Interval size measure
edited
... or by frequancy frequency ratios.
Logarithmic
All logarithmic measures can be combined b…
...
or by frequancyfrequency ratios.
Logarithmic
All logarithmic measures can be combined by adding and subtracting them.
Gross
Intervals are somtetimessometimes expressed in
For "atonal" music it was replaced by the number of 12edo-semitones.
Proposal: The relative interval measure is the number of steps between two pitches of an equal tuning, sometimes called degrees (of an edo). For generators, the backslash notation is used d\edo, but it is also a ratio (of a logarithmic measure).
Fine
...
12edo is requied.required. Some people
Other measures include the Eka, 1\16 octave, Normal diesis: 1\31 octave; the Méride: 1\43 octave; the Holdrian comma: 1\53 octave; the Morion: 1\72 octave; the Farab: 1\144 octave; the Mem: 1\205 octave (used by Hi-pi Instruments); the Tredek: 1\270 octave; the Eptaméride or Savart: 1\301 of an octave; the Gene: 1\311 octave; the Dröbisch Angle: 1\360 octave; the Squb: 1\494 octave; the Iring: 1\600 octave; the Skisma: 1\612 octave; the Delfi: 1\665 octave; the Woolhouse: 1\730 octave; the millioctave (mO), 1\1000 octave; the fine cent or deciFarab: 1\1440 octave; the Iota: 1\1700 octave; the Harmos: 1\1728octave; the Mina: 1\2460 octave; the Tina: 1\8539 octave; the Purdal: 1\9900 octave; the Türk sent: 1\10600 octave; the Prima: 1\12276 octave, the Jinn: 1\16808 octave, the Jot: 1\30103 octave; the Imp: 1\31920 octave; the Flu: 1\46032 octave; and the MIDI Tuning Standard unit: 1\196608 octave. Not based on the octave are the Grad: 1/12 of a Pythagorean comma and the Hekt: 1/1300 part of 3, ie 3^(1/1300).
See Logarithmic Interval Measures
...
between two neigbouringneighbouring pitches in
see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
Ratio
Interval size measure
edited
... see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
Ratio
... to multiply oder or …
...
see also: Kirnberger Atom http://arxiv.org/abs/0907.5249
Ratio
...
to multiply oderor divide:
a pure fifth increased by a major third gives the major seventh 3/2*5/4 = 15/8,
which is a diatonic semitone below an octave (2/1)/(15/8) = 2/1*8/15 = 16/15.
downmajor 2nd
D#v / Ev / Fv / Gbv perfperfect 2nd
E
3
...
downmajor 3rd
F#v / Gv / Abv
major 3rd3rd, dim 4th
F# / Gb
6
480
M3, P4, d5
major 3rd, perfperfect 4th, dim
F# / G / Ab minoraug 3rd, minor 4th
G
Fx / G
7
560
...
up 4th, updim 5th
F#^ / G^ / Ab^
major 4th4th, dim 5th
G# / Abb
8
...
downaug 4th, down 5th
G#v / Av / Bbv minoraug 4th, minor 5th
Gx / Ab
9
720
A4, P5, m6
aug 4th, perfperfect 5th, minor
G# / A / Bb
major 5th5th, dim 6th
A / Bbb
10
800
...
up 5th, upminor 6th
G#^ / A^ / Bb^ minoraug 5th, minor 6th
A# / Bb
11
17edo
edited
... Intervals
Degree
Cents
Names of
Intervals
ups and downs notation
Cents
Approximate …
...
Intervals
Degree
Cents
Names of
Intervals
ups and downs notation Cents
Approximate
Ratios*
Temperament(s)
generated
0
0
Unison
...
P1
C 0
1/1
1
70.59
Super Unison/
Minor Second minminor 2nd
m2
Db 70.59
25/24, 26/25, 33/32
2
141.18
Augmented Unison/
Neutral Second
...
~2
Dv 141.18
13/12, 12/11, 14/13
Bleu
3
211.765
Major Second/
Sub Third majmajor 2nd
M2
D 211.765
9/8, 25/22, 8/7, 28/25
Machine
4
282.35
Minor Third/
Super Second minminor 3rd
m3
Eb 282.35
13/11, 75/64, 7/6
Huxley
5
352.94
Augmented Second/
Neutral Third/
...
~3
Ev 352.94
11/9, 16/13
Maqamic/hemif
6
423.53
Major Third/
Sub Fourth majmajor 3rd
M3
E 423.53
32/25, 33/26, 9/7, 14/11, 51/40
Skwares
7
494.11
Perfect Fourth perfperfect 4th
P4
F 494.11
4/3
Supra
8
564.71
Super Fourth
Diminished Fifth
up 4th, dimdiminished 5th
^4, d5
F^, Gb 564.71
11/8, 18/13
Progress
9
635.29
Augmented Fourth/
Sub Fifth augaugmented 4th,
down 5th
A4, v5
F#, Gv 635.29
16/11, 13/9, 23/16
Progress
10
705.88
Perfect Fifth perfperfect 5th
P5
G 705.88
3/2
Supra
11
776.47
Super Fifth/
Minor Sixth minminor 6th
m6
Ab 776.47
25/16, 52/33, 14/9, 11/7
Skwares
12
847.06
Augmented Fifth/
Neutral Sixth/
...
~6
Av 847.06
13/8, 18/11
Maqamic/hemif
13
917.65
Major Sixth/
Sub Seventh majmajor 6th
M6
A 917.65
17/10, 22/13, 128/75, 12/7
Huxley
14
988.235
Minor Seventh/
Super Sixth minminor 7th
m7
Bb 988.235
16/9, 44/25, 7/4, 25/14
Machine
15
1058.82
Augmented Sixth/
Neutral Seventh/
...
~7
Bv 1058.82
11/6, 24/13, 13/7
Bleu
16
1129.41
Major Seventh/
Sub Octave majmajor 7th
M7
B 1129.41
25/13, 48/25, 64/33
17
1200
Perfect Octave
octave
P8
C 1200
2/1
Chord Names
Ups and down notation can be used to name 17edo chords. 0-4-7-10 = C Eb F G = Cm(11) = C minor add eleven (approximates 6:7:8:9)
0-3-6-10 = C D E G = C(9) = C add nine (approximates 1/(6:7:8:9) = 1/1 - 9/8 - 9/7 - 3/2)
0-3-7-10 = C D F G = C4(9) = C four add nine
0-2-7-10 = C Dv F G = C4(v9) = C four add down-nine (approximates 12:13:16:18)
0-3-8-10 = C D F^ G = C.^4(9) = C up-four add nine (approximates 8:9:11:12)
0-4-10 = C Eb G = Cm = C minor
0-5-10 = C Ev G = C~ = C mid
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0-6-10-15 = C E G Bv = C(~7) = C mid seven
0-5-10-15 = C Ev G Bv = C.~7 = C dot mid seven
0-4-7-10 = C Eb F G = Cm(11) = C minor add eleven (approximates 6:7:8:9)
0-3-6-10 = C D E G = C(9) = C add nine (approximates 1/(6:7:8:9) = 1/1 - 9/8 - 9/7 - 3/2)
0-3-7-10 = C D F G = C4(9) = C four add nine
0-2-7-10 = C Dv F G = C4(v9) = C four add down-nine (approximates 12:13:16:18)
0-3-8-10 = C D F^ G = C.^4(9) = C up-four add nine (approximates 8:9:11:12)
For a more complete list, see Ups and Downs Notation - Chord names in other EDOs.
Selected just intervals by error