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Scales
Scales

... Chromatic Scales are made up entirely of half steps. When ascending, the scale uses sharps, when descending it uses flats.Listen ...
Mr Allen`s Final Review
Mr Allen`s Final Review

... Tempo- speed of music. How fast or slow a piece should be played. Andante Slow), Moderato, (Moderate) Allegro (Fast), Presto (Very Fast) ½ Step - is the smallest written musical interval (minor 2nd), on a piano, notes a ½ Step apart have no other pitches between them. These are often ‘accidentals’ b ...
microtonal scale exploration in Central
microtonal scale exploration in Central

... intervals and two larger that linger around the pure minor third. A pure major third lies in between these two minor thirds (the two smaller intervals 204+180 make 384 cents), by which an nice enchainment of fifths arises that is mirrored at the same time. Another mirror of intervals can be found be ...
Chapter 3
Chapter 3

... Diatonic sounds more stable, because it draws most of its material from the notes of the scale it uses. Chromatic sounds a little wilder, because it often departs from the key of the piece and uses tones that are not considered part of the scale. ...
A Wonderful Savior
A Wonderful Savior

... That shadows a dry, thirsty land; He hideth my life in the depths of His love, And covers me there with His hand, And covers me there with His hand. ...
Music, Mathematics and Bach --------~--------
Music, Mathematics and Bach --------~--------

... Why small integer ratios should be pleasant is not universally agreed upon either, but there are some likely explanations. To start with, a sound which sounds musical (has a definite pitch) has a periodic waveform. Such a waveform can be decomposed (Fourier analyzed)l into sine waves of various freq ...
MUL 2010 “Enjoyment of Music
MUL 2010 “Enjoyment of Music

... (also, diminuendo) ...
AUGMENTED SIXTH CHORDS Definition
AUGMENTED SIXTH CHORDS Definition

... The Gr6 in major may be spelled with a doubly augmented fourth instead of a perfect fifth to show the resolution of the pitches in the direction of the inflection (see partwriting below). A6 chords are most often built on the note a half step above the dominant (b6) of the scale in both major and mi ...
• Melody = a succession of pitches at specific durations that begins
• Melody = a succession of pitches at specific durations that begins

... a  'piece'  =  a  musical  composition  which  is  played  on  instruments.   ...
Ben Johnston Pantonality Generalized
Ben Johnston Pantonality Generalized

... instruments or voices. Pitches were constrained by a chromatic system of temperament which determined whether a sound was considered musically “in tune” or “out of tune”. Combinations of pitches were, for the most part, restricted to triadic structures; dissonances were treated according to strict c ...
Intro to Musical Acoustics
Intro to Musical Acoustics

... • Periodic waveforms have a fundamental frequency, f0, and a harmonic spectrum: spectral energy just at frequencies that are integer multiples of f0. • These harmonic components are called harmonics, overtones, or partials . • Some musical instruments produce inharmonic sounds: bells, drums, etc. ...
Introduction to Musical Acoustics handout pdf
Introduction to Musical Acoustics handout pdf

Appendix 18 The Correlation Between Sound and Color
Appendix 18 The Correlation Between Sound and Color

... that a string's pitch (frequency) was exactly one octave lower than the pitch created when the string's length was halved. For example, if string produced an A (440 Hz) note when plucked, then moving the bridge to the midpoint of the string would cause it to produce the A one octave above (880 Hz). ...
History of Music Theory - Totally Ratted Limited
History of Music Theory - Totally Ratted Limited

Harmonics - Homework References
Harmonics - Homework References

... Tri-tone: an augmented fourth or diminished fifth; an extremely dissonant sound (so dissonant, it was historically associated with the devil) The ratio between a tri-tone and fundamental frequency is √2:1 (a complex ratio, resulting in dissonance) Pythagoras discovered that when an octave (not a str ...
Name: Motina Barracks Course: Music 101 Report Summary A scale
Name: Motina Barracks Course: Music 101 Report Summary A scale

... A scale is a group of eight note which is arrange in a particular order. Every Major scale has eight tones which is called an octave. The numbers 1 2 3 4 5 6 7 8 are called degrees. While the musical alphabet is A B C D E FG and the first and eighth note have the same name for example (C D E F G A B ...
Pythagorean tuning
Pythagorean tuning

... This succession of eleven 3:2 intervals spans across a wide range of frequency (on a piano keyboard, it encompasses 77 keys). Since notes differing in frequency by a factor of 2 are given the same name, it is customary to divide or multiply the frequencies of some of these notes by 2 or by a power of ...
Frequency
Frequency

Elements of Music - Harmony
Elements of Music - Harmony

... **If a melody centers around the note C, it is said to be in the Key of C. Keys can also be major or minor. Each key has a family of chords associated with it. Modulation is the process of changing from one key center (tonic) to another. Sometimes a piece of music will have several different key cen ...
Up and Down the Scale
Up and Down the Scale

...  He then noticed that a very melodious tone also came when the string was divided into 1/3 – 2/3.  When the larger portion of the string was played against the ...
Major Keys and Scales
Major Keys and Scales

... and culture. (D 9-12) ...
Serial Music - Toot Hill School
Serial Music - Toot Hill School

... Transposed. The Prime Order would sound the same, but it would start on a different note ie. all notes would be moved up or down by the same interval / distance. Vertically. Notes of the tone row are played at the same time. Chords formed in this way are called chord clusters as the notes are often ...
PPT only
PPT only

...  Intervals of notes that when played together sound conflicting  Interference pattern between overtones ...
CHAPTER 4
CHAPTER 4

... sufficiently differentiated so as to show the pitches (relative distance from one pitch to the next). ...
Mathematics and Music (Mathematical World, Vol. 28)
Mathematics and Music (Mathematical World, Vol. 28)

... the sound of instruments and the human voice. Chapter 11 starts with the old observation that two pitches played simultaneously sound ‘‘harmonious’’ when the ratio of their frequencies is rational with small numerator and denominator. It is shown how a scale constructed by using only a just fifth ne ...
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Just intonation



In music, just intonation (sometimes abbreviated as JI) or pure intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a pure or just interval. The two notes in any just interval are members of the same harmonic series. Frequency ratios involving large integers such as 1024:927 are not generally said to be justly tuned. ""Just intonation is the tuning system of the later ancient Greek modes as codified by Ptolemy; it was the aesthetic ideal of the Renaissance theorists; and it is the tuning practice of a great many musical cultures worldwide, both ancient and modern.""Just intonation can be contrasted and compared with equal temperament, which dominates Western instruments of fixed pitch (e.g., piano or organ) and default MIDI tuning on electronic keyboards. In equal temperament, all intervals are defined as multiples of the same basic interval, or more precisely, the intervals are ratios which are integer powers of the smallest step ratio, so two notes separated by the same number of steps always have exactly the same frequency ratio. However, except for doubling of frequencies (one or more octaves), no other intervals are exact ratios of small integers. Each just interval differs a different amount from its analogous, equally tempered interval.Justly tuned intervals can be written as either ratios, with a colon (for example, 3:2), or as fractions, with a solidus (3 ⁄ 2). For example, two tones, one at 300 Hertz (cycles per second), and the other at 200 hertz are both multiples of 100 Hz and as such members of the harmonic series built on 100 Hz. Thus 3/2, known as a perfect fifth, may be defined as the musical interval (the ratio) between the second and third harmonics of any fundamental pitch.
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