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"Neutral diatonic" or "Neutron[7]" | Intervals in 7-edo | Related scales | Alphabet | Music | Ear Training | Commas

"Neutral diatonic" or "Neutron[7]"


7-edo divides the 1200-cent octave into 7 equal parts, making its smallest interval 171.428¢, or the seventh root of 2. It is the fourth prime edo, after 2edo, 3edo and 5edo.

Equal-heptatonic scales are used in non-western music in African cultures as well as an integral part of early Thai and early Chinese music. It has been speculated in "Indian music:history and structure", that the Indian three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones).
7-tet can be thought of as result of stacking seven 11/9s on top of each other, and then tempering to remove the comma (2^-2 3^-14 11^7). As a temperament, William Lynch gives it the name "Neutron[7]" just as the whole tone scale of 12 ET is known as "Hexe[6]".

Typically, 7-edo exists as the tuning for pentatonic scales in traditional thai music with the other two pitches acting as auxiliary tones. However, it can be used as an interesting diatonic scale choice as well in tunings such as 14 EDO or 21 EDO.

The seventh of 7-edo is almost exactly the 29th harmonic (29/16), which can have a very agreeable sound with harmonic timbres. However it also finds itself nested between ratios such as 20/11 and 9/5, which gives it considerably higher harmonic entropy than 7/4, a much simpler overtone seventh.

Similarly, in equi-heptatonic systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. One of the most impressive areas in Africa in which a pen-equidistant heptatonic scale is combined with a distinctively harmonic style based on singing in intervals of thirds plus fifths, or thirds plus fourths, is the eastern Angolan culture area. This music is heptatonic and non-modal; i.e., there is no concept of major or minor thirds as distinctive intervals. In principle all the thirds are neutral, but in practice the thirds rendered by the singers often approximate natural major thirds (386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system. For the notation of such music, a seven-line stave is most appropriate, with each horizontal line representing one pitch level.
("African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009)

A Thai xylophone measured by Morton (1974) "varied only plus or minus 5 cents," from 7-TET. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.

Intervals in 7-edo

Interval
Cents
Closest diatonic
interval name
The "neighborhood" of just intervals
0
0
unison / prime
exactly 1/1
1
171.429
second
6.424¢ from Ptolemy (neutral) second 11/10
3.215¢ from second 54/49
-1.006¢ from the 29th subharmonic 32/29
-10.975¢ from major second (small whole tone) 10/9
2
342.857
third
-4.55¢ from neutral third 11/9
3
514.286
fourth
16.24¢ from just fourth 4/3 (498.045¢)
-5.265¢ from wide fourth 27/20
4
685.714
fifth
5.265 ¢ from narrow fifth 40/27
-16.241¢ from just fifth 3/2 (701.955¢)
5
857.143
sixth
4.551¢ from neutral sixth 18/11
6
1028.571
seventh
10.975¢ from (Didymus) minor seventh 9/5
-6.424¢ from neutral seventh 20/11
1.006¢ from the 29th harmonic 29/16
-3.215¢ from seventh 49/27
7 (0)
1200
eighth
exactly 2/1

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Related scales

  • Related in a lateral way to traditional Thai music. Subset of 14 EDO and 21 EDO.

Notation

  • Rotatable on a five-line staff without accidentals.

Harmony

There is no distinction between Major or Minor; each pitch class is unique.

Melody

There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429 c) works well as a basic step for melodic progression.
The step from seventh to octave is too large for the leading tone.

Relative tuning accuracy

7-edo is the third zeta integral edo.

Alphabet

William Lynch proposes using numbers 1 through 7 as the nominals of 7 ET with # signs being possible to expand to 14 EDO or even 21 EDO.
The alphabet can be written in three ways:
Plain numbers: 1 2 3 4 5 6 7
In Japanese number abbreviations: い に さん し ご ろ な い
In Chinese/Kanji numbers: 一 二 三 四 五 六七 

Music



Ear Training

7 EDO ear-training exercises by Alex Ness available here.

Commas

7 EDO tempers out the following commas. (Note: This assumes val < 7 11 16 20 24 26 |.)

Comma
Monzo
Cents
Name 1
Name 2
Name 3
2187/2048
| -11 7 >
113.69
Apotome


135/128
| -7 3 1 >
92.18
Major Chroma
Major Limma
Pelagic Comma
25/24
| -3 -1 2 >
70.67
Chromatic semitone
Chroma

250/243
| 1 -5 3 >
49.17
Maximal Diesis
Porcupine Comma

20000/19683
| 5 -9 4 >
27.66
Minimal Disease
Tricot Comma

81/80
| -4 4 -1 >
21.51
Syntonic Comma
Didymos Comma
Meantone Comma
1600000/1594323
| 9 -13 5 >
6.15
Amity Comma


36/35
| 2 2 -1 -1 >
48.77
Septimal Quarter Tone


525/512
| -9 1 2 1 >
43.41
Avicenna
Avicenna's Enharmonic Diesis

64/63
| 6 -2 0 -1 >
27.26
Septimal Comma
Archytas' Comma
Leipziger Komma
875/864
| -5 -3 3 1 >
21.90
Keema


5120/5103
| 10 -6 1 -1 >
5.76
Hemi Family


6144/6125
| 11 1 -3 -2 >
5.36
Cornwell


4375/4374
| -1 -7 4 1 >
0.40
Ragisma


394839/394762
| 47 -7 -7 -7 >
0.34
Akjaysma
5\7 Octave Comma

100/99
| 2 -2 2 0 -1 >
17.40
Ptolemies


121/120
| -3 -1 -1 0 2 >
14.37
Batista


176/175
| 4 0 -2 -1 1 >
9.86
Valinorsma


65536/65219
| 16 0 0 -2 -3 >
8.39
Organisma


243/242
| -1 5 0 0 -2 >
7.14
Rasta


385/384
| -7 -1 1 1 1 >
4.50
Keenanisma


4000/3993
| 5 -1 3 0 -3 >
3.03
Wizard Harry