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Fibonacci Pitch Sequences -
The defining relation of these sequences is expressed fn + fn + 1 ≡ fn + 2 (mod 12), ... Fibonacci pitch class sequences in both cyclic and conventional format.
[ Fibonacci_Pitch_Sequences.pdf - Read/Download File

Fibonacci Pitch Sequences: Beyond Mod 12 -
Table 1 shows the mod 24 collection, table 2 shows the inverse Fibonacci mod 24 ... The number of unique residues present in a general Fibonacci pitch class ...
[ Fibonacci_Pitch_Sequences_II.pdf - Read/Download File

The Sound of Numbers - Saint Joseph's University
May 31, 2008 ... discovery of the Fibonacci numbers and Pascal's triangle. Pages from .... PART II: MATHEMATICS AND MUSIC IN THE ANCIENT WORLD .... inversion correspond to rotation and reflection of the pitch class circle, respectively.
[ proposal.pdf - Read/Download File

ties such as pitch, volume, and timbre that give the composition its framework. ( see [l]s [4]). ... 2. Given an integer n > 2, is there a Fibonacci sequence of period n in a group (7 .... First of all9 if we are given a prime p > 5, set n = (p - l)/2orn=p+l 9.
[ wilcox.pdf - Read/Download File

A Style of Music Characterized by Fibonacci [Numbers]
note-lengths derived from the Fibonacci sequence in Il canto sospeso (1956). György Ligeti [9] ... to do with Fibonacci. I set out to create my own tuning system. ... This is an interesting tuning, but it is not very economical in terms of pitch space.
[ mongoven_CongressusNumerantium2010.pdf - Read/Download File

Overview of Pitch and Time Organization in Stockhausen's
2. Pitch “axis” created by repetitive prolongation and time pulse set by regular attacks .... The piece makes extensive use of the Fibonacci series in which each el-.
[ Stockhausen.pdf - Read/Download File

Setting Time - Geek O'Clock
Setting Time. Setting time on the Fibonacci is as simple as reading it! Well, that's not the best pitch line I ... set the clock to the correct hour. That is from ... Page 2 ...
[ SettingTime.pdf - Read/Download File

2 sampling of some of the interesting properties that Fibonacci numbers possess. We delve into the ..... two pitches, each of which is represented by the same musical note. ... Let Mn denote the set of all n ! n matrices with entries in С. Definition ...
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PRESENTATION 2 1. What did you like about the presentation? (1) I
(2) The explanation of pitch classes and octaves as well as tuning systems was very helpful and ... (17) Two solid conjectures, Primality tests, Finance, and Fibonacci ... (45) Great job going through solutions with pre-set formulas on the board. I.
[ CumulativeFeedback.pdf - Read/Download File

An Exploration of Algorithmic Composition via the Fibonacci Sequence
Dec 14, 2010 ... based “automatic composition” software called “MusiCom”2. .... current note Fibonacci number is used to index the pitch set (relative to the ...
[ Colin-Sullivan_Algorithmic-Composition-Fibonacci_Theory.pdf - Read/Download File

A Three-Part Study in the Connections Between Music and
May 10, 2014 ... different cent-measures to pitches, as seen in Table 2. Pitch. C. C# ..... These two- measure sets toy with the math and the possible unique outcomes of minuets from ..... Ernö Lendvai, Béla Bartók, and the Fibonacci Numbers.
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Psychoacoustic Properties of Fibonacci Sequences
two years earlier Fn-2, because they are all mature and can reproduce: F. F. F n n n. = ... 1202, Fibonacci set up one of the most interesting sequences in number theory. ... subjects were told to change the pitch of a sine tone until it matched the  ...
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Important Changes (Version 2.0) Introduction and - apeSoft
Event Pitch Jitter (Pad 1 and Pad 2) superimpose at current note pitch a random ... FM synthesis consist of a simple patch of modulating/carrier oscillator set with ... The ratio of two consecutive Fibonacci numbers numbers converges on the.
[ Stria_user_guide.pdf - Read/Download File

An Analysis of Mathematical Symmetries Used in Music - Digital
If any adjacent Fibonacci numbers are divided by each other {2/3 ..... pitch class from the number of elements it has, a mirror image is created, and this is.
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chapter 8 - Academic Program Pages at Evergreen
game theory, magic squares, Fibonacci numbers, and so on, to provide them with .... preserves the pitch-class content of the three-note groups (see Figure 3b). Figure 3c ... the matrices: the P-matrix for Piano 1, the I-matrix for Piano II. Even the.
[ Fauvel8.pdf - Read/Download File

chicken selecting pitches from the current pitch set ... Figure 1. pitch set example used in Figure 2. .... the second slice dominates, according to the Fibonacci.
[ sc-paper-short.pdf - Read/Download File

self-similar pitch structures, their duals, and rhythmic analogues
idea for realizing analogues of self-similar pitch structures in the rhythmic domain . .... operative has a representation as a set of values between 1 and 2, where the fi ..... Canright's study of Fibonacci rhythmic patterns (Canright 1992). In Clough ...
[ self_sim.pdf - Read/Download File

The Music of Claude Debussy by Richard S. Parks - jstor
of rhythm.2 Thus most aspects of Debussy's music would seem to be taken ... 4Other studies using pc sets as a means of dealing with pitch in Debussy include Ethan ..... Fibonacci and Lucas summation series (1 1 2 3 5 8 . . . and. 3 4 7 11 18  ...
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Full Text - International Journal of Humanities and Social Science
2. As applied to the organization of time in the Variations for PianoOp. ... Fibonacci series, where GM points within a series of nested Golden Sections correspond ... interval axis between hexachords in each row and a property of pitch-class ...
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structures, rather than invoking one single pitch set, render the identity of ... from the Golden Section ratios of Ernó Lendvai and the Fibonacci number series. In many ... Chapter 2: Octatonic collections created through whole-tone partitions of.
[ treatisefinal.pdf - Read/Download File

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