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A perfect prime is also called a unison . It is two notes that are the same pitch . A perfect octave is the "same" note an octave - 12 half-steps - higher or lower. A perfect 5th is 7 half-steps. A perfect fourth is 5 half-steps.

Perfect intervals

Listen to the octave , perfect fourth , and perfect fifth .

Major and minor intervals

Seconds, thirds, sixths, and sevenths can be major intervals or minor intervals . The minor interval is always a half-step smaller than the major interval.

    Major and minor intervals

  • 1 half-step = minor second (m2)
  • 2 half-steps = major second (M2)
  • 3 half-steps = minor third (m3)
  • 4 half-steps = major third (M3)
  • 8 half-steps = minor sixth (m6)
  • 9 half-steps = major sixth (M6)
  • 10 half-steps = minor seventh (m7)
  • 11 half-steps = major seventh (M7)

Major and minor intervals

Listen to the minor second , major second , minor third , major third , minor sixth , major sixth , minor seventh , and major seventh .

Give the complete name for each interval.

Fill in the second note of the interval given.

Augmented and diminished intervals

If an interval is a half-step larger than a perfect or a major interval, it is called augmented . An interval that is a half-step smaller than a perfect or a minor interval is called diminished . A double sharp or double flat is sometimes needed to write an augmented or diminished interval correctly. Always remember, though, that it is the actual distance in half steps between the notes that determines the type of interval, not whether the notes are written as natural, sharp, or double-sharp.

Some diminished and augmented intervals

Listen to the augmented prime , diminished second , augmented third , diminished sixth , augmented seventh , diminished octave , augmented fourth , and diminished fifth . Are you surprised that the augmented fourth and diminished fifth sound the same?

Write a note that will give the named interval.

As mentioned above, the diminished fifth and augmented fourth sound the same. Both are six half-steps, or three whole tones , so another term for this interval is a tritone . In Western Music , this unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval).

You have probably noticed by now that the tritone is not the only interval that can be "spelled" in more than one way. In fact, because of enharmonic spellings , the interval for any two pitches can be written in various ways. A major third could be written as a diminished fourth, for example, or a minor second as an augmented prime. Always classify the interval as it is written; the composer had a reason for writing it that way. That reason sometimes has to do with subtle differences in the way different written notes will be interpreted by performers, but it is mostly a matter of placing the notes correctly in the context of the key , the chord , and the evolving harmony . (Please see Beginning Harmonic Analysis for more on that subject.)

Enharmonic intervals

Any interval can be written in a variety of ways using enharmonic spelling. Always classify the interval as it is written.

Inverting intervals

To invert any interval, simply imagine that one of the notes has moved one octave, so that the higher note has become the lower and vice-versa. Because inverting an interval only involves moving one note by an octave (it is still essentially the "same" note in the tonal system), intervals that are inversions of each other have a very close relationship in the tonal system.

Inverting intervals

    To find the inversion of an interval

  1. To name the new interval, subtract the name of the old interval from 9.
  2. The inversion of a perfect interval is still perfect.
  3. The inversion of a major interval is minor, and of a minor interval is major.
  4. The inversion of an augmented interval is diminished and of a diminished interval is augmented.

What are the inversions of the following intervals?

  1. Augmented third
  2. Perfect fifth
  3. Diminished fifth
  4. Major seventh
  5. Minor sixth
  1. Diminished sixth
  2. Perfect fourth
  3. Augmented fourth
  4. Minor second
  5. Major third

Summary

Here is a quick summary of the above information, for reference.

The examples given name the note reached if one starts on C, and goes up the named interval.
Number of half steps Common Spelling Example, from C Alternate Spelling Example, from C Inversion
0 Perfect Unison (P1) C Diminished Second D double flat Octave (P8)
1 Minor Second (m2) D flat Augmented Unison C sharp Major Seventh (M7)
2 Major Second (M2) D Diminished Third E double flat Minor Seventh (m7)
3 Minor Third (m3) E flat Augmented Second D sharp Major Sixth (M6)
4 Major Third (M3) E Diminished Fourth F flat Minor Sixth (m6)
5 Perfect Fourth (P4) F Augmented Third E sharp Perfect Fifth (P5)
6 Tritone (TT) F sharp or G flat Augmented Fourth or Diminished Fifth F sharp or G flat Tritone (TT)
7 Perfect Fifth (P5) G Diminished Sixth A double flat Perfect Fourth (P4)
8 Minor Sixth (m6) A flat Augmented Fifth G sharp Major Third (M3)
9 Major Sixth (M6) A Diminished Seventh B double flat Minor Third (m3)
10 Minor Seventh (m7) B flat Augmented Sixth A sharp Major Second (M2)
11 Major Seventh (M7) B Diminished Octave C' flat Minor Second (m2)
12 Perfect Octave (P8) C' Augmented Seventh B sharp Perfect Unison (P1)

    Summary notes: perfect intervals

  • A perfect prime is often called a unison. It is two notes of the same pitch.
  • A perfect octave is often simply called an octave. It is the next "note with the same name".
  • Perfect intervals - unison, fourth, fifth, and octave - are never called major or minor

    Summary notes: augmented and diminished intervals

  • An augmented interval is one half step larger than the perfect or major interval.
  • A diminished interval is one half step smaller than the perfect or minor interval.

    Summary notes: inversions of intervals

  • To find the inversion's number name, subtract the interval number name from 9.
  • Inversions of perfect intervals are perfect.
  • Inversions of major intervals are minor, and inversions of minor intervals are major.
  • Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Pitch notation. OpenStax CNX. Aug 20, 2011 Download for free at http://cnx.org/content/col11353/1.3
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