RE: Just Interval Progressions

There are many ways to arrive at the "most consonant" just
intervals. The following is the output of a program that
approaches that subject from the perspective of least common
multiple. As most of you must know by now, I favor this as a
measure because it correlates with a physical property of the
composite sound, i. e. the length of the pattern. Also, the
concept is independent of "limits" as in 5-limit, 7-limit, etc.

Note that for two notes, it doesn't matter whether you are using
the frequency or the wavelength as your measure of pitch. For
three or more notes, you must use the wavelength as the measure
of pitch for the concept to be valid.

In cases where there are more then two intervals given, i. e. 4/3
and 7/5 the first is the "common" interval that most closely
approximates the exact interval.

In cases where triads are listed, it is possible to make triads
with the given LCM and the given base wavelength.

Marion

LCM: 12 LCM#: 1 Chord: 1
2 3 g Perfect Fifth 3/2
1 2 c Unison 1/1

LCM: 12 LCM#: 1 Chord: 2
2 4 f Perfect Fourth 4/3
1 3 c Unison 1/1

LCM: 15 LCM#: 2 Chord: 3
2 5 a Major Sixth 5/3
1 3 c Unison 1/1

LCM: 20 LCM#: 3 Chord: 4
2 5 e Major Third 5/4
1 4 c Unison 1/1

LCM: 28 LCM#: 4 Chord: 5
2 7 a+ Harmonic Minor Seventh 7/4
1 4 c Unison 1/1

LCM: 30 LCM#: 5 Chord: 6
2 6 d# Minor Third 6/5
1 5 c Unison 1/1

LCM: 35 LCM#: 6 Chord: 7
2 7 f Perfect Fourth 4/3 7/5
1 5 c Unison 1/1

LCM: 40 LCM#: 7 Chord: 8
2 8 g# Minor Sixth 8/5
1 5 c Unison 1/1

LCM: 42 LCM#: 8 Chord: 9lx.cld

2 7 d Major Tone 9/8 7/6
1 6 c Unison 1/1

LCM: 45 LCM#: 9 Chord: 10
2 9 a#+ Minor Seventh 9/5
1 5 c Unison 1/1

LCM: 56 LCM#: 10 Chord: 11
2 8 d Major Tone 9/8 8/7
1 7 c Unison 1/1

LCM: 60 LCM#: 11 Chord: 12
3 5 a Major Sixth 5/3
2 4 f Perfect Fourth 4/3
1 3 c Unison 1/1

LCM: 60 LCM#: 11 Chord: 13
3 6 g Perfect Fifth 3/2
2 5 e Major Third 5/4
1 4 c Unison 1/1

LCM: 60 LCM#: 11 Chord: 14
3 15 g Perfect Fifth 3/2
2 12 d# Minor Third 6/5
1 10 c Unison 1/1

LCM: 60 LCM#: 11 Chord: 15
3 20 a Major Sixth 5/3
2 15 e Major Third 5/4
1 12 c Unison 1/1

LCM: 63 LCM#: 12 Chord: 16
2 9 e Major Third 5/4 9/7
1 7 c Unison 1/1

LCM: 66 LCM#: 13 Chord: 17
2 11 a#+ Minor Seventh 9/5 11/6
1 6 c Unison 1/1

LCM: 70 LCM#: 14 Chord: 18
2 7 f Perfect Fourth 4/3 7/5
1 5 c Unison 1/1

LCM: 70 LCM#: 14 Chord: 19
2 10 f# Diminished Fifth 64/45 10/7
1 7 c Unison 1/1

LCM: 72 LCM#: 15 Chord: 20
3 9 g Perfect Fifth 3/2
2 8 f Perfect Fourth 4/3
1 6 c Unison 1/1

LCM: 72 LCM#: 15 Chord: 21
3 12 g Perfect Fifth 3/2
2 9 d Major Tone 9/8
1 8 c Unison 1/1

LCM: 77 LCM#: 16 Chord: 22
2 11 g Perfect Fifth 3/2 11/7
1 7 c Unison 1/1

LCM: 84 LCM#: 17 Chord: 23
3 7 a+ Harmonic Minor Seventh 7/4
2 6 g Perfect Fifth 3/2
1 4 c Unison 1/1

LCM: 84 LCM#: 17 Chord: 24
2 12 a Major Sixth 5/3 12/7
1 7 c Unison 1/1

LCM: 84 LCM#: 17 Chord: 25
3 21 a+ Harmonic Minor Seventh 7/4
2 14 d Major Tone 9/8 7/6
1 12 c Unison 1/1

LCM: 88 LCM#: 18 Chord: 26
2 11 f Perfect Fourth 4/3 11/8
1 8 c Unison 1/1

LCM: 90 LCM#: 19 Chord: 27
3 9 a#+ Minor Seventh 9/5
2 6 d# Minor Third 6/5
1 5 c Unison 1/1

LCM: 90 LCM#: 19 Chord: 28
3 10 a Major Sixth 5/3
2 9 g Perfect Fifth 3/2
1 6 c Unison 1/1

LCM: 90 LCM#: 19 Chord: 29
3 15 a Major Sixth 5/3
2 10 c#+ Minor Tone 10/9
1 9 c Unison 1/1

LCM: 90 LCM#: 19 Chord: 30
3 18 a#+ Minor Seventh 9/5
2 15 g Perfect Fifth 3/2
1 10 c Unison 1/1

LCM: 91 LCM#: 20 Chord: 31
2 13 a#+ Minor Seventh 9/5 13/7
1 7 c Unison 1/1

LCM: 99 LCM#: 21 Chord: 32
2 11 d# Minor Third 6/5 11/9
1 9 c Unison 1/1
LCM: 104 LCM#: 22 Chord: 33
2 13 g# Minor Sixth 8/5 13/8
1 8 c Unison 1/1

LCM: 110 LCM#: 23 Chord: 34
2 11 c# Semitone 16/15 11/10
1 10 c Unison 1/1

LCM: 117 LCM#: 24 Chord: 35
2 13 f# Diminished Fifth 64/45 13/9
1 9 c Unison 1/1

LCM: 120 LCM#: 25 Chord: 36
3 8 g# Minor Sixth 8/5
2 6 d# Minor Third 6/5
1 5 c Unison 1/1

LCM: 120 LCM#: 25 Chord: 37
4 15 b Major Seventh 15/8
3 12 g Perfect Fifth 3/2
2 10 e Major Third 5/4
1 8 c Unison 1/1

LCM: 120 LCM#: 25 Chord: 38
3 24 g# Minor Sixth 8/5
2 20 f Perfect Fourth 4/3
1 15 c Unison 1/1




SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: Octave Stretch for 19-tone Equal
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