sister-in-law Dorothy, of Reno, Nevada, and two nephews Brad and Barry.
Though beset by bouts of illness, sometimes quite painful, Lou never stopped working, teaching, and learning. He recently completed a new book Poems and
Pieces, currently in press, which juxtaposes poetry with a selection of works for the Javanese gamelan. In addition to revising the Third Symphony, Lou completed
revisions and additions to his second opera Young Caesar; completed the construction of an ecologically-friendly straw-bale house of his own design in Joshua
Tree, California; bought a used Mercedes diesel auto, which he had converted to run on bio-diesel fuel (that is, any form of vegetable oil); and was preparing once
again to teach his course on Javanese gamelan for Cabrillo College in Santa Cruz.
As pianist Sarah Cahill pointed out, ‘Lou's passing is so symbolic of the end of an era. His deep connections to Schoenberg, Ives, Cowell, and Cage made him a real
icon, even beyond his own compositional career.’ Born in Portland, Oregon, in 1917, Lou grew up in the San Francisco Bay area, studied music at San Francisco
State College, composition with Henry Cowell and Arnold Schoenberg, and pioneered with John Cage in creating and performing works for percussion ensemble.
Moving to New York in 1943, Harrison worked as a music critic for the Herald Tribune, hired by Virgil Thomson, and wrote also for Modern Music and New Music
Quarterly.
La Homa Kanto 99
Lou had previously corresponded with Charles Ives, and during this New York period conducted the premiere of Ives’s Third Symphony, which won the Pulitzer
Prize. Ives wrote to Lou ‘As you are very much to blame for getting me into that Pulitzer Prize street, and for having a bushel of letters to answer and for having a
check of $500 thrown over by the Trustees of Colum-Uni-, you have got to help me by taking 1/2 of this (somewhere enclosed)…’
Fusing Asian with Western music
Lou returned to California in 1953, where he settled in Aptos, near Santa Cruz. Life in California, though difficult for a struggling composer, brought him into close
contact with Asian musics, which inspired melodic and modal experiments, leading to a panoply of works fusing Asian with Western music in unique and beautiful
ways. Some of these works are composed directly for traditional Asian instruments, such as the many compositions for Javanese gamelan; others combine Asian
and Western instruments, one of the most successful being Pacifika Rondo (1963); and still others, such as the magnificent Piano Concerto (1985) borrow musical
forms or styles from Asian sources, so thoroughly integrated into the musical texture that their diverse origins are buried beneath the surface of Lou’s melodic magic.
Harrison’s major works include four symphonies, two operas, the Piano Concerto, major dance scores including Solstice (for Jean Erdman) and Rhymes With Silver
(for Mark Morris), the Strict Songs which, when recorded by the Louisville Symphony, introduced many listeners to pure intonation, and many chamber works of
great power and beauty, such as the Suite for Piano, the Grand Duo for vn and pf, the Varied Trio for vn, pf, and percussion, and the String Quartet Set. These
works will, I’m sure, stand the test of time.
Harrison pioneered in many fields: music for percussion orchestra; the use of pure or Just Intonation rather than equal temperament; the creation of new
instruments; the introduction of gamelan music and new composition for that ensemble; and teaching world music, which he did for decades at Mills College, San
Jose State, and Cabrillo College.
Lou was a founding spirit of the Cabrillo Music Festival, which has grown to be one of the most important venues for new music. In 2001, under the baton of Marin
Alsop, the Cabrillo Festival performed Lou’s first opera, Rapunzel that had been premiered at the 92nd St. Y in New York City in 1959; over the years other
conductors including Gerhard Samuel, Carlos Chavez, and Dennis Russell Davies have led the Cabrillo Festival orchestra in presenting Harrison’s music, along with that
of hundreds of other contemporary composers.
100 La Homa Kanto
A fearless pacifist, outspoken environmentalist
On social issues Lou was fearless and outspoken. A pacifist, he protested both in words and music against atomic testing, the Vietnam War, and militarism in
general. He was an early supporter of environmental causes, championing the use of renewable fuels, paper recycled, or even better made from fast-growing,
easily renewable hemp or kenaf. An advocate for Gay Rights, Lou never hesitated to make his views public. In 1963, at the University of Hawaii, Lou fired off a letter
to the student paper, protesting one previously published: ‘In the present population explosion, calling homosexuals sick strikes this reader as a case of pots and
kettles.’
Mr. Ricardo Trimillos, then a graduate student, recalls: ‘Lou was not only a wonderful artist; he was a passionate and committed citizen. I remember his letter
defending gay rights back in '63 when being gay was hardly on anyone's radar screen. He signed it as ‘Composer in Residence’ for the contemporary festival, which
upset some faculty members. However, for me he brought home the ‘ideology’ of understanding music in its cultural context in a very dramatic way. For me that
was an important lesson, not taught, but learned.’
Harrison left a voluminous musical legacy of over 300 compositions. Over the past decade, his work has been rapidly growing in international acclaim. New CDs appear
regularly; festivals and performances have been increasingly abundant. As of this writing, a memorial tribute in Santa Cruz is being organized, and others will follow.
Contagious enthusiasm, generosity, and love
For me, Lou inspired not only through his music, with its continuous search for beauty heedless of current styles or fads, but also through his contagious enthusiasm,
generosity, and love. Seldom would I come away from a visit to Lou’s Aptos home without the exciting feeling of having learned something remarkable, whether
about music, architecture, politics, or literature. Lou filled his place in the world fully and energetically – it’s hard to imagine what the world will feel like without him.
(Fredric Lieberman, composer and ethnomusicologist, teaches at the University of California, Santa Cruz. With co-author Leta Miller, he has written Lou Harrison:
Composing a World (1998) and a second book on Lou Harrison is forthcoming from the U. of Illinois.) ©2003 Fredric Lieberman, all rights reserved.
San Francisco Classical Voice, Oakland, California, USA
La Homa Kanto 101
Lou Harrison Pentatonic #1 3-limit Intonation
Lou Harrison Pentatonic #1 5-limit Intonation
102 La Homa Kanto
Lou Harrison Pentatonic #2 7-limit Intonation
Lou Harrison Pentatonic #2 11-limit Intonation
La Homa Kanto 103
Lou Harrison Pentatonic #3 13-limit Intonation
Lou Harrison Pentatonic #3 17-limit Intonation
104 La Homa Kanto
Lou Harrison Pentatonic #4 19-limit Intonation
Lou Harrison Pentatonic #4 23-limit Intonation
La Homa Kanto 105
Lou Harrison Pentatonic #5 29-limit Intonation
Lou Harrison Pentatonic #5 31-limit Intonation
106 La Homa Kanto
INSTRUMENTATION
Ludisto Unu (Player One)
Ludisto Du (Player Two)
Ludisto Tri (Player Three)
Ludisto Kvar (Player Four)
Player 1 to 4 (Sampled ‘1967 William Dowd French Double Harpsichord’ – Akai S3000XL Midi Stereo Digital Sampler and four 61-key Midi Keyboards) Transposed score
116 La Homa Kanto
PERFORMANCE NOTES
In this score, accidentals apply only to the subsequent note in sections utilizing proportional notation, whereby in sections utilizing standard metric notation,
accidentals apply throughout the bar.
fermata (approximately 2”)
long comma (approximately 1”)
short comma (approximately 0.5”)
The notation utilized in the score is based on Benjamin Johnston’s ‘Extended Just Intonation’. It contains 23 unique symbols, which may be combined in any
manner – 5 identical to conventional sharp (Ú), flat (Û), double sharp (#), double flat ($), and natural (Ö) accidentals (raising, lowering or neutralizing a tone by 25/24
and 625/576, or 70.672 and 141.345 cents). Additional symbols include (() and ()), raising or lowering a tone by 81/80 (one syntonic comma), or 21.506 cents,
as well as the following utonal and otonal sets of symbols for each partial chroma up to the thirty-first harmonic: (+) and (*), lowering or raising a tone by 36/35 (one
septimal comma), or 48.770 cents; (,) and (-), raising or lowering a tone by 33/32 (one undecimal comma), or 53.273 cents; (.) and (/), raising or lowering a
tone by 65/64 (one tridecimal comma), or 26.841 cents; (0) and (1), raising or lowering a tone by 51/50 (one septendecimal comma), or 34.283 cents; (2) and
(3), lowering or raising a tone by 96/95 (one nonadecimal comma), or 18.128 cents; (4) and (5), raising or lowering a tone by 46/45 (one trivigesimal comma), or
38.051 cents; (6) and (7), raising or lowering a tone by 145/144 (one nonavigesimal comma), or 11.981 cents; and finally, (8) and (9), raising or lowering a tone
by 31/30 (one untrigesimal comma), or 56.767 cents.
raised by 25/24, or one small just chromatic semitone (70.672 cents)
lowered by 25/24, or one small just chromatic semitone (70.672 cents)
La Homa Kanto 117
raised by 25/24 plus 25/24, or 625/576 (141.345 cents)
lowered by 25/24 minus 25/24, or 625/576 (141.345 cents)
raised or lowered to natural tone
raised by 81/80, or one syntonic comma (21.506 cents)
lowered by 81/80, or one syntonic comma (21.506 cents)
raised by 25/24 plus 81/80, or 135/128 (92.179 cents)
lowered by 25/24 minus 81/80, or 135/128 (92.179 cents)
raised by 25/24 plus 81/80 plus 81/80, or 2187/2048 (113.685 cents)
lowered by 25/24 minus 81/80 minus 81/80, or 2187/2048 (113.685 cents)
lowered by 36/35, or one septimal comma (48.770 cents)
raised by 36/35, or one septimal comma (48.770 cents)
lowered by 36/35 plus 81/80, or 729/700 (70.277 cents)
raised by 36/35 minus 81/80, or 729/700 (70.277 cents)
lowered by 25/24 minus 36/35, or 15/14 (119.443 cents)
118 La Homa Kanto
raised by 25/24 plus 36/35, or 15/14 (119.443 cents)
lowered by 25/24 minus 36/35 plus 81/80, or 243/224 (140.949 cents)
raised by 25/24 plus 36/35 minus 81/80, or 243/224 (140.949 cents)
raised by 33/32, or the 33rd harmonic (53.273 cents)
lowered by 33/32, or the 33rd harmonic (53.273 cents)
raised by 33/32 minus 81/80, or 55/54 (31.767 cents)
lowered by 33/32 plus 81/80, or 55/54 (31.767 cents)
lowered by 25/24 plus 33/32, or 100/99 (17.399 cents)
raised by 25/24 plus 33/32, or 100/99 (17.399 cents)
lowered by 25/24 plus 33/32 minus 81/80, or 45/44 (38.906 cents)
raised by 25/24 minus 33/32 plus 81/80, or 45/44 (38.906 cents)
raised by 65/64 (26.841 cents)
lowered by 65/64 (26.841 cents)
raised by 65/64 plus 81/80, or 1053/1024 (48.348 cents)
La Homa Kanto 119
lowered by 65/64 minus 81/80, or 1053/1024 (48.348 cents)
raised by 65/64 minus 81/80, or 325/324 (5.335 cents)
lowered by 65/64 plus 81/80, or 325/324 (5.335 cents)
lowered by 25/24 plus 65/64, or 40/39 (43.831 cents)
raised by 25/24 minus 65/64, or 40/39 (43.831 cents)
lowered by 25/24 plus 65/64 minus 81/80, or 27/26 (65.337 cents)
raised by 25/24 minus 65/64 plus 81/80, or 27/26 (65.337 cents)
raised by 51/50 (34.283 cents)
lowered by 51/50 (34.283 cents)
raised by 51/50 minus 81/80, or 136/135 (12.777 cents)
lowered by 51/50 plus 81/80, or 136/135 (12.777 cents)
raised by 25/24 plus 51/50, or 17/16 (104.955 cents)
lowered by 25/24 minus 51/50, or 17/16 (104.955 cents)
raised by 25/24 plus 51/50 minus 81/80, or 85/81 (83.449 cents)
120 La Homa Kanto
lowered by 25/24 minus 51/50 plus 81/80, or 85/81 (83.449 cents)
lowered by 96/95 (18.128 cents)
raised by 96/95 (18.128 cents)
lowered by 96/95 plus 81/80, or 512/513 (ß3.378 cents)
raised by 96/95 minus 81/80, or 512/513 (ß3.378 cents)
lowered by 96/95 minus 81/80, or 486/475 (39.635 cents)
raised by 96/95 plus 81/80, or 486/475 (39.635 cents)
lowered by 25/24 minus 96/95, or 20/19 (88.801 cents)
raised by 25/24 plus 96/95, or 20/19 (88.801 cents)
lowered by 25/24 minus 96/95 minus 81/80, or 81/76 (110.307 cents)
raised by 25/24 plus 96/95 plus 81/80, or 81/76 (110.307 cents)
raised by 46/45 (38.051 cents)
lowered by 46/45 (38.051 cents)
raised by 46/45 plus 81/80, or 207/200 (59.557 cents)
La Homa Kanto 121
lowered by 46/45 minus 81/80, or 207/200 (59.557 cents)
raised by 46/45 minus 81/80, or 736/729 (16.544 cents)
lowered by 46/45 plus 81/80, or 736/729 (16.544 cents)
raised by 25/24 plus 46/45, or 115/108 (108.723 cents)
lowered by 25/24 minus 46/45, or 115/108 (108.723 cents)
raised by 25/24 plus 46/45 plus 81/80, or 69/64 (130.229 cents)
lowered by 25/24 minus 46/45 minus 81/80, or 69/64 (130.229 cents)
raised by 145/144 (11.981 cents)
lowered by 145/144 (11.981 cents)
raised by 145/144 plus 81/80, or 261/256 (33.487 cents)
lowered by 145/144 minus 81/80, or 261/256 (33.487 cents)
lowered by 25/24 plus 145/144, or 30/29 (58.692 cents)
raised by 25/24 minus 145/144, or 30/29 (58.692 cents)
lowered by 25/24 plus 145/144 minus 81/80, or 243/232 (80.198 cents)
122 La Homa Kanto
raised by 25/24 minus 145/144 plus 81/80, or 243/232 (80.198 cents)
raised by 31/30 (56.767 cents)
lowered by 31/30 (56.767 cents)
raised by 31/30 plus 81/80, or 837/800 (78.273 cents)
lowered by 31/30 minus 81/80, or 837/800 (78.273 cents)
raised by 31/30 minus 81/80, or 248/243 (35.261 cents)
lowered by 31/30 plus 81/80, or 248/243 (35.261 cents)
raised by 25/24 plus 31/30, or 155/144 (127.439 cents)
lowered by 25/24 minus 31/30, or 155/144 (127.439 cents)
raised by 25/24 plus 31/30 plus 81/80, or 279/256 (148.946 cents)
lowered by 25/24 minus 31/30 minus 81/80, or 279/256 (148.946 cents)
raised by 25/24 plus 31/30 plus 81/80 plus 81/80, or 22599/20480 (170.452 cents)
lowered by 25/24 minus 31/30 minus 81/80 minus 81/80, or 22599/20480 (170.452 cents)
La Homa Kanto 123
3-limit tuning matrix no. 1 ‘key of C’ (Program 01)
NOTE C D")) D E") E( F – – G A") A( B") B(
KEY C C! D D! E F F! G G! A A! B
CENTS +00 ß10 +04 ß06 +08 ß02 +00 +02 ß08 +06 ß04 +10
5-limit tuning matrix no. 1 ‘key of C’ (Program 02)
NOTE C D") D E" E F – – G A" A B") B
KEY C C! D D! E F F! G G! A A! B
CENTS +00 +12 +04 +16 ß14 ß02 +00 +02 +14 ß16 ß04 ß12
5-limit tuning matrix no. 2 ‘key of C’ (Program 03)
NOTE C D") D E" E F – – G A" A B" B
KEY C C! D D! E F F! G G! A A! B
CENTS +00 +12 +04 +16 ß14 ß02 +00 +02 +14 ß16 +18 ß12
7-limit tuning matrix no. 1 ‘key of G’ (Program 04)
NOTE C C: D E; E* F+( F: G A; ( A* B; B*
KEY C C! D D! E F F! G G! A A! B
CENTS +00 +19 +04 ß33 +35 ß29 +17 +02 ß14 +33 ß31 +37
124 La Homa Kanto
7-limit tuning matrix no. 2 ‘key of G’ (Program 05)
NOTE C C: D E; E* F+( F: G A; ( A* B; B
KEY C C! D D! E F F! G G! A A! B
CENTS +00 +19 +04 ß33 +35 ß29 +17 +02 ß14 +33 ß31 ß12
11-limit tuning matrix no. 1 ‘key of G’ (Program 06)
NOTE C C, D – – E-( FD( F, G – – A-( BE) – –
KEY C C! D D! E F F! G G! A A! B
CENTS +00 ß47 +04 +00 ß45 +37 ß49 +02 +00 ß47 +49 +00
11-limit tuning matrix no. 2 ‘key of G’ (Program 07)
NOTE C C, D – – E-( F+( F, G – – A( BE) B
KEY C C! D D! E F F! G G! A A! B
CENTS +00 ß47 +04 +00 ß45 ß29 ß49 +02 +00 +06 +49 ß12
11-limit tuning matrix no. 3 ‘key of G’ (Program 08)
NOTE CD( – – D – – EE FD( F, G – – A-( B- – –
KEY C C! D D! E F F! G G! A A! B
CENTS +39 +00 +04 +00 ß31 +37 ß49 +02 +00 ß47 +35 +00
La Homa Kanto 125
11-limit tuning matrix no. 4 ‘key of G’ (Program 09)
NOTE C C, D – – E-( FD( F, G – – AE BE) – –
KEY C C! D D! E F F! G G! A A! B
CENTS +00 ß47 +04 +00 ß45 +37 ß49 +02 +00 ß33 +49 +00
13-limit tuning matrix no. 1 ‘key of D’ (Program 10)
NOTE C. CN( D EO E/( F.( FN( G GN( A( BO B/
KEY C C! D D! E F F! G G! A A! B
CENTS +27 ß35 +04 +42 ß19 +46 ß37 +02 ß33 +06 +44 ß39
13-limit tuning matrix no. 2 ‘key of D’ (Program 11)
NOTE C. CN( D EO E/( F.( FN( G AO A( BO B/
KEY C C! D D! E F F! G G! A A! B
CENTS +27 ß35 +04 +42 ß19 +46 ß37 +02 +41 +06 +44 ß39
17-limit tuning matrix no. 1 ‘key of D’ (Program 12)
NOTE C1( CP D EQ( E0 F1( FP G GP A( BQ( B0
KEY C C! D D! E F F! G G! A A! B
CENTS ß13 +05 +04 +03 +21 ß15 +03 +02 +07 +06 +05 +23
126 La Homa Kanto
17-limit tuning matrix no. 2 ‘key of D’ (Program 13)
NOTE C1( DQ D EQ( E0 F1( FP G AQ( A( BQ( B0
KEY C C! D D! E F F! G G! A A! B
CENTS ß13 ß01 +04 +03 +21 ß15 +03 +02 +01 +06 +05 +23
19-limit tuning matrix no. 1 ‘key of A’ (Program 14)
NOTE C2( CV( D DV( E( F2( FV( G2( GV( A( BW B3
KEY C C! D D! E F F! G G! A A! B
CENTS +13 +10 +04 +14 +08 +01 +08 +05 +12 +06 ß01 +06
23-limit tuning matrix no. 1 ‘key of A’ (Program 15)
NOTE C5( CX( D DX( E( F5( FX( G5 GX( A( BY B4(
KEY C C! D D! E F F! G G! A A! B
CENTS ß17 +30 +04 +34 +08 ß18 +28 ß36 +32 +06 ß20 +48
23-limit tuning matrix no. 2 ‘key of A’ (Program 16)
NOTE C5( CX( D DX( E( F5( FX( G5( GX( A( BY B4(
KEY C C! D D! E F F! G G! A A! B
CENTS ß17 +30 +04 +34 +08 ß18 +28 ß15 +32 +06 ß20 +48
La Homa Kanto 127
29-limit tuning matrix no. 1 ‘key of E’ (Program 17)
NOTE C6( C^( D6( D^( E( F6( F^( G6( G^( A( A^( B(
KEY C C! D D! E F F! G G! A A! B
CENTS +33 ß20 +37 ß16 +08 +32 ß22 +35 ß18 +06 ß35 +10
31-limit tuning matrix no. 1 ‘key of E’ (Program 18)
NOTE C9( C`( D9( D`( E( F9( F`( G9( G`( A( – – B(
KEY C C! D D! E F F! G G! A A! B
CENTS ß35 +49 ß31 +53 +08 ß37 +47 ß33 +51 +06 +00 +10
31-limit tuning matrix no. 2 ‘key of E’ (Program 19)
NOTE C9( C`( D9( D`( E( F9( F`( G9( G`( A( – – A`((KEY C C! D D! E F F! G G! A A! B
CENTS ß35 +49 ß31 +53 +08 ß37 +47 ß33 +51 +06 +00 ß45
128 La Homa Kanto
Ben Johnston’s Fifty-Three-Tone Just Division of the Octave Relative Pitch: A4=440Hz / C4 (middle C)=261.6255654Hz
DEGREE NUMBER
NOTE INTERVAL RATIO (FRACTION)
RATIO (DECIMAL)
FREQUENCY (HERTZ)
CENTS TUNING
ÐÑ ÐÒ ÐÓ ÐÔ ÐÕ ÐÖ Ð× ÐØ ÐÙ ÑÐ ÑÑ ÑÒ ÑÓ ÑÔ ÑÕ ÑÖ Ñ× ÑØ ÑÙ ÒÐ ÒÑ ÒÒ ÒÓ ÒÔ ÒÕ ÒÖ
C C(
D$) C!
C!( D") D"
C#( D) D
D( E$ D! E") E" D# E) E
E( F" E! F) F
F( G$)
F!
unison syntonic comma
diminished second, or great diesis grave or small just chromatic semitone, or minor half-tone
Pythagorean acute or large limma just diatonic semitone, or major half-tone
great limma, acute or large half-tone acute or large double augmented octave
just minor tone just major tone (9th harmonic)
acute or large tone diminished third
augmented second (75th harmonic) Pythagorean minor third, or trihemitone
just minor third double augmented second
grave or small major third just major third (5th harmonic)
Pythagorean major third, or ditone (81st harmonic) diminished fourth augmented third
grave or small fourth just and Pythagorean perfect fourth
acute or large fourth grave or small double diminished fifth
grave or small augmented fourth
1/1 81/80
128/125 25/24
135/128 16/15 27/25
1125/1024 10/9 9/8
729/640 144/125 75/64 32/27 6/5
625/512 100/81
5/4 81/64 32/25 125/96
320/243 4/3
27/20 512/375 25/18
1.000000 1.012500 1.024000 1.041667 1.054688 1.066667 1.080000 1.098633 1.111111 1.125000 1.139063 1.152000 1.171875 1.185185 1.200000 1.220703 1.234568 1.250000 1.265625 1.280000 1.302083 1.316872 1.333333 1.350000 1.365333 1.388889
261.626 264.896 267.905 272.527 275.933 279.067 282.556 287.430 290.695 294.329 298.008 301.393 306.592 310.075 313.951 319.367 322.995 327.032 331.120 334.881 340.658 344.527 348.834 353.195 357.206 363.369
0.000 21.506 41.059 70.672 92.179 111.731 133.238 162.851 182.404 203.910 225.416 244.969 274.582 294.135 315.641 345.255 364.807 386.314 407.820 427.373 456.986 476.539 498.045 519.551 539.104 568.717
+00 +22 +41 ß29 ß08 +12 +33 ß37 ß18 +04 +25 +45 ß25 ß06 +16 +45 ß35 ß14 +08 +27 ß43 ß23 ß02 +20 +39 ß31
La Homa Kanto 129
DEGREE NUMBER
NOTE INTERVAL RATIO (FRACTION)
RATIO (DECIMAL)
FREQUENCY (HERTZ)
CENTS TUNING
Ò× ÒØ ÒÙ ÓÐ ÓÑ ÓÒ ÓÓ ÓÔ ÓÕ ÓÖ Ó× ÓØ ÓÙ ÔÐ ÔÑ ÔÒ ÔÓ ÔÔ ÔÕ ÔÖ Ô× ÔØ ÔÙ ÕÐ ÕÑ ÕÒ ÕÓ
ÐÑ
F!(G") G" F#( G) G
G( A$ G!
A") A" G# A) A
A( B$) A!
A!( B") B"
A#( B) B
B( C" B! C)
C
just tritone, or augmented fourth (45th harmonic) diminished fifth
acute or large diminished fifth acute or large double augmented fourth
grave or small fifth just and Pythagorean perfect fifth (3rd harmonic)
acute or large fifth diminished sixth
augmented fifth (25th harmonic) Pythagorean minor sixth
just minor sixth double augmented fifth grave or small major sixth
just major sixth Pythagorean major sixth (27th harmonic)
diminished seventh augmented sixth
acute or large augmented sixth Pythagorean minor seventh
acute or large minor seventh acute or large double augmented sixth
grave or small major seventh just diatonic major seventh (15th harmonic)
Pythagorean major seventh diminished octave
meantone augmented seventh (125th harmonic) grave or small octave
octave
45/32 64/45 36/25
375/256 40/27 3/2
243/160 192/125 25/16 128/81
8/5 625/384 400/243
5/3 27/16 128/75 125/72
225/128 16/9 9/5
1875/1024 50/27 15/8
243/128 48/25 125/64 160/81
2/1
1.406250 1.422222 1.440000 1.464844 1.481481 1.500000 1.518750 1.536000 1.562500 1.580247 1.600000 1.627604 1.646091 1.666667 1.687500 1.706667 1.736111 1.757813 1.777778 1.800000 1.831055 1.851852 1.875000 1.898438 1.920000 1.953125 1.975309
2.000000
367.911 372.090 376.741 383.241 387.593 392.438 397.344 401.857 408.790 413.433 418.601 425.823 430.659 436.043 441.493 446.508 454.211 459.889 465.112 470.926 479.051 484.492 490.548 496.680 502.321 510.987 516.791
523.251
590.224 609.776 631.283 660.896 680.449 701.955 723.014 743.014 772.627 792.180 813.686 843.300 862.852 884.359 905.865 925.418 955.031 976.537 996.090
1017.596 1047.210 1066.762 1088.269 1109.775 1129.328 1158.941 1178.494
1200.000
ß10 +10 +31 ß39 ß20 +02 +23 +43 ß27 ß08 +14 +43 ß37 ß16 +06 +25 ß45 ß23 ß04 +18 +47 ß33 ß12 +10 +29 ß41 ß22
+00
130 La Homa Kanto
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2005
La Homa Kanto Copyright © 2005 Andrián Pertoutwww.pertout.com • PO Box 4172 • Richmond East • Victoria 3121 • Australia
Made in Australia International Copyright Secured
for Harmonically Tuned Synthesizer Quartet
This whole round living world – the Human Music – rouses &– delights me, it stirs me to a “trans-ethnic”, a planetary music.
Hommage à Lou Harrison (1917-2003)
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La Homa Kanto 137
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138 La Homa Kanto
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152 La Homa Kanto
Andrián Pertout
Symétrie intégrante for Flute, Organ and Electronics
No. 394
Composed between November, 2005 and January, 2006
Commissioned by Andrew Blackburn, Jean Penny and the Melbourne City Council for the
2007 Melbourne Town Hall Organ Project
Premier: 6 July, 2007 (Melbourne Town Hall, 2007 Melbourne Town Hall Organ Project, Melbourne, Australia)
Duration: 12’30”
Copyright © 2006 Andrián Pertout
PROGRAMME NOTES
‘Symétrie intégrante’ or ‘Integral Symmetry’ represents a musical exploration of two distinct structural concepts – integrality and symmetry – and attempts to present
a discourse on the matter via the utilization of hexatonic and octatonic symmetrical scale formations. Also incorporated within compositional design is the notion of
symmetry, with the proportions 1:1, 2:1, 2:1, 4:1, 1:1, 2:1, 1:1 (denoting the duration of the seven distinct sections) intended to mirror the intervallic proportions of
the synthetic scales. Additive processes have also been utilized to facilitate melodic development, as well as various other compositional techniques that include
the reorganization of melodic material into four-part inverted and retrograde augmentation canons in the proportions 2:1, 3:1, 5:1, and 4:1.
integral /"Int@gr@l/ adj. 1. belonging as a part of the whole: the integral parts of the human body. 2. necessary to the completeness of the whole. 3. made up of parts which together form a whole. 4. Mathematics relating to or being an integer
(a whole number); not fractional. –n. 5. an integral whole. 6. Mathematics the result of the operation inverse to the differentiation; an expression from which a given function, equation, or system of equations
is derived by differentiation. –integrality /Int@"gr&l@ti/ n. –integrally adv.
symmetry /"sIm@tri/ n. –ries. 1. the correspondence, in size, form, and arrangement, of parts on opposite sides of a plane, line, or point; regularity of form or arrangement with reference to corresponding parts. 2. the proper or due proportion
of the parts of a body or whole to one another with regard to size and form; excellence of proportion.
(The Macquarie Essential Dictionary)
The pitch material employed in ‘Symétrie intégrante’ is based on Hexatonic (Six-tone Symmetrical, or Ditone) and Octatonic (Eight-tone Symmetrical) scales, freely
juxtaposing their modal derivatives, as well as their respective three and four unique transpositions. Featured in the work is the Hexatonic Major scale (consisting of a
succession of alternating minor third and minor second intervals, and in the key of C generating the pitches C, D!, E, G, A" and B), Hexatonic Minor scale (consisting
of a succession of alternating minor second and minor third intervals, and in the key of C generating the pitches C, D", E, F, G! and A), Octatonic Major scale
(consisting of a succession of alternating major and minor second intervals, and in the key of C generating the pitches C, D, E", F, G", A", A' and B), and the
Octatonic Minor scale (consisting of a succession of alternating minor and major second intervals, and in the key of C generating the pitches C, D", E", E', F!, G, A
and B").
156 Symétrie intégrante
Hexatonic Major (Six-tone Symmetrical, or Ditone Scale)
Hexatonic Minor (Six-tone Symmetrical, or Ditone Scale)
Symétrie intégrante 157
Octatonic Major (Eight-tone Symmetrical Scale)
Octatonic Minor (Eight-tone Symmetrical Scale)
158 Symétrie intégrante
INSTRUMENTATION
Piccolo, Concert Flute (with B foot attachment), Bass Flute
Organ (The Melbourne Town Hall Grand Organ: 4 Manuals, 149 Ranks, 116 Registers)
(Manual)
(Pedal)
“On May 25, 2001, the City of Melbourne welcomed the Grand Organ back to Town Hall. The organ was built in 1929 by William Hill & Son and Norman &
Beard Ltd., London & Melbourne. While all of the existing ranks were carefully restored to retain the original voice of the organ, new ranks of pipes were built
to complete gaps that existed in the 1929 design. The tonal design has carefully followed the original nature of the organ – that of a Grand
Romantic/Orchestral Concert Hall Organ. The exterior appearance of the organ has remained unchanged. The interior layout of the organ has been modified
to allow for public viewing areas from the back of the instrument. In this way, the public can safely view most of the organ without posing any risk of damage
to the instrument. This massive project (totalling A$4.2 million including the renovation of the chambers and organ) returns a civic icon to the City of
Melbourne and its visitors.” The Schantz Organ Company Inc., Orrville, Ohio, USA
Electronics (operator)
Hardware Requirements:
PC Laptop (Intel[R] Core[TM]2 CPU [email protected] or higher Pentium-compatible CPU)
Software Requirements:
Microsoft Windows XP Professional Version 2002, Service Pack 2
Magix Samplitude Professional 8.0 Digital Audio Workstation, plus a selection of DX and VST audio plug-ins Transposed score
Symétrie intégrante 159
PERFORMANCE NOTES
All instruments, with the following exceptions, sound as written in the score: the piccolo sounds an octave higher than written; the bass flute sounds an octave
lower than written.
In this score, accidentals apply only to the subsequent note in sections utilizing proportional notation, whereby in sections utilizing standard metric notation,
accidentals apply throughout the bar.
The opening section (A) denoted as ‘F.E. (as fast and even as possible)’ should be performed at a tempo producing the equivalent of (or as close to) semiquavers
at Ê=180, while the following section (B) denoted as ‘la metà del primo tempo’ should in striking contrast be performed at a tempo producing the equivalent of
quavers at Ê=180, and therefore notes at half the speed of the opening. The aforementioned pattern should be followed throughout, with only distinct tempo
markings adhered to in accordance to general rudiments of music. The same rules apply to section (H), which presents an accelerando poco a poco from ‘la metà
del primo tempo’, or quavers at Ê=180 that gradually accelerates up to optimum speed in section (I) [‘F.E. (as fast and even as possible)’], or semiquavers at
Ê=180. Section (J) presenting a retrograde of (H).
The instrumentalists should both be amplified; the piccolo and flutes in mono; while the organ, in a stereo microphone configuration incorporating the great and
swell. Further to this, a mixing console and speaker system accommodating 5-channel sound diffusion should be utilized. There is also a requirement to include an
operator (a third performer) to manage the technology. Flute pizz. combination of key click, diaphragm kick, and flicking of the tongue
160 Symétrie intégrante
�
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Pedal
Manual
F.E. (as fast and even as possible)
A
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�Great: Principle Chorus to Mixture
Pedal: Principle Chorus to Mixture
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�� �
Symétrie intégranteAndrián Pertout, No. 394
2005-2006
Symétrie intégrante Copyright © 2006 Andrián Pertoutwww.pertout.com • PO Box 4172 • Richmond East • Victoria 3121 • Australia
Made in Australia International Copyright Secured
for Flute, Organ and Electronics
Commissioned by Andrew Blackburn, Jean Penny and the Melbourne City Council
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162 Symétrie intégrante
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Symétrie intégrante 163
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164 Symétrie intégrante
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Symétrie intégrante 165
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Symétrie intégrante 169
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Symétrie intégrante 171
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Pedal: 32', 16', 8', 4' Flue Stops plus Contra Fagotto 32'
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AP • 394
172 Symétrie intégrante
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Symétrie intégrante 201
Andrián Pertout
Tres Imágenes Norteñas for Shakuhachi and Harpsichord
No. 396
Composed between June and August, 2006
Composed for Anne Norman and Peter Hagen as part of the
2006 Australia-Japan Year of Exchange Celebrations
Premier: 10 December, 2006 (Richmond Town Hall, Richmond, Melbourne, Australia)
Duration: 9’14”
Copyright © 2006 Andrián Pertout
PROGRAMME NOTES
‘Tres Imágenes Norteñas’ or ‘Three Northern Images’ was especially composed for Anne Norman (shakuhachi) and Peter Hagen (harpsichord) as part of the ‘2006
Australia-Japan Year of Exchange Celebrations’ and the Melbourne Composers’ League ‘From a Silence Well’ project. The work represents an attempt to explore
some of the aesthetic principles of Japanese art music, incorporating a combination of gagaku (court orchestra music) and shomyo (Buddhist chant) concepts of
“elastic or breath rhythm” and “stereotyped rhythmic patterns”, the juxtaposition of polymodal and polytonal pitch materials based on the In, Hirajoshi and
Kumoijoshi scales, as well as a contemporary interpretation of the tripartite jo-ha-kyô form common to not only the gagaku genre, but also to nagauta (kabuki theatre
music) and nohgaku (noh drama music).
The “three basic rhythmic structures” of gagaku (“units of eight, four, or two beats”) have been utilized in the work, including nobe-byoshi (8/4), haya-byoshi (4/4),
and a fast tada-byoshi section grouping two and three pulses, generally referred to as yatara-byoshi (in this particular case represented via 2/8+3/8). A musical
construct hence modelled on the Japanese jo-ha-kyô form – or theoretical framework of gagaku – with its three slow, medium and fast tempos essentially
delineating the “introduction, exposition and denouement” of jo-ha-kyô and schematically producing sequential motivic acceleration. The harmonic strategy
adopted in the compositional approach has been to preserve the nuances of each individual pentatonic scale type and four distinct modes as much as possible via
the segregation of auxiliary tones from primary scale tones. Auxiliary tones have therefore been only utilized as ornamental secondary scale tones, and hence
immaterial to the vertical harmony. The shakuhachi allocated with the In scale, while the right and left hand harpsichord parts, the Hirajoshi and Kumoijoshi scales
respectively. The pitch levels of the latter two scales – serving as the accompaniment, and collectively forming ten-note polymodal and polytonal chords –
positioned a tritone above, and a perfect fourth below the tonal centre of the In scale.
“In the West, music has been defined in terms of aural form in motion, but in gagaku both the formal and progressive elements have been minimized, leaving only
the beauty of sound, the exotic creature in a slightly clouded drop of amber,” states William P. Malm in his 1959 publication of Japanese Music and Musical
Instruments. The minimalist nature of the simple melody adopted in ‘Tres Imágenes Norteñas’ illustrative of this statement, with melodic development centred mainly
on transformation rather than invention, hence displaying a clear focus on texture and mood.
206 Tres Imágenes Norteñas
Modes Generated by the In Scale
In Scale
2nd Mode In Scale
3rd Mode In Scale
4th Mode In Scale
5th Mode In Scale
Tres Imágenes Norteñas 207
Modes Generated by the Hirajoshi Scale
Hirajoshi Scale
2nd Mode Hirajoshi Scale
3rd Mode Hirajoshi Scale
4th Mode Hirajoshi Scale
5th Mode Hirajoshi Scale
208 Tres Imágenes Norteñas
Modes Generated by the Kumoijoshi Scale
Kumoijoshi Scale
2nd Mode Kumoijoshi Scale
3rd Mode Kumoijoshi Scale
4th Mode Kumoijoshi Scale
5th Mode Kumoijoshi Scale
Tres Imágenes Norteñas 209
INSTRUMENTATION
Shakuhachi (Japanese bamboo flute)
(7-hole 1.8 D Shaku)
(2.4 A Shaku)
Harpsichord
(Single Manual)
Transposed score
210 Tres Imágenes Norteñas
PERFORMANCE NOTES
All instruments, with the following exceptions, sound as written in the score: the 2.4 A Shakuhachi sounds a perfect fourth lower than written.
In this score, accidentals apply throughout the bar.
The ornamental upward and downward arpeggios in the harpsichord part should be performed at the rate of successive hemidemisemiquaver (sixty-fourth note)
triplets/sextuplets, or alternatively, as fast as possible. Further to that, they should be accented and commenced on the beat, hence not rhythmically anticipated to
allow the final note to coincide with the beginning of the bar.
Upward and downward arpeggios notated as consecutive grace notes should likewise adopt the same performance directions abovementioned.
Tres Imágenes Norteñas 211
Other notation incorporating grace notes (suggesting unaccented short single and double appoggiaturas) should be approached in the usual manner, subscribing
to common contemporary performance practices.
Shakuhachi
blow air through the instrument to produce air tones (white noise) in addition to the normal tone
mura-iki explosive breath – introduction of overtones and white noise into the normal tone via the
augmentation of air pressure and modification of embouchure
senza vibrato – slow to fast vibrato
normal ‘regular’ vibrato
fast vibrato – senza vibrato – slow to fast vibrato
pitch bend (raise and return to fundamental pitch)
senza vibrato
212 Tres Imágenes Norteñas
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Tres Imágenes NorteñasAndrián Pertout, No. 396
2006
Tres Imágenes Norteñas Copyright © 2006 Andrián Pertoutwww.pertout.com • PO Box 4172 • Richmond East • Victoria 3121 • Australia
Made in Australia International Copyright Secured
for Shakuhachi and Harpsichord
Composed for Anne Norman and Peter Hagen
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226 Tres Imágenes Norteñas
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Tres Imágenes Norteñas 229