Interval

The distance between two pitches or notes. Intervals may be measured in a number of ways; e.g., by counting the number of semitones, subtracting frequencies, etc. Counting semitones is used in set theory. However, the most common method is by counting letter names; e.g. C, D, E, F includes 4 letters - thus, C to F is called a fourth and is always a fourth, no matter how the notes may be altered by sharps or flats. This is called the "general size" of the interval. However, each general interval may have several "specific sizes"; e.g. a third could be major, minor, diminished, augmented?, etc. The specific size is determined by 1. the general size, and 2. the number of semitones it contains. (Solomons Musical Glossary)

The distance in pitch between two notes, harmonic if they are played together, melodic if they are played in succession.
Perfect : the prime, fourth, fifth, and octave.
Major : the second?, third, sixth?, and seventh? of the major scale.
Minor : a chromatic half step smaller.
Augmented? : a chromatic half step larger than perfect and major.
Diminished : a chromatic half step smaller than perfect and minor.

An interval is a combination of two tones. It is also the distance between or the difference between two tones. When these two tones are sounded together the result is an harmonic interval, and when they are sounded one after the other the result is a melodic interval. The quality of an interval is determined by its size and by the relationship of its position to the keynote.

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Augmented Interval A musical interval slightly increased in pitch by the addition of a sharp?.
Diminished Interval A perfect or minor interval reduced by a semitone.

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Perfect Interval The Perfect Interval is a Major Interval where the lower tone is found in the Major Scale of the upper tone as well as the upper tone is found in the Major Scale of the lower tone. The Major 6th to the right is Major as D is part of the Major Scale of F? but F is not part of the Major Scale of D?. Therefore it is not a Perfect Interval. The Perfect Fourth to the lower right is Perfect because F is found in the Major Scale of C? and C is found in the Major Scale of F?. Perfect Intervals may be a 1st, 4th, 5th and 8th.

There are five types of intervals: major (indicated by M), minor (m), perfect (P), diminished (dim.), and augmented? (Aug.).

A major interval contracted - by lowering the upper note or raising the lower note - by one half step becomes minor, and contracted by another half step becomes diminished.

A perfect interval contracted by a half step becomes diminished, and contracted by another half step (not usually practical), becomes doubly diminished.

A perfect or a major interval expanded by a half step becomes augmented?. (Byre, Joseph; Basic Principles of Music)

The distance in pitch between two notes, which is expressed in terms of the number of notes of the diatonic scale? which they comprise (e.g. third, fifth, ninth?) and a qualifying word (perfect, imperfect?, major, minor, augmented?, or diminished). The number is determined by the position of the notes on the staff?, the qualifying word by the number of tones and semitones in the interval. Thus (no clef) C - G is always a third, while (F clef) C - G is a major third, being a distance of two tones, and (G clef) C - G is a minor third, being a distance of a tone and a half. (Collin's Music Encyclopedia)

Click Here to Calculate Music Intervals in any Octave

Note	Interval	Ratio	Numerator	Denominator	Decimal
C	First	1:1	1	1	1
	Pythagorean Komma?	81:80	81	80	0.9765625
	Enharmonic	128:125	128	125	0.9765625
C#	Lesser Chromatic Semitone?	25:24	25	24	0.96
	Leimma?	256:243	256	243	0.94921875
	Greater Chromatic Semitone?	135:128	135	128	0.94814815
	Minor Semitone?	17:16	17	16	0.94117647058824
	Major (Diatonic) Semitone	16:15	16	15	0.9375
Db	Minor Second	27:25	27	25	0.925993
	Minor Tone?	10:9	10	9	0.9
D	Major Second	9:8	9	8	0.8888889
D#	Augmented Second?	75:64	75	64	0.853333333
	Minor Third (Pythagoras)	32:27	32	27	0.84375
Eb	Minor Third	6:5	6	5	.833333333
E	Major Third	5:4	5	4	0.8
	Major Third (Pythagoras)	81:64	81	64	0.79012345679012
E#	Diminished Fourth?	32:25	32	25	0.78125
Fb	Augmented Third?	125:96	125	96	0.768
F	Perfect Fourth	4:3	4	3	0.75
F#	Augmented Fourth?	25:18	25	18	0.72
	Tritone?	45:32	45	32	0.711111111
	Diminished Fifth?	64:45	64	45	0.703125
Gb	Diminished Fifth?	36:25	36	25	0.69444444
G	Perfect or Major Fifth	3:2	3	2	0.66666667
G#	Augmented Fifth?	25:16	25	16	0.64
Ab	Minor Sixth?	8:5	8	5	0.625
A	Major Sixth	5:3	5	3	0.6
A#	Augmented Sixth?	125:72	125	72	0.576
	Harmonic Seventh?	7:4	7	4	0.57142857142857
	Dominant or Minor Seventh?	16:9	16	9	0.5625
Bb	Minor or Tonic Seventh?	9:5	9	5	0.55556
B	Major Seventh	15:8	15	8	0.53333
B#	Diminished Octave?	48:25	48	25	0.52083333
Cb	Augmented Seventh?	125:64	125	64	0.512
C	Octave	2:1	2	1	0.5
	Minor Ninth?	32:15	32	15	0.46875
	Major Ninth	9:4	9	4	0.44444444
	Harmonic or Minor Tenth?	7:3	7	3	0.42857143
	Minor Tenth?	12:5	12	5	0.4166667
	Major Tenth?	5:2	5	2	.4
	Perfect Eleventh?	8:3	8	3	0.375
	Harmonic Eleventh?	11:4	11	4	0.363636
	Augmented Eleventh?	45:16	45	16	0.355556
	Perfect Twelfth?	3:1	3	1	0.333333
	Augmented Twelfth?	25:8	25	8	0.32
	Minor Thirteenth?	16:5	16	5	0.3125
	Harmonic Thirteenth?	13:4	13	4	0.30769231
	Major Thirteenth?	10:3	10	3	0.3
	Harmonic Fourteenth?	7:2	7	2	0.28571429
	Dominant Fourteenth?	32:9	32	9	0.28125
	Tonic Fourteenth?	18:5	18	5	0.27777778
	Major Fourteenth?	15:4	15	4	0.26666667
	Double Octave?, Fifteenth	4:1	4	1	0.25

(Some notes from Professor Haughton's "Natural Philosophy", page 181.)

See Also

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05 - The Melodic Relations of the sounds of the Common Scale
1.23 - Power of Harmonics through Summation Tones
12.42 - Tone
Chord
Compound Interval
Figure 8.5 - Summation Tones
Figure 8.6 - Difference Tones
Frequency
Fundamental
Note
Overtone
Overtone series
Part 11 - SVP Music Model
Proportion
Ratio
Scale
Scale of Locked Potentials
Resultant Tone
Tone
Undertone

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