Understanding Guerino Mazzola's Performance Theory Structure
Explore Guerino Mazzola's insightful theories on combining tempo, tuning, and dynamics in performance, delving into dimensions E, H, L, and the interplay between symbolic and physical elements. Gain a deeper understanding of product field relationships and examples of map structures in music theory.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Guerino Mazzola (Spring 2025): Performance Theory II STRUCTURE THEORY II.3 (Fr Feb 07) Combining tempo, tuning, and dynamics
Have three dimensions E, H, L with similar map structures to e, h, l: Guerino Mazzola (Spring 2025): Performance Theory E symbolic onset time E in q physical onset time e in sec. H physical pitch h in Ct. symbolic pitch H in St. L physical loudness l in dB. symbolic loudness L in Vl.
Tempo: T(E) = 1/slope(E) = 1/(de/dE) [ /sec] Guerino Mazzola (Spring 2025): Performance Theory e1- e0= E0 E1slope(E) dE = E0 E11/T(E) dE [sec] Intonation: S(H) = 1/slope(H) = 1/(dh/dH) [St/Ct] h1- h0= H0 H1slope(H) dH = H0 H11/S(H) dH [Ct] Dynamics: I(L) = 1/slope(L) = 1/(dl/dL) [Vl/dB] l1- l0= L0 L1slope(L) dL = L0 L11/I(L) dL [dB]
Putting it all together? Guerino Mazzola (Spring 2025): Performance Theory H E H L symbolic pitch H physical pitch h (e,h,l) (E,H,L) L physical onset time e symbolic onset time E E
Product field: tempo-intonation EH Z(E,H)=(T(E), S(H)) H Guerino Mazzola (Spring 2025): Performance Theory E H [1/2-tone/Ct] S(H) E [ /sec] T(E)
Necessary to look at the map as a whole, since this one is not a product of the three coordinate maps in general! Guerino Mazzola (Spring 2025): Performance Theory EH L E H L symbolic pitch H physical pitch h (e,h,l) = EH L(E,H,L) (E,H,L) physical onset time e symbolic onset time E Discuss examples!
Guerino Mazzola (Spring 2025): Performance Theory M.C. Escher: Balcony
Reconsider the one-dimensional case, Tempo slope(E) = de/dE [sec./ ], T(E) = 1/slope(E) = dE/de [ /sec.] Guerino Mazzola (Spring 2025): Performance Theory T(E).x [sec.] T(E) = 1/slope x 1 look backward! slope e = e(E) [ ] E 1
look backward! Guerino Mazzola (Spring 2025): Performance Theory EH (e, h + y) ( E/ h, H/ h) 1 y ( E/ e, H/ e) h 1 (e + x, h) H x e E vertical tangent arrow horizontal tangent arrow
Product field of tempo-intonation, special case: EH Guerino Mazzola (Spring 2025): Performance Theory (0, S(H)) (T(E), S(H)) (e, h + y) 1 (1, 1) y h 1 (e + x, h) H (T(E), 0) x e E (T(E), S(H)) = (T(E), 0) + (0, S(H)) (1, 1) = (1,0) + (0, 1)
Guerino Mazzola (Spring 2025): Performance Theory ( E/ e + E/ h, ( H/ e + H/ h) (e, h + y) ( E/ h, H/ h) 1 (1, 1) y ( E/ e, H/ e) h 1 (e + x, h) H x e E ( E/ e, H/ e) + ( E/ h, H/ h) (1, 1) = (1,0) + (0, 1)
Guerino Mazzola (Spring 2025): Performance Theory 1 1 h 1 H 1 1 1 e E performance field diagonal field
Performance fields for onset time, pitch, and loudness Guerino Mazzola (Spring 2025): Performance Theory EH L H h (e,h,l) = EH L(E,H,L) (E,H,L) E e performance field diagonal field
Infinitesimal character: Guerino Mazzola (Spring 2025): Performance Theory Theodor W. Adorno ( Der getreue Korrepetitor ): Theodor W. Adorno ( Der getreue Korrepetitor ): Walter Benjamin hat das Verm gen der Phantasie als die Gabe, im unendlich Kleinen zu interpolieren definiert. Das beleuchtet blitzhaft die wahre Interpretation. (...) In the densely intervowen score texture we may discover minimal cavities, where the significative performance finds its refuge. (...) Walter Benjamin has defined the power of phantasy as being the gift to interpolate in the infinitely small . This flashes at once the real performance. (...) Theodor W. Adorno Im dicht gewobenen Zusammenhang des Notentextes sind die minimalen Hohlr ume zu entdecken, in denen sinnverleihende Interpretation ihre Zuflucht findet. (...) The medium of artistic phantasy is not de decrease of precision, but the more precise. Walter Benjamin Das Medium k nstlerischer Phantasie ist nicht ein Weniger an Genauigkeit, sondern das noch Genauere.
