5-limit tuning and intervals

Sonata for Microtonal Piano (Ben Johnston)

Sonata for Microtonal Piano is a sonata for specifically microtonally tuned piano by Ben Johnston written in 1964 (see also just intonation). When the movements are played in an alternate order the piece is titled Grindlemusic. The piece uses, "chains of just tuned (untempered) triadic intervals over the whole piano range," with very few, only seven, piano keys having octave equivalents, thus providing eighty-one different pitches (there are eighty-eight white and black keys total). "Effectively, for the listener, there are three main gradations of consonance/dissonance: (1) smooth untempered [ major and minor] thirds and fifths, which have the least amount of harshness caused by acoustical beats; (2) compounds of these...; and (3) chromatic or enharmonic intervals...which sound 'out of tune.'" [note the difference between 'keyboard distance' in this tuning and pitch or interval distance: for example a fifteenth, two keys with fifteen notes between them, on a normally tuned keyboard is a double octave, while in this tuning a fifteenth is slightly sharper than that] "This suggested...the possibility of two opposite systems for the deployment of pitches: one that synchronized pitch choices with the layout of consonant and dissonant intervals on the keyboard [see: tonality], and a violently contrasting one in which the system for choosing pitches, a twelve-tone-row procedure derived largely from certain practices of Berg and late Schoenberg [see: twelve-tone technique], either ignores or flaunts the consonance/dissonance keyboard layout [see: atonality]. There are two contrasting movements of each of these types." "This makes possible a Janus[two]-faced work, in which, with only the third movement similarly located in both versions, permutations of the placement of the other three movements creates an alter-ego relationship between the two versions, called respectively Sonata for Microtonal Piano and Grindlemusic. In the Sonata version, the movements correspond to the classical sonata scheme: the 'sonata-allegro,' the 'scherzo,' the songlike 'slow movement,' and the 'finale,' which is in this case a meditative adagio. All movements, however are cast in the common ballad mold, AABA, as is each of the two entire versions, the Sonata and Grindlemusic." In the words of the composer: "The Sonata, whether presented as beauty or as the beast, is a monstrous parody-enigma, allusive, referential, sometimes derisive, distorted, a tissue of familiarity in radically strange garb....Whatever the closing mood brings to mind, it is overlaid with irony and derision. The Sonata sequence poses the challenge: fast, faster, slow, slower. When, in the Sonata's finale, the knots are finally untied, will it be clear from what Houdini has escaped?" "All tempos, all phrase and section lengths, and in certain parts of the 'finale' (which opens Grindlemusic, the sequence closing with the 'scherzo'), even note-to-note timings conform to a proportional scheme derived from a single pattern of changes in AABA form. This pattern is associated with two distinct motivic groups at different points in the work." The piece has been recorded and released on: * Microtonal Piano by Ben Johnston (1997). Phillip Bush, piano. Koch International Classics 3-7369-2. "Though the piece was recorded as the Sonata, and though Johnston and I both agree that a live performance of Grindlemusic would contain subtle alterations, the metric modulations between movements are nevertheless worked out to arrive at identical tempos in each version. Therefore I feel that a passable sense of Grindlemusic can be experienced by simply reprogramming the tracks on your compact disc player. To program the tracks for Grindlemusic, select the track order 9, 6, 8, 7." The Sonata being track order 6, 7, 8, 9. 8, being B, stays in the same place. (Wikipedia).

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J. S. Bach - Flute & Viola Sonatas - (2CD)

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From playlist Classical Music

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Bach - Cello Suite No. 1 in G Major BWV1007 - Mov. 1-3/6

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From playlist Brilliant Music

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Peace for Triple Piano (stereographic projection version)

The original spherical video: https://youtu.be/HcRW3FMuttY The Making of "Peace for Triple Piano": https://youtu.be/x1zJoU6Luss A flat video version of "Peace for Triple Piano", an exploration of symmetries through space and time, with Vi Hart.

From playlist Spherical video

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J.S. Bach: Suites for Guitar

Streaming & Downloads : https://brilliant-classics.lnk.to/SuitesforGuitarID More information: https://www.brilliantclassics.com/articles/j/js-bach-suites-for-guitar/ Composer: Johann Sebastian Bach Artist: Luigi Attademo (guitar) J.S. Bach composed no original works for guitar, and altho

From playlist Classical Music

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Tchaikovsky - Piano Concerto 1 (B Flat Minor)

The Piano Concerto No. 1 in B flat minor, Op. 23, was composed by Pyotr Ilyich Tchaikovsky between November 1874 and February 1875. ▶️ More from Tchaikovsky: https://www.youtube.com/playlist?list=PLO09Th4dLYVlIvoB8xErShIMa2qGD-4Fv 🔔 Subscribe to The Wicked North for the very best in clas

From playlist Brilliant Music

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Mozart - Piano Concerto No.21, K.467 / Yeol Eum Son

2011 Tchaikovsky Competition - Piano Round II, Phase II Mozart - Concerto for Piano and Orchestra No. 21 in C major, K.467 Yeol Eum Son (South Korea)

From playlist Classical Music

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The Mathematical Problem with Music, and How to Solve It

There is a serious mathematical problem with the tuning of musical instruments. A problem that even Galileo, Newton, and Euler tried to solve. This video is about this problem and about some of the ways to tackle it. It starts from the basic physics of sound, proves mathematically why s

From playlist Summer of Math Exposition 2 videos

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Edward T. Cone Concert - Pre-Concert Talk

Edward T. Cone Concert - Pre-Concert Talk Sebastian Currier, Miranda Cuckson, Michael Atkinson, Blair McMillen, David Rakowski February 8, 2014 In 1982, Ligeti wrote his Horn Trio, calling it a homage to Brahms. It was an important turning point in Ligeti’s musical style, when his modern­i

From playlist Artist in Residence

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Wolfgang Amadeus Mozart - Piano Concerto No. 21 - Andante

Piano Concerto No. 21 - Andante "Elvira Madigan"

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Bartok: Solo Violin Sonata ("Melodia")

The 3rd movement from Bartok's Solo Violin Sonata. Played by Ivry Gitlis.

From playlist experimental classical

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Bronwyn Hajek: Shock Me Amadeus

Associate Professor Bronwyn Hajek, applied mathematician at the University of South Australia, is an expert in developing and solving mathematical models using nonlinear PDEs. During her upcoming SMRI visit, Hajek and her USyd collaborator Dr Robby Marangell will apply Lie symmetry method

From playlist SMRI Interviews

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Scarlatti - 13 Keyboard Sonatas K 1, K 466 .. + Presentat° (Century's recording : Dubravka Tomšič)

Domenico Scarlatti (1685-1757) - 13 Keyboard Sonatas. 🎧 Qobuz https://bit.ly/2RmxvB5 Apple Music https://apple.co/329duQM 🎧 Amazon Music https://amzn.to/3v5Re8t Tidal https://bit.ly/2NBQHbX 🎧 Deezer https://bit.ly/39oBgN2 Spotify https://spoti.fi/3clDtKS 🎧 Youtube Music https://bit.ly/3Wni

From playlist Classical Music

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Lecture 9. Sonata-Allegro Form: Mozart and Beethoven

Listening to Music (MUSI 112) A brief foray into the formal characteristics of contemporary popular music is used to launch this lecture on musical form. After a discussion of the "verse-chorus" form often used in popular music, Professor Wright proceeds to take students into the realm of

From playlist Listening to Music with Craig Wright

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Lecture 10. Sonata-Allegro and Theme and Variations

Listening to Music (MUSI 112) Professor Wright delves into sonata-allegro form in some depth in this lecture. He focuses especially on characterizing four types of music found within a sonata: thematic, transitional, developmental, and cadential. He then moves on to discuss a different fo

From playlist Listening to Music with Craig Wright

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Nocturne Andromeda - Oliver Lugg

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From playlist Music Compositions

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Edward T. Cone Concert Talk - William Bolcom

William Bolcom Composer December 5, 2009 Renowned composer and pianist William Bolcom discusses his career as a composer and performer with Artist-in-Residence Derek Bermel. More videos on http://video.ias.edu

From playlist Edward T. Cone Concert Series Discussion

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Chopin - Classical Music for Relaxation

♫ Buy the MP3 album on the Official Halidon Music Store: https://bit.ly/2qCETYn 🎧 Listen to "Chopin: Essential Classics" on Spotify: http://spoti.fi/2mKTQnk 💿 Order “100 Songs Piano” (4CD Box Set) on Amazon: USA: https://amzn.to/2EI1BYi IT: https://amzn.to/2REBKWY FR: https://amzn.to/2

From playlist Classical Music

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Lecture 18. Piano Music of Mozart and Beethoven

Listening to Music (MUSI 112) This lecture addresses the history of the modern piano and its music. Undertaking a detailed discussion of the different forms of the piano from the early eighteenth through twentieth centuries, Professor Wright also shows how the instrument evolved through a

From playlist Listening to Music with Craig Wright

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Khatia Buniatishvili: Tchaikovsky - Piano Concerto No. 1 in B-flat minor, Op. 23 (Klaus Makela & OP)

Khatia Buniatishvili: Piano Concerto No. 1 in B-flat minor, Op. 23 (Klaus Makela & Orchestre de Paris). Live at Philharmonie de Paris, 2022. I do not own the rights to this video. I just wanted to share this beautiful concerto with everyone.

From playlist Classical

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Chopin - Piano Solo

🎵 Buy "Chopin: Complete Nocturnes" on the Halidon Music Store: http://bit.ly/3s9DYfX​ 🎧 Stream the album on Spotify: https://spoti.fi/3eb3I67​ 🍎 iTunes & Apple Music: https://apple.co/3afWmND 💿 Order "Chopin: Classical Piano Masterpieces" (Vinyl) on Amazon! ✨ USA: https://amzn.to/3LmqJSl

From playlist Classical Music

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