Index of Intervals

Interval Calculator
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The Note is the one at the given interval above C, with chromatic and commatic inflections. The Vector shows the interval in terms of the product of powers of constituant prime intervals. The Name is the most descriptive name of the interval. An † after the name means that its octave complement (inversion) is not listed. The Interval is a normalized fraction showing the frequency ratio between the notes. Cents is the size of the interval in 100ths of an ET semitone. The Pitch Bend Adjustment is the MIDI pitch bend value added to the ET tuning to produce the interval. Hold the mouse over the red button to hear the lower note of the interval (always a C), over the green to hear the higher note, or over the blue to hear the notes simultaneously.

Some of the intervals have additional commentary that you can see in the status bar by holding the mouse over the interval name.

Click on an interval's ratio to multiply the "accumulator" (shown in the results box) by it. Alt-click on it to divide by it. This allows combining intervals. Hit Escape to restore the accumulator to unity (1/1). The status box shows the accumulator results when it changes.

You can clear the blue status line at any time by hitting Enter.

White=Just Scale Red=Equal Temperament Scale Yellow=Pythagorean Scale
Green=Miscellaneous Intervals Blue=Extended Harmonics (septimal and up)

Note
Vector
Interval Name/Function
Interval
Cents
PBA
C
11
Unison
1/1
0
0
Also known as a perfect prime, or "barbershop 1th".
C+
5-134
Syntonic Comma
81/80
21.506
881
A small interval between the just major 3rd and the Pythagorean major 3rd, where the 81st harmonic (which is the Pythagorean major 3rd) meets the 80th (an octave of the 5th harmonic, or just major 3rd).
B#+++
312
Pythagorean Comma
531441/524288
23.46
961
Also known as a Pythagorean augmented 7th, which would be wider than a just octave, and is here normalized by lowering it an octave.
C7
7-13-2
Septimal Comma †
64/63
27.264
1117
This is the amount by which a grave minor 7th is narrowed to form a Septimal 7th.
C
2315-13-2
23-Limit Comma †
46/45
38.051
1559
This is the amount by which a raised 4th degree of the just major scale is sharped to tune to the 23rd harmonic.
Dbb-
5-3
Diminished 2nd
128/125
41.059
1682
C13
13-1513-1
Tredecimal Comma †
40/39
43.831
1795
C+7
7-15-132
Septimal Quartertone †
36/35
48.77
1998
This is the amount by which a just major 3rd is widened to form a septimal major 3rd.
C11
11131
Undecimal Comma †
33/32
53.273
2182
This is the amount by which a perfect 4th is widened to tune to the 11th harmonic.
C#
523-1
Chroma
25/24
70.672
-1201
A short name for the chromatic semitone, also known as an augmented prime or minor chroma.
Db
715-131
Septimal Minor 2nd
21/20
84.467
-636
This is technically the distance the 7th of a just barbershop 7th chord moves down to "resolve".
Db--
3-5
Grave Minor 2nd
256/243
90.225
-400
Also known as a Pythagorean minor 2nd.
C#+
5133
Acute Chroma
135/128
92.179
-320
Also known as an acute augmented prime, a major chroma or a limma ascendant. This is the wider chroma seen in places such as between the natural and raised 4th of the just major scale.
Db
17-132
Septendecimal Chroma
18/17
98.955
-43
This is interval by which the just half-diminished and the just diminished 7th chords differ.
Db
21/12
Equal Temperament Minor 2nd
1.0595/1
100
0
This interval divides the octave into 12 equal parts.
Db
171
Septendecimal Minor 2nd †
17/16
104.955
203
This is the harmonic used to form the just flatted 9th and diminished 7th chords.
Db-
5-13-1
Minor 2nd
16/15
111.731
481
C#++
37
Pythagorean Apotome
2187/2048
113.685
561
Or a Pythagorean augmented prime, or Pythagorean chroma.
C#+7
7-15131
Septimal Chroma
15/14
119.443
796
This is the interval by which the just major 7th and the just barbershop 7th chords differ.
Db
5-233
Acute Minor 2nd
27/25
133.238
1361
This wide minor 2nd is found in places like between the raised tonic and the supertonic degrees of the just major scale.
D7-
5131
"delta" major 2nd †
35/32
155.14
-1837
So-called because it is the first interval in the tenor when singing "Darkness on the Delta" in just intonation. It's a septimal 2nd flatter than a just major 3rd.
Ebb--
3-10
Pythagorean Diminished 3rd
65536/59049
180.405
-801
D-
513-2
Major 2nd
10/9
182.404
-721
Also known as a minor wholetone or a 5-limit major 2nd.
D
21/6
Equal Temperament Major 2nd
1.1225/1
200
0
This interval divides the octave into 6 equal parts.
D
32
Acute Major 2nd
9/8
203.91
160
Also known as a major wholetone, a Pythagorean major 2nd or the 9th harmonic.
Ebb-
5-23-2
Grave Diminished 3rd
256/225
223.463
961
This is simply formed with two just minor 2nds.
D7
7-1
Septimal Major 2nd
8/7
231.174
1277
Also known as a super-major 2nd. This is the inversion of the 7th in the just "barbershop 7th" chord.
Ebb
5-332
Diminished 3rd
144/125
244.969
1842
Eb7-
713-1
Septimal Minor 3rd
7/6
266.871
-1357
Also known as a sub-minor 3rd. This is the 3rd at the top of a just "barbershop 7th chord", narrower than a just minor 3rd by a septimal quartertone.
D#
5231
Augmented 2nd
75/64
274.582
-1041
This is a 5-limit chroma wider than an acute major 2nd.
E11 13
13111-1
Tredecimal Minor 3rd †
13/11
289.21
-442
Eb-
3-3
Grave Minor 3rd
32/27
294.135
-240
Also known as a Pythagorean minor 3rd.
Eb
191
Overtone Minor 3rd †
19/16
297.513
-102
Also known as a 19-limit minor 3rd, or an undevigintimal minor 3rd.
Eb
21/4
Equal Temperament Minor 3rd
1.1892/1
300
0
This interval divides the octave into 4 equal parts.
Eb
5-131
Minor 3rd
6/5
315.641
641
D#++
39
Pythagorean Augmented 2nd
19683/16384
317.595
721
Eb717
1717-1
Septendecimal Minor 3rd
17/14
336.13
1480
This is the interval heard at the top of the diminished 7th chord.
Eb-11
1113-2
Undecimal Median 3rd
11/9
347.408
-2154
This is the interval heard at the top of an augmented 11th chord.
Fb--
3-8
Pythagorean Diminished 4th
8192/6561
384.36
-641
E
51
Major 3rd
5/4
386.314
-561
Also known as a just major 3rd, or a 5-limit major 3rd.
E
21/3
Equal Temperament Major 3rd
1.2599/1
400
0
This interval divides the octave into 3 equal parts.
E+
34
Acute Major 3rd
81/64
407.82
320
Also known as a Pythagorean major 3rd.
Fb
5-2
Diminished 4th
32/25
427.373
1121
E7+
7-132
Septimal Major 3rd
9/7
435.084
1437
Also known as a super-major 3rd. This is the 3rd at the top of a just half-diminished 7th chord, wider than a just major 3rd.
E#
533-1
Augmented 3rd
125/96
456.986
-1762
F7
7131
Septimal 11th †
21/16
470.781
-1197
Also known as the 21st harmonic.
Gbb----
3-13
Pythagorean Doubly-Diminished 5th
2097152/1594323
474.585
-1041
Narrow enough to sound like a 4th. This is heard in Chords such as the Swiss and Eulenspiegel 6th chords, where a raised 2nd degree meets a flatted 6th degree.
F
3-1
Perfect 4th
4/3
498.045
-80
Also known as a just perfect 4th.
F
25/12
Equal Temperament Perfect 4th
1.3348/1
500
0
F+
5-133
Acute ("Wolf") 4th
27/20
519.551
801
Also known as a "wolf" 4th, or a 5-limit perfect 4th.
E#+++
311
Pythagorean Augmented 3rd
177147/131072
521.505
881
Gbb
5-33-1
Doubly-Diminished 5th
512/375
539.104
1602
Narrow enough to sound like a 4th. This is heard in Chords such as the Swiss and Eulenspiegel 6th chords, where a raised 2nd degree meets a flatted 6th degree.
F11
111
11th Harmonic †
11/8
551.318
-1994
Also known as an undecimal tritone.
F#
523-2
Augmented 4th
25/18
568.717
-1281
This is the tritone that is a just chroma wider than a perfect 4th.
Gb7-
715-1
Septimal Diminished 5th
7/5
582.512
-716
Gb--
3-6
Pythagorean Diminished 5th
1024/729
588.27
-480
F#+
5132
Acute Augmented 4th
45/32
590.224
-400
This is the tritone between the 4th and 7th degrees of the just major scale.
When resolved outward by just minor 2nds, lead to a just minor 6th.
F#
21/2
Equal Temperament Tritone
1.4142/1
600
0
This is exactly half an octave, or more accurately, the square root of an octave.
Gb
1713-1
Septendecimal Diminished 5th
17/12
603
123
This is the interval of the 3rd and 7th of a just diminished 7th chord.
Gb-
5-13-2
Grave Diminished 5th
64/45
609.776
400
This is the tritone between the 7th and 4th degrees of the just major scale.
F#++
36
Pythagorean Augmented 4th
729/512
611.73
480
Gb7-
7-151
Septimal Augmented 4th
10/7
617.488
716
F#23
231
23rd Harmonic †
23/16
628.274
1158
Gb
5-232
Diminished 5th
36/25
631.283
1281
This is a 5-limit chroma narrower than a just perfect 5th.
F##
5331
Doubly-Augmented 4th
375/256
660.896
-1602
Wide enough to sound like a 5th. This is heard in Chords such as the Swiss and Eulenspiegel 6th chords, where a flatted 6th degree meets a raised 2nd degree.
Abb--
3-11
Pythagorean Diminished 6th
262144/177147
678.495
-881
This is the "wolf" interval famous for being the only out-of-tune 5th in a Pythagorean keyboard tuning, when G# and Eb are played.
G-
513-3
Grave ("Wolf") 5th
40/27
680.449
-801
Also known as a "wolf" 5th, or a 5-limit perfect 5th. This interval is heard in the supertonic chord of the just major scale.
G
27/12
Equal Temperament Perfect 5th
1.4983/1
700
0
This is the 5th heard on a properly tuned piano.
G
31
Perfect 5th
3/2
701.955
80
This is the generator for all Pythagorean intervals.
F##++++
313
Pythagorean Doubly-Augmented 4th
1594323/1048576
725.415
1041
Wide enough to sound like a 5th. This is heard in Chords such as the Swiss and Eulenspiegel 6th chords, where a flatted 6th degree meets a raised 2nd degree.
Abb
5-331
Diminished 6th
192/125
743.014
1762
Ab7-
713-2
Septimal Minor 6th
14/9
764.916
-1437
Also known as a sub-minor 6th.
G#
52
Augmented 5th
25/16
772.627
-1121
Made simply by staking two just major 3rds.
G#7 11
1117-1
Undecimal Augmented 5th †
11/7
782.492
-717
Ab-
3-4
Grave Minor 6th
128/81
792.18
-320
Also known as a Pythagorean minor 6th.
Ab
22/3
Equal Temperament Minor 6th
1.5874/1
800
0
Ab
17131
Septendecimal Minor 6th †
51/32
806.91
283
Tuning of a just flatted 9th over the 5th scale degree.
Ab
5-1
Minor 6th
8/5
813.686
561
G#++
38
Pythagorean Augmented 5th
6561/4096
815.64
641
A13
131
13th Harmonic †
13/8
840.528
-2436
Also known as a tredecimal 6th, or tredecimal 13th.
Bbb
725-13-1
Septimal Diminished 7th II
49/30
849.383
-2073
This forms the exterior notes of the 30:35:42:49 diminished 7th chord
A+11
11-132
Undecimal Median 6th
18/11
852.592
-1942
Bbb---
3-9
Pythagorean Diminished 7th
32768/19683
882.405
-721
A
513-1
Major 6th
5/3
884.359
-641
Bbb
71315-2
Septimal Diminished 7th I
42/25
898.153
-76
This forms the exterior notes of the 25:30:35:42 diminished 7th chord
A
23/4
Equal Temperament Major 6th
1.6818/1
900
0
A+
33
Acute Major 6th
27/16
905.865
240
Also known as a Pythagorean major 6th.
Bbb
1715-1
Septendecimal Diminished 7th †
17/10
918.642
764
This forms the exterior notes of the just diminished 7th chord.
Bbb-
5-23-1
Diminished 7th
128/75
925.418
1041
This is a 5-limit chroma narrower than a grave minor 7th.
A7+
7-131
Septimal Major 6th
12/7
933.129
1357
Also known as a super-major 6th.
A#
533-2
Augmented 6th
125/72
955.031
-1842
This is a 5-limit chroma wider than a just major 6th.
Bb7
71
Septimal Minor 7th
7/4
968.826
-1277
This forms the exterior notes of the just barbershop 7th chord.
A#+
5232
Acute Augmented 6th
225/128
976.537
-961
Bb-
3-2
Grave Minor 7th
16/9
996.09
-160
Also known as a Pythagorean Minor 7th.
Bb
25/6
Equal Temperament Minor 7th
1.7818/1
1000
0
Bb7
7-152
Septimal Augmented 6th
25/14
1003.802
156
Bb
5-132
Minor 7th
9/5
1017.596
721
Also known as a 5-limit minor 7th. This forms the exterior notes of the just minor 7th and just half-diminished 7th chords.
A#++
310
Pythagorean Augmented 6th
59049/32768
1019.55
801
B
1113-1
Undecimal Median 7th †
11/6
1049.363
-2074
This forms the exterior notes of the harmonic minor-major 7th chord.
B-
523-3
Grave Major 7th
50/27
1066.762
-1361
This is the interval between the supertonic and raised tonic degrees of the just major scale.
B713
1317-1
Tredecimal Major 7th †
13/7
1071.702
-1159
This forms the exterior notes of the harmonic augmented-major 7th chord.
Cb--
3-7
Pythagorean Diminished Octave
4096/2187
1086.315
-561
B
5131
Major 7th
15/8
1088.269
-481
B
211/12
Equal Temperament Major 7th
1.8877/1
1100
0
B+
35
Acute Major 7th
243/128
1109.775
400
Cb-
5-13-3
Grave Diminished Octave
256/135
1107.821
320
Cb
5-231
Diminished Octave
48/25
1129.328
1201
B#
53
Augmented 7th
125/64
1158.941
-1682
Dbb---
3-12
Pythagorean Diminished 2nd
1048576/531441
1176.54
-961
Considered an inverse (descending) interval, this is here normalized by raising it an octave.
C-
513-4
Grave ("Wolf") Octave
160/81
1178.494
-881
C
21
Octave
2/1
1200
0

Interval Calculator

This tool lets you combine intervals together, or find differences between intervals, using the "accumulator", which is initialized to a value of 1/1 (unison). Since pitch is logarithmic, remember that intervals are combined by multiplication and division. To multiply the accumulator by an interval, enter it in the operand box below and hit <Enter>. To divide the accumulator by it, enter its inverse. Hit <Esc> to reset the accumulator to 1/1. The results are displayed in the results box:

"old accumulator * value entered = new accumulator   cents:nnn   pba:nnn".

You can also click on an interval in the index to factor it into the product. Right-click or Option-click to factor it out of the product.

Operand:
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