To find connections between tonality, 12-tone, set theory, and modes of limited transposition in order to create equally logical pitch networks that give the same musical pay-off of tonal and modal harmony but allow for manipulating pitch collections more freely and at the same time utilize the entire chromatic or micro-tonal landscape.
Refining the question:
"To find connections between tonality, 12-tone, set theory, and modes of limited transposition"
- Diatonic tonality consists of a set of 7 pitches that center around 1 central pitch.
- Set theory allows for a central pitch collection or collections that are smaller or larger than a diatonic scale but maintain their intervallic content under transformations.
- 12-tone rows must contain all 12 pitches, however smaller subsets may be derived allowing for relationships of maintaining the intervallic content with in the subsets.
- Modes of limited transposition are treated like diatonic scales with the idea of a centrally important pitch. These scales are created by utilizing repeated pitch sets that limit the amount of transpositions to less than 12.
- If you were to have a continuum of how these relate you might use a spectrum based on repetition at the octave. For example: sets that repeat before the octave (sets smaller than the octave), modes of limited trans. fit between sets smaller than the octave and scales because they are both, scales (octave repeating) and 12-tone rows, and finally sets that are larger than the octave (set theory).
- Scales and modes are ordered vs. Sets and Tone Rows are unordered.
- Scales and modes can freely modulate but require a modulating chord or progression, while sets and tone rows freely transpose with the need of a modulating device.
- Scales and modes require a central pitch axis, while sets and tone rows may have this but it is not required.
- Scales and modes are more one-dimensional while sets and row allow for more dimensions of interpretation. ***
- Interval cycling can be used to link these 4 things.
- Viewed as a continuum interval cycles could be classified as smaller than the octave, at the octave, and larger than the octave.
- Interval cycles can be used for equal temperament or alternate methods of tuning.
"in order to create equally logical pitch networks that give the same musical pay-off of tonal and modal harmony"
- The problem with atonal music that I have is the inability to place a logical path for pitch selection when working with a gestural motive.
- Most frequently this problem arises in the harmonizing of a gestural motive although can be problematic in the development of a linear atonal melody or gesture.
- The musical pay-off of tonality is clear directed motion to well established and convincing "goals". A listener need not be overly analytical to be able to interpret and make sense of the music.
- Modes of limited transposition can also offer this while giving more options to the composer of tonal and harmonic coloring.
"but allow for manipulating pitch collections more freely and at the same time utilize the entire chromatic or micro-tonal landscape."
- Tonal music and modal harmony are more rigid in the movement from one key center to the next. In order to do so requires a modulating chord or progression. It is this strict harmonic structure that allows for smooth transitions that are easy to follow aurally.
- Atonal music is less strict in the movement from one set or row at a given pitch level to the next. This is because there is no required modulating device. It is generally explained as the composers talent for voice leading and other music elements that accounts for convincing musical motion.
- It is my hypothesis that pitch sets can be organized in such a way as to create rules of modulation that allow atonal (non pitch axis-centric) music to guide the ear as effortlessly as tonal music.
- Modulation through the 6 prototypes of Quinn.
