- published: 28 Aug 2013
- views: 1776
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Important to musical set theory, a pitch class is, "all pitches related to each other by octave, enharmonic equivalence, or both." Thus, using scientific pitch notation, the pitch class "C" is the set
although there is no formal upper or lower limit to this sequence, only a limited number of these pitches are audible to the human ear. Pitch class is important because human pitch-perception is periodic: pitches belonging to the same pitch class are perceived as having a similar quality or color, a property called "octave equivalence".
Psychologists refer to the quality of a pitch as its "chroma". A chroma is an attribute of pitches (as opposed to tone height), just like hue is an attribute of color. A pitch class is a set of all pitches that share the same chroma, just like "the set of all white things" is the collection of all white objects.
Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects.
The modern study of set theory was initiated by Georg Cantor and Richard Dedekind in the 1870s. After the discovery of paradoxes in naive set theory, numerous axiom systems were proposed in the early twentieth century, of which the Zermelo–Fraenkel axioms, with the axiom of choice, are the best-known.
Set theory is commonly employed as a foundational system for mathematics, particularly in the form of Zermelo–Fraenkel set theory with the axiom of choice. Beyond its foundational role, set theory is a branch of mathematics in its own right, with an active research community. Contemporary research into set theory includes a diverse collection of topics, ranging from the structure of the real number line to the study of the consistency of large cardinals.
A brief explanation of the differences between pitch and pitch class. I also explain octave designation and enharmonic equivalence.
This is part of a lecture in a series. Information about the whole course and how to follow it in sequence can be found here: http://cochranemusic.com/scale-theory-music-course
A short video on how to find the prime form of a pitch-class set. To get the most from the video, you should be familiar with pitch-class integers, clock faces, transposition and inversion of pitch-class sets, and normal order.
This video corresponds with material from chapter 9 in your text. In particular, it focuses on material from pages 166 - 173. 0:00 Introductions 1:41 Pitch Class Notation 4:19 Pitch Class Intervals 7:06 Pitch Class and Mod 12 10:20 Normal Order 14:47 Breaking Ties 17:04 Transpositionally Symmetrical Sets
Rihard's Mathematics Project (VWO) "Pitch Class Set Composition" Opus 1.2
The pitch class shifter is a new feature introduced in SoundPrism Pro for the iPad. The iPhone does not support the pitch class shifter at the moment.
A description of inversion and how to invert sets of pitch classes.
Brief description of musical set theory and how it differs from tonal music that uses scales. It covers basic set concepts like integer notation and normal order.
How to describe the quality of non-triadic chords
A brief explanation of the differences between pitch and pitch class. I also explain octave designation and enharmonic equivalence.
This is part of a lecture in a series. Information about the whole course and how to follow it in sequence can be found here: http://cochranemusic.com/scale-theory-music-course
A short video on how to find the prime form of a pitch-class set. To get the most from the video, you should be familiar with pitch-class integers, clock faces, transposition and inversion of pitch-class sets, and normal order.
This video corresponds with material from chapter 9 in your text. In particular, it focuses on material from pages 166 - 173. 0:00 Introductions 1:41 Pitch Class Notation 4:19 Pitch Class Intervals 7:06 Pitch Class and Mod 12 10:20 Normal Order 14:47 Breaking Ties 17:04 Transpositionally Symmetrical Sets
Rihard's Mathematics Project (VWO) "Pitch Class Set Composition" Opus 1.2
The pitch class shifter is a new feature introduced in SoundPrism Pro for the iPad. The iPhone does not support the pitch class shifter at the moment.
A description of inversion and how to invert sets of pitch classes.
Brief description of musical set theory and how it differs from tonal music that uses scales. It covers basic set concepts like integer notation and normal order.
How to describe the quality of non-triadic chords
Live from Mt. Pleasant the 2016 ASA Girls Fast Pitch Class "A" 14U Northern National Championship. Tournament information: http://gfp.tournamentasa.com/i!/tournaments/tournamentDetails.php?TID=6941
Live from Mt. Pleasant the 2016 ASA Girls Fast Pitch Class "A" 14U Northern National Championship. Tournament information: http://gfp.tournamentasa.com/i!/tournaments/tournamentDetails.php?TID=6941
Live from Mt. Pleasant the 2016 ASA Girls Fast Pitch Class "A" 14U Northern National Championship. Tournament information: http://gfp.tournamentasa.com/i!/tournaments/tournamentDetails.php?TID=6941
Live from Mt. Pleasant the 2016 ASA Girls Fast Pitch Class "A" 14U Northern National Championship. Tournament information: http://gfp.tournamentasa.com/i!/tournaments/tournamentDetails.php?TID=6941
Babies' Brains Benefit from Music Lessons, Even Before They Can Walk and Talk After completing the first study of its kind, researchers at McMaster University have discovered that very early musical training benefits children even before they can walk or talk. They found that one-year-old babies who participate in interactive music classes with their parents smile more, communicate better and show earlier and more sophisticated brain responses to music. The findings were published recently in the scientific journals Developmental Science and Annals of the New York Academy of Sciences. "Many past studies of musical training have focused on older children," says Laurel Trainor, director of the McMaster Institute for Music and the Mind. "Our results suggest that the infant brain might be p...
Here she comes
Breathing life in to my thoughts
There she goes
Leaves a portrait in my soul
Rolling in madness
She does everything to me
Wherever she goes you know the devil dances
And the gods lay down in defeat
Am I living
Crazy woman can't you see
That I'm giving
Giving to you can you dig
I wanna live
To learn the truth before my door
Don't you know
I'm a simple man for all I know
This might be the hard way
But it's easier for me
To take all the changes that are always amazin'
But to never let 'em fence me in
Am I living
Crazy woman can't you see
That I'm giving
Giving to you can you dig
Me I'm only searchin' for the things I really need
I can't rely on anyone to sow and grow my seeds
I started out on empty promise I was living on my dreams
I was a runaway son and now I'm up out of the water
And I can barely barely breathe
Rolling down the road
Rolling down the road
Rolling down the road
Rolling down the road
Rolling down the road
Listen listen
Hear the music play
Listen listen
Hear the music play yeah
Listen listen
Hear the music play
Listen listen
Hear the music play
Am I living
Crazy woman can't you see
That I'm giving
Giving to you can you dig