Black-oil equations

File:Augmented second on C.png

Augmented second on C. My name: Lindsey Gavin
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In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.

They are notated as follows:

PI(a,b) = b - a

For example C4 to DTemplate:Music4 My name: Lindsey Gavin
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Home town: Vemdalen
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Address: Buanvagen 79

Look into my weblog :: http://www.hostgator1centcoupon.info/ is 3 semitones:

PI(0,3) = 3 - 0

While C4 to DTemplate:Music5 My name: Lindsey Gavin
My age: 28
Country: Sweden
Home town: Vemdalen
Postal code: 840 92
Address: Buanvagen 79

Look into my weblog :: http://www.hostgator1centcoupon.info/ is 15 semitones:

PI(0,15) = 15 - 0

However, under octave equivalence these are the same pitches (DTemplate:Music4 & DTemplate:Music5, My name: Lindsey Gavin
My age: 28
Country: Sweden
Home town: Vemdalen
Postal code: 840 92
Address: Buanvagen 79

Look into my weblog :: http://www.hostgator1centcoupon.info/), thus the #Pitch-interval class may be used.

Pitch-interval class

File:Octave and augmented second on C.png

Octave and augmented second on C My name: Lindsey Gavin
My age: 28
Country: Sweden
Home town: Vemdalen
Postal code: 840 92
Address: Buanvagen 79

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In musical set theory, a pitch-interval class (PIC, also ordered pitch class interval and directed pitch class interval) is a pitch interval modulo twelve.

The PIC is notated and related to the PI thus:

PIC(0,15) = PI(0,15) mod 12 = (15 - 0) mod 12 = 15 mod 12 = 3

Equations

Using integer notation and modulo 12, ordered pitch interval, ip, may be defined, for any two pitches x and y, as:

• $\mathrm{ip}⟨x,y⟩=y-x$

and:

• $\mathrm{ip}⟨y,x⟩=x-y$

the other way.

One can also measure the distance between two pitches without taking into account direction with the unordered pitch interval, similar to the interval of tonal theory. This may be defined as:

• $\mathrm{ip}(x,y)=|y-x|$

The interval between pitch classes may be measured with ordered and unordered pitch class intervals. The ordered one, also called directed interval, may be considered the measure upwards, which, since we are dealing with pitch classes, depends on whichever pitch is chosen as 0. Thus the ordered pitch class interval, i<x, y>, may be defined as:

• $\mathrm{i}⟨x,y⟩=y-x$ (in modular 12 arithmetic)

Ascending intervals are indicated by a positive value, and descending intervals by a negative one.

See also

• Interval class