Pythagorean diatonic scale on C  Play (help·info).

Diatonic scale on C  Play (help·info) 12-tone equal tempered and  Play (help·info) just intonation.

Pythagorean (tonic) major chord on C  Play (help·info) (compare  Play (help·info) equal tempered and  Play (help·info) just).

Pythagorean tuning (Greek: Πυθαγόρεια κλίμακα) is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2 (the perfect fifth), "found in the harmonic series."^[1] This interval is chosen because it is one of the most consonant. Attributed to Pythagoras (sixth century BC), "the Pythagorean system would appear to be ideal because of the purity, of the fifths, but other intervals, particularly the major third, are so badly out of tune that major chords [may be considered] a dissonance."^[1][2]

The Pythagorean scale is any scale which may be constructed from only perfect fifths and octaves^[3] or the gamut of (all 12) pitches constructed from only perfect fifths and octaves and from which specific scales may be drawn. See: generated collection. For example, the series of fifths generated above gives seven notes, a diatonic major scale on C in Pythagorean tuning, shown in notation on the top right.

Method[link]

Pythagorean tuning is based on a stack of intervals called perfect fifths, each tuned in the ratio 3:2, the next simplest ratio after 2:1. Starting from D for example (D-based tuning), six other notes are produced by moving six times a ratio 3:2 up, and the remaining ones by moving the same ratio down:

E♭—B♭—F—C—G—D—A—E—B—F♯—C♯—G♯

This succession of eleven 3:2 intervals spans across a wide range of frequency (on a piano keyboard, it encompasses 77 keys). Since notes differing in frequency by a factor of 2 are given the same name, it is customary to divide or multiply the frequencies of some of these notes by 2 or by a power of 2. The purpose of this adjustment is to move the 12 notes within a smaller range of frequency, namely within the interval between the base note D and the D above it (a note with twice its frequency). This interval is typically called the basic octave (on a piano keyboard, an octave encompasses only 13 keys ).

For instance, the A is tuned such that its frequency equals 3:2 times the frequency of D — if D is tuned to a frequency of 288 Hz, then A is tuned to 432 Hz. Similarly, the E above A is tuned such that its frequency equals 3:2 times the frequency of A, or 9:4 times the frequency of D — with A at 432 Hz, this puts E at 648 Hz. Since this E is outside the above-mentioned basic octave (i.e. its frequency is more than twice the frequency of the base note D), it is usual to halve its frequency to move it within the basic octave. Therefore, E is tuned to 324 Hz, a 9:8 above D. The B at 3:2 above that E is tuned to the ratio 27:16 and so on. Starting from the same point working the other way, G is tuned as 3:2 below D, which means that it is assigned a frequency equal to 2:3 times the frequency of D — with D at 288 Hz, this puts G at 192 Hz. This frequency is then doubled (to 384 Hz) to bring it into the basic octave.

When extending this tuning however, a problem arises: no stack of 3:2 intervals (perfect fifths) will fit exactly into any stack of 2:1 intervals (octaves). For instance a stack such as this, obtained by adding one more note to the stack shown above

A♭—E♭—B♭—F—C—G—D—A—E—B—F♯—C♯—G♯

will be similar but not identical in size to a stack of 7 octaves. More exactly, it will be about a quarter of a semitone larger (see Pythagorean comma). Thus, A♭ and G♯, when brought into the basic octave, will not coincide as expected. The table below illustrates this, showing for each note in the basic octave the conventional name of the interval from D (the base note), the formula to compute its frequency ratio, its size in cents, and the difference in cents (labeled ET-dif in the table) between its size and the size of the corresponding one in the equally tempered scale.

In the formulas, the ratios 3:2 or 2:3 represent an ascending or descending perfect fifth (i.e. an increase or decrease in frequency by a perfect fifth), while 2:1 or 1:2 represent an ascending or descending octave.

The major scale based on C, obtained from this tuning is^[4]:

In equal temperament, pairs of enharmonic notes such as A♭ and G♯ are thought of as being exactly the same note — however, as the above table indicates, in Pythagorean tuning they have different ratios with respect to D, which means they are at a different frequency. This discrepancy, of about 23.46 cents, or nearly one quarter of a semitone, is known as a Pythagorean comma.

To get around this problem, Pythagorean tuning ignores A♭, and uses only the 12 notes from E♭ to G♯. This, as shown above, implies that only eleven just fifths are used to build the entire chromatic scale. The remaining fifth (from G♯ to E♭) is left badly out-of-tune, meaning that any music which combines those two notes is unplayable in this tuning. A very out-of-tune interval such as this one is known as a wolf interval. In the case of Pythagorean tuning, all the fifths are 701.96 cents wide, in the exact ratio 3:2, except the wolf fifth, which is only 678.49 cents wide, nearly a quarter of a semitone flatter.

If the notes G♯ and E♭ need to be sounded together, the position of the wolf fifth can be changed. For example, a C-based Pythagorean tuning would produce a stack of fifths running from D♭ to F♯, making F♯-D♭ the wolf interval. However, there will always be one wolf fifth in Pythagorean tuning, making it impossible to play in all keys in tune.

Size of intervals[link]

The table above shows only intervals from D. However, intervals can be formed by starting from each of the above listed 12 notes. Thus, twelve intervals can be defined for each interval type (twelve unisons, twelve semitones, twelve intervals composed of 2 semitones, twelve intervals composed of 3 semitones, etc.).

Frequency ratio of the 144 intervals in D-based Pythagorean tuning. Interval names are given in their shortened form. Pure intervals are shown in bold font. Wolf intervals are highlighted in red.^[5] Numbers larger than 999 are shown as powers of 2 or 3. Other versions of this table are provided here and here.

Approximate size in cents of the 144 intervals in D-based Pythagorean tuning. Interval names are given in their shortened form. Pure intervals are shown in bold font. Wolf intervals are highlighted in red.^[5]

As explained above, one of the twelve fifths (the wolf fifth) has a different size with respect to the other eleven. For a similar reason, each of the other interval types, except for the unisons and the octaves, has two different sizes in Pythagorean tuning. This is the price paid for seeking just intonation. The tables on the right and below show their frequency ratios and their approximate sizes in cents. Interval names are given in their standard shortened form. For instance, the size of the interval from D to A, which is a perfect fifth (P5), can be found in the seventh column of the row labeled D. Strictly just (or pure) intervals are shown in bold font. Wolf intervals are highlighted in red.^[5]

The reason why the interval sizes vary throughout the scale is that the pitches forming the scale are unevenly spaced. Namely, the frequencies defined by construction for the twelve notes determine two different semitones (i.e. intervals between adjacent notes):

1. The minor second (m2), also called diatonic semitone, with size
   Failed to parse (Missing texvc executable; please see math/README to configure.): S_1 = {256 \over 243} \approx 90.225 \ \hbox{cents}

 (e.g. between D and E♭)

1. The augmented unison (A1), also called chromatic semitone, with size
   Failed to parse (Missing texvc executable; please see math/README to configure.): S_2 = {3^7 \over 2^{11}} = {2187 \over 2048} \approx 113.685 \ \hbox{cents}

 (e.g. between E♭ and E)

Conversely, in an equally tempered chromatic scale, by definition the twelve pitches are equally spaced, all semitones having a size of exactly

Failed to parse (Missing texvc executable; please see math/README to configure.): S_E = \sqrt[12]{2} = 100.000 \ \hbox{cents}.

As a consequence all intervals of any given type have the same size (e.g., all major thirds have the same size, all fifths have the same size, etc.). The price paid, in this case, is that none of them is justly tuned and perfectly consonant, except, of course, for the unison and the octave.

For a comparison with other tuning systems, see also this table.

By definition, in Pythagorean tuning 11 perfect fifths (P5 in the table) have a size of approximately 701.955 cents (700+ε cents, where ε ≈ 1.955 cents). Since the average size of the 12 fifths must equal exactly 700 cents (as in equal temperament), the other one must have a size of 700−11ε cents, which is about 678.495 cents (the wolf fifth). Notice that, as shown in the table, the latter interval, although enharmonically equivalent to a fifth, is more properly called a diminished sixth (d6). Similarly,

• 9 minor thirds (m3) are ≈ 294.135 cents (300−3ε), 3 augmented seconds (A2) are ≈ 317.595 cents (300+9ε), and their average is 300 cents;
• 8 major thirds (M3) are ≈ 407.820 cents (400+4ε), 4 diminished fourths (d4) are ≈ 384.360 cents (400−8ε), and their average is 400 cents;
• 7 diatonic semitones (m2) are ≈ 90.225 cents (100−5ε), 5 chromatic semitones (A1) are ≈ 113.685 cents (100+7ε), and their average is 100 cents.

In short, similar differences in width are observed for all interval types, except for unisons and octaves, and they are all multiples of ε, the difference between the Pythagorean fifth and the average fifth.

Notice that, as an obvious consequence, each augmented or diminished interval is exactly 12ε (≈ 23.460) cents narrower or wider than its enharmonic equivalent. For instance, the d6 (or wolf fifth) is 12ε cents narrower than each P5, and each A2 is 12ε cents wider than each m3. This interval of size 12ε is known as a Pythagorean comma, exactly equal to the opposite of a diminished second (≈ −23.460 cents). This implies that ε can be also defined as one twelfth of a Pythagorean comma.

Pythagorean intervals[link]

Four of the above mentioned intervals take a specific name in Pythagorean tuning. In the following table, these specific names are provided, together with alternative names used generically for some other intervals. Notice that the Pythagorean comma does not coincide with the diminished second, as its size (524288:531441) is the reciprocal of the Pythagorean diminished second (531441:524288). Also ditone and semiditone are specific for Pythagorean tuning, while tone and tritone are used generically for all tuning systems. Interestingly, despite its name, a semiditone (3 semitones, or about 300 cents) can hardly be viewed as half of a ditone (4 semitones, or about 400 cents). All the intervals with prefix sesqui- are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave.

History[link]

The syntonic tuning continuum^[6].

Because of the wolf interval, this tuning is rarely used nowadays, although it is thought to have been widespread. In music which does not change key very often, or which is not very harmonically adventurous, the wolf interval is unlikely to be a problem, as not all the possible fifths will be heard in such pieces.

Because most fifths in Pythagorean tuning are in the simple ratio of 3:2, they sound very "smooth" and consonant. The thirds, by contrast, most of which are in the relatively complex ratios of 81:64 (for major thirds) and 32:27 (for minor thirds), sound less smooth.^[7] For this reason, Pythagorean tuning is particularly well suited to music which treats fifths as consonances, and thirds as dissonances. In western classical music, this usually means music written prior to the 15th century. As thirds came to be treated as consonances, so meantone temperament, and particularly quarter-comma meantone, which tunes thirds to the relatively simple ratio of 5:4, became more popular. However, meantone presented its own harmonic challenges, and its wolf intervals proved to be even worse than those of the Pythagorean tuning (so much so that it often required 19 keys to the octave as opposed to the 12 in Pythagorean tuning), so it is not suitable for all music.

From around the 18th century, as the desire grew for instruments to change key, and therefore to avoid a wolf interval, this led to the widespread use of well temperaments and eventually equal temperament.

Discography[link]

• Gothic Voices – Music for the Lion-Hearted King (Hyperion, CDA66336, 1989), directed by Christopher Page (Leech-Wilkinson)
• Lou Harrison performed by John Schneider and the Cal Arts Percussion Ensemble conducted by John Bergamo - Guitar & Percussion (Etceter Records, KTC1071, 1990): Suite No. 1 for guitar and percussion and Plaint & Variations on "Song of Palestine"

See also[link]

• Enharmonic scale
• List of meantone intervals
• List of musical intervals
• Regular temperament
• Shí-èr-lǜ
• Temperament
• Timaeus (dialogue), in which Plato discusses Pythagorean tuning
• Whole-tone scale

References[link]

Footnotes[link]

Notations[link]

• Daniel Leech-Wilkinson (1997), "The good, the bad and the boring", Companion to Medieval & Renaissance Music. Oxford University Press. ISBN 0-19-816540-4.

External links[link]

• "A Pythagorean tuning of the diatonic scale", with audio samples.
• "Pythagorean Tuning and Medieval Polyphony", by Margo Schulter.

Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer. He was a student of Henry Cowell, Arnold Schoenberg, and K. P. H. Notoprojo (formerly called K.R.T. Wasitodiningrat, informally called Pak Cokro).

Harrison is particularly noted for incorporating elements of the music of non-Western cultures into his work, with a number of pieces written for Javanese style gamelan instruments, including ensembles constructed and tuned by Harrison and his partner William Colvig. The majority of his works are written in just intonation rather than the more widespread equal temperament. Harrison is one of the most prominent composers to have worked with microtones.

Biography[link]

Harrison was born in Portland, Oregon, but moved with his family to a number of locations around the San Francisco Bay Area as a child. He graduated from Burlingame High School in Burlingame, California in 1934, then he moved to San Francisco.^[1] The diverse music which he was to be exposed to there, including Cantonese opera, Native American music, Mexican music, and jazz as well as classical music, was to have a major influence on him. He also heard recordings of Indonesian music early in life.

Harrison took Henry Cowell's "Music of the Peoples of the World" course, and also studied counterpoint and composition with him. He later went to the University of California at Los Angeles to work at the dance department as a dancer and accompanist. While there, he took lessons from Arnold Schoenberg which led to an interest in Schoenberg's twelve-tone technique.^[2] The pieces he was writing at this time, however, were largely percussive works using unconventional materials, such as car brake drums, as musical instruments. These pieces were similar to those being written by John Cage around the same time, and the two sometimes worked together.

In 1943, Harrison moved to New York City where he worked as a music critic for the Herald Tribune.^[2] While there he met Charles Ives, became his friend, and did a good deal in bringing Ives to the attention of the musical world, which had largely ignored him up to that point. With the assistance of his mentor Cowell, Harrison prepared and conducted the premiere of Ives's Symphony No. 3, and in return received help from Ives financially. When Ives won the Pulitzer Prize for Music for that piece, he gave half of the money to Harrison. Harrison also edited a large number of Ives's works, receiving compensation often in excess of what he billed (Miller and Lieberman 1998).

As well as Ives, Harrison supported and promoted the music of other unconventional American composers, including Edgard Varèse and Carl Ruggles as well as Alan Hovhaness.^[3] Later during his time in North Carolina, Harrison taught at Black Mountain College. In 1947, he suffered a nervous breakdown, and moved back to California.

Following in the path of Canadian composer Colin McPhee, who had done extensive research in Indonesian music in the 1930s and wrote a number of compositions incorporating Balinese and Javanese elements, Harrison's style began to change, showing the influence of gamelan music more clearly if only in timbre: "It was the sound itself that attracted me. In New York, when I changed gears out of twelve tonalism, I explored this timbre. The gamelan movements in my Suite for Violin, Piano, and Small Orchestra [1951] are aural imitations of the generalized sounds of gamelan" (ibid, p. 160). Virgil Thomson (with whom Harrison also studied) gave him a copy of Harry Partch's book on musical tuning, Genesis of a Music, which prompted Harrison to start writing music in just intonation. He did not abandon equal temperament altogether, but often expressed a desire to do so. In an oft-quoted comment referring to the frequency ratios used in just intonation, he said, "I'd long thought that I would love a time when musicians were numerate as well as literate. I'd love to be a conductor and say, 'Now, cellos, you gave me 10:9 there, please give me a 9:8 instead,' I'd love to get that!"

Although much influenced by Asian music, Harrison did not visit the continent until a 1961 trip to Japan and Korea and a 1962 trip to Taiwan (ibid, p. 141). He and his partner William Colvig later constructed a tuned percussion ensemble, using resonated aluminum keys and tubes, as well as oxygen tanks and other found percussion instruments. They called this "an American gamelan," in order to distinguish it from those in Indonesia. [They also constructed?] gamelan-type instruments tuned to just pentatonic scales from unusual materials such as tin cans and aluminium furniture tubing. He wrote "La Koro Sutro" for these instruments and chorus, as well as "Suite for Violin and American Gamelan." In addition, Harrison played and composed for the Chinese guzheng zither, and presented (with Colvig, his student Richard Dee, and the singer Lily Chin) over 300 concerts of traditional Chinese music in the 1960s.[1]

He was a composer-in-residence at San Jose State University in San Jose, California during the 1960s. The university honored him with an all-Harrison concert in Morris Daley Auditorium in 1969, featuring dancers, singers, and musicians. The highlight of the concert was the world premiere of Harrison's depiction of the story of Orpheus, which utilized soloists, the San Jose State University a capella choir, as well as a unique group of percussionists.

Like many other 20th-century composers, Harrison found it hard to support himself with his music, and took a number of other jobs to earn a living, including record salesman, florist, animal nurse, and forestry firefighter.

Harrison was outspoken about his political views, such as his pacifism (he was an active supporter of the international language Esperanto), and the fact that he was gay. He was also politically active and informed, including knowledge of gay history. He wrote many pieces with political texts or titles, writing, for instance, Homage to Pacifica for the opening of the Berkeley Headquarters of the Pacifica Foundation, and accepting commissions from the Portland Gay Men's Chorus (1988 and 1985) and by the Seattle Men's Chorus to arrange (1987) his Strict Songs, originally for eight baritones, for "a chorus of 120 male singing enthusiasts. Some of them good; some not so good. But the number is so fabulous" (ibid, p. 98). Lawrence Mass (ibid, p. 190) describes:

With Lou Harrison...being gay is something affirmative. He's proud to be a gay composer and interested in talking about what that might mean. He doesn't feel threatened that this means he won't be thought of as an American composer who is also great and timeless and universal.

Janice Giteck (ibid, p. 194) describes Harrison as:

unabashedly androgynous in his way of approaching creativity. He has a vital connection to the feminine as well as to the masculine. The female part is apparent in the sense of beingness. But at the same time, Lou is very male, too, ferociously active and assertive, rhythmic, pulsing, and aggressive.

On November 2, 1990, the Brooklyn Philharmonic premiered Harrison's fourth symphony, which he titled Last Symphony. He combined native American music, ancient music, and Asian music, tying it all together with lush orchestral writing. A special inclusion was a series of Navajo "Coyote Stories." He made a number of revisions to the symphonies before completing a final version in 1995, which was recorded by Barry Jekowsky and the California Symphony for Argo Records at Skywalker Ranch in Nicasio, California in March 1997. The CD also included Harrison's Elegy, to the Memory of Calvin Simmons (a tribute to the former conductor of the Oakland Symphony, who drowned in a boating accident in 1982), excerpts from Solstice, Concerto in Slendro, and Double Music (his collaboration with John Cage).^[4]

Harrison and Colvig built two full Javanese-style gamelan, modeled on the instrumentation of Kyai Udan Mas at U.C. Berkeley. One was named Si Betty for the art patron Betty Freeman; the other, built at Mills College, was named Si Darius/Si Madeliene. Harrison taught at Mills College for several years, where one of his students was Jin Hi Kim.

Personal life[link]

Harrison lived for many years with Bill Colvig in Aptos, California. He and Colvig purchased land in Joshua Tree, California, where they designed and built the Harrison House Retreat, a straw bale house.

Harrison died in Lafayette, Indiana, from a heart attack while on his way to a festival of his music at The Ohio State University.

Harrison's music[link]

Many of Harrison's early works are for percussion instruments, often made out of what would usually be regarded as junk or found objects such as garbage cans and steel brake drums. He also wrote a number of pieces using Schoenberg's twelve tone technique, including the opera Rapunzel and his Symphony on G (Symphony No. 1) (1952). Several works feature the tack piano, a kind of prepared piano with small nails inserted into the hammers to give the instrument a more percussive sound.

Harrison's mature musical style is based on "melodicles", short motifs which are turned backwards and upsidedown to create a musical mode the piece is based on. His music is typically spartan in texture but lyrical, and harmony usually simple or sometimes lacking altogether, with the focus instead being on rhythm and melody. Ned Rorem describes, "Lou Harrison's compositions demonstrate a variety of means and techniques. In general he is a melodist. Rhythm has a significant place in his work, too. Harmony is unimportant, although tonality is. He is one of the first American composers to successfully create a workable marriage between Eastern and Western forms." Listeners to Harrison's music are often surprised that such a modern, innovative composer actually wrote lyrical melodies and often richly harmonized and orchestrated them, much in the tradition of the late Romantic composers.

Another component of Harrison's aesthetic is what Harry Partch would call corporeality, an emphasis on the physical and the sensual including live, human, performance and improvisation, timbre, rhythm, and the sense of space in his melodic lines, whether solo or in counterpoint, and most notably in his frequent dance collaborations.

Among Harrison's better known works are the Concerto in Slendro, Concerto for Violin with Percussion Orchestra, Organ Concerto with Percussion (1973), which was given at the Proms in London in 1997; the Double Concerto (1981–82) for violin, cello, and Javanese gamelan; the Piano Concerto (1983–85) for piano tuned in Kirnberger #2 (a form of well temperament) and orchestra, which was written for Keith Jarrett;^[5] and a Concerto for Piano and Javanese Gamelan; as well as four numbered orchestral symphonies. He also wrote a large number of works in non-traditional forms. Harrison was fluent in several languages including American Sign Language, Mandarin and Esperanto, and several of his pieces have Esperanto titles and texts, most notably La Koro Sutro (1973).

Like Charles Ives, Harrison completed four symphonies. He typically combined a variety of the musical forms and languages that he preferred. This is quite apparent in the fourth symphony, recorded by the California Symphony for Argo Records, as well as his third symphony, which was performed and broadcast by the Dennis Russell Davies and the San Francisco Symphony Orchestra.

Films[link]

• 1986 – Lou Harrison : "cherish, conserve, consider, create." Directed by Eric Marin.
• 1995 – Musical Outsiders: An American Legacy – Harry Partch, Lou Harrison, and Terry Riley. Directed by Michael Blackwood.
• 2012 - Lou Harrison: A World of Music. Directed by Eva Soltes.

Works[link]

Chamber Works[link]

• Ariadne, flute & percussion
• At the Tomb of Charles Ives, chamber orchestra
• Concerto for Flute & Percussion
• Concerto for Organ with Percussion Orchestra, percussion ensemble, organ and ensemble
• Concerto for Pipa with String Orchestra, Asian instrument and ensemble
• New First Suite for Strings, string orchestra
• Pacifika Rondo, chamber orchestra
• Por Gitaro, guitar solo
• Praise for the Beauty of Hummingbirds, mixed quintet
• Rhymes with Silver, violoncello and ensemble, mixed quintet
• Serenade for Guitar with optional Percussion, mixed duo, guitar solo
• Seven Pastorales, chamber orchestra
• Solstice, octet (flute, oboe, trumpet, 2 cellos, string bass, celesta, tack piano)
• Songs in the Forest, mixed quartet
• String Quartet Set
• Suite for Cello and Harp
• Suite for Percussion (for five percussionists, 1942)
• Suite for Violin with American Gamelan
• Suite for Violin with String Orchestra
• Suite for Violoncello and Piano
• Suites for Cello and String Orchestra
• The Perilous Chapel, mixed quartet
• Varied Trio, Rice Bowls, Violin, Vibraphone, Piano

Orchestral Works[link]

• A Parade
• Elegiac Symphony
• Music for Violin with Various Instruments, European, Asian, and African, string solo and orchestra
• Symphony No. 4
• Symphony On G

Vocal Works[link]

• Air from Rapunzel, high voice and ensemble
• Alma Redemptoris Mater, low voice and ensemble
• La Koro Sutro, mixed chorus and gamelan, mixed chorus and ensemble
• Mass to Saint Anthony, mixed chorus and ensemble
• Strict Songs, baritone solo, chorus and chamber orchestra
• Three Songs, men's chorus and ensemble

Piano Works[link]

• Six Sonatas for Cembalo, piano solo, harpsichord solo

Opera[link]

• Rapunzel
• Young Caesar

References[link]

This article's citation style may be unclear. The references used may be made clearer with a different or consistent style of citation, footnoting, or external linking. (January 2010)

This article includes a list of references, but its sources remain unclear because it has insufficient inline citations. Please help to improve this article by introducing more precise citations. (January 2010)

• Kennedy, Michael (2006), The Oxford Dictionary of Music, 985 pages, ISBN 0-19-861459-4
• Miller, Leta E. and Lieberman, Frederic (1998). Lou Harrison: Composing a World. Oxford University Press. ISBN 0-19-511022-6.

External links[link]

Archives[link]

• Lou Harrison Archive at the University of California, Santa Cruz
• San Jose State University School of Music & Dance

Obituaries and remembrances[link]

• Obituary from the Musical Times
• Remembrance by Don Gillespie, from NewMusicBox
• I remember Lou, from Other Minds

Interviews[link]

• Duffie, Bruce. “Composer Lou Harrison: A Conversation With Bruce Duffie.” April 1987.
• Golden, Barbara. “Conversation with Lou Harrison.” eContact! 12.2 — Interviews (2) (April 2010). Montréal: CEC.
• Clark, Philip. "Chimes of Freedom" The Wire, August 2002, pp 28–32

Other links[link]

• Lou Harrison: Middle Period Works
• New Albion Artists: Lou Harrison
• Peermusic Classical: Lou Harrison Composer's Publisher and Bio
• Lou Harrison artist page from Frog Peak Music site
• Other Minds: Lou Harrison
• Lou Harrison Documentary Project
• Lou Harrison: an interview by Dr Geoff Smith
• Rapunzel by William Morris, inspiration for Lou Harrison's opera

Listening[link]

• Art of the States: Lou Harrison seven works by the composer
• Lou Harrison tribute from Other Minds Festival 9, 2003
• Epitonic.com: Lou Harrison including tracks from Rhymes With Silver and La Koro Sutro
• Del Sol Quartet:Tear with Harrison's Song of Palestine from String Quartet Set by Del Sol Quartet

This article relies largely or entirely upon a single source. Please help improve this article by introducing citations to additional sources. Discussion about the problems with the sole source used may be found on the talk page. (July 2011)

This biographical article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (July 2011)

Simone Vitale (born 1 March 1986 in Sora) is an Italian footballer who currently plays as a defender for Frosinone Calcio.

References[link]

External links[link]

• Pescara Calcio profile
• TuttoCalciatori profile

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