By J. Mawhin, M. Willem
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Additional info for Critical Point Theory and Hamiltonian Systems
Here is a hierarchical list of the twelve pitches. Primary Level 1. TONIC: the home pitch. In tonal music, all other pitches ultimately point back to tonic. 2. DOMINANT: This pitch a perfect fifth above the tonic is the primary pointer to the tonic. 3. MEDIANT: If it is a major third above the tonic determines a major mode; a minor third above the tonic determines minor. Secondary Level 4. All other diatonic pitches. The four remaining pitches in a typical seven note scale. These would be the second, fourth, sixth and seventh degrees.
This melody is in the key of E phrygian, one of the minor modes that will be discussed in chapter 12. 3 E as Tonic of a phrygian melody œ ˙ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ ˙. R œ & D T T D D M T T D T C would not be heard as tonic in the first phrase of Amazing Grace, shown below, even though it begins and ends with C. The first C sounds like a pickup note to the F. C to F is the dominant to tonic relationship and makes the F sound like the home pitch. The establishment of F as tonic is reinforced by holding the F for two counts.
Etc. ‰ œ œ œ œ œ œ œ œ œ &œ œ œ fast swing Montgomery used the dotted quarter note implying resolved at the end of the eight measure phrase. Jazz Theory Resources 3 8 over 44. 54 Rhythm in Jazz Performance 33 Dotted quarter-note accents: fast swing &c Ó ‰ œ. œ. œ œ œ J j j & j œ. œ. œ œ œ œ œ. œ j j œ œ . œ . œ œ œ œj œ . œ . Jœ œ œ œ. ˙ œ J œ œ . œj œ œ The repeated notes of ex. 55 make the focus of this idea clearly rhythmic. It is related to the rhythm in ex. 53 but resolved the conflict at the end of every four rather than eight measure phrase.