7edo: Difference between revisions

{{EDO intro|7}}

7edo can be thought of as the result of stacking seven [[11/9]]'s on top of each other, and then tempering to remove the comma {{monzo| -2 -14 0 0 7 }}. As a temperament, [[William Lynch]] gives it the name "Neutron[7]" just as the whole tone scale of [[12edo]] is known as "Hexe[6]".

7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].

The seventh of 7edo 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.

A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.

7edo is the unique intersection of [[meantone]] and [[porcupine]] temperaments.

=== Observations ===

7edo unifies the seven diatonic scales—Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian—into a single one.  

Subset of [[14edo]] and [[21edo]].  

There is a [[Neutral Scale|neutral]] feel between whole tone scale and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.

The step from seventh to octave is too large for the leading tone.

It has often been stated that 7edo approximates tunings used in Thai classical music. This is a myth unsupported by empirical studies of the instruments.<ref>Garzoli, John. [http://iftawm.org/journal/oldsite/articles/2015b/Garzoli_AAWM_Vol_4_2.pdf "The Myth of Equidistance in Thai Tuning."]</ref>

|+ Intervals of 7edo

|  

|  

|  

| [[39/32]] (+0.374)<br>[[11/9]] (-4.551)

| [[18/11]] (+4.551)<br>[[64/39]] (-0.374)

|[[File:0-1028,57 seventh (7-EDO).mp3|frameless]]

Sharps (#) and flats (b) have no effect in 7edo, because the apotome ([[2187/2048]]) is [[tempered out]]. Therefore, 7edo can be notated on a five-line staff without accidentals.  Alternatively, a seven-line stave can be used, with each horizontal line representing one pitch level. There is no distinction between major or minor, so every interval has the [[interval quality]] "perfect" instead.

|+ Notation of 7edo

* [[ups and downs notation]] is identical to circle-of-fifths notation;

* mixed and pure [[sagittal notation]] are identical to circle-of-fifths notation.

|+ Solfege of 7edo

! Standard [[solfege]]<br>(movable do)

! [[Uniform solfege]]<br>(1 vowel)

[[File:7ed2-001.svg|alt=alt : Your browser has no SVG support.]]

 

[[:File:7ed2-001.svg|7ed2-001.svg]]

{{Uniform map|13|6.5|7.5}}

7edo [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 7 11 16 20 24 26 }}.  

! [[Harmonic limit|Prime<br>Limit]]

![[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints</ref>

![[Monzo]]

![[Cent]]s

![[Color notation/Temperament Names|Color Name]]

!Name(s)

|3

|[[2187/2048]]

|{{monzo| -11 7 }}

|113.69

|Lawa

|Apotome, Pythagorean chromatic semitone

|5

|[[135/128]]

|92.18

|Layobi

|Major chroma, major limma, pelogic comma

|[[25/24]]

|{{monzo| -3 -1 2 }}

|70.67

|Yoyo

|Classic chromatic semitone, dicot comma

|5

|[[250/243]]

|{{monzo| 1 -5 3 }}

|49.17

|Triyo

|Maximal diesis, porcupine comma

|5

|[[20000/19683]]

|{{monzo| 5 -9 4 }}

|27.66

|Saquadyo

|Minimal diesis, tetracot comma

|5

|{{monzo| -4 4 -1 }}

|21.51

|Gu

|Syntonic comma, Didymus comma, meantone comma

|5

|[[1600000/1594323|(14 digits)]]

|{{monzo| 9 -13 5 }}

|6.15

|Saquinyo

|[[Amity comma]]

|[[36/35]]

|{{monzo| 2 2 -1 -1 }}

|48.77

|Septimal quartertone

|7

|

[[525/512]]

|{{monzo| -9 1 2 1 }}

|43.41

|Lazoyoyo

|Avicennma, Avicenna's enharmonic diesis

|7

|[[64/63]]

|{{monzo| 6 -2 0 -1 }}

|27.26

|Septimal comma, Archytas' comma, Leipziger Komma

|7

|{{monzo| -5 -3 3 1 }}

|21.90

|Keema

|7

|[[5120/5103]]

|{{monzo| 10 -6 1 -1 }}

|5.76

| Hemifamity

|[[6144/6125]]

|{{monzo| 11 1 -3 -2 }}

|5.36

| Porwell

|7

|[[4375/4374]]

|{{monzo| -1 -7 4 1 }}

|0.40

|Zoquadyo

|Ragisma

|7

|<abbr title="140737488355328/140710042265625">(30 digits)</abbr>

|{{monzo| 47 -7 -7 -7 }}

|0.34

|Trisa-rugu

|[[Akjaysma]], 5\7 octave comma

|11

|[[100/99]]

|{{monzo| 2 -2 2 0 -1 }}

|17.40

|Luyoyo

|11

|

[[121/120]]

|{{monzo| -3 -1 -1 0 2 }}

|14.37

|Lologu

|[[176/175]]

|{{monzo| 4 0 -2 -1 1 }}

|9.86

|Lurugugu

|Valinorsma

|11

|{{monzo| 16 0 0 -2 -3 }}

|8.39

|Satrilu-aruru

|Orgonisma

|11

|[[243/242]]

|{{monzo| -1 5 0 0 -2 }}

|7.14

|Lulu

|Rastma

|11

|[[385/384]]

|{{monzo| -7 -1 1 1 1 }}

|4.50

|Lozoyo

|Keenanisma

|[[4000/3993]]

|{{monzo| 5 -1 3 0 -3 }}

|3.03

|Triluyo

| Wizardharry

|13

|[[27/26]]

|{{monzo| -1 3 0 0 0 -1 }}

|65.33

|thu unison

|small tridecimal third tone

|13

|[[65/64]]  

|{{monzo| -6 0 1 0 0 1 }}

|26.84

|

|wilsorma

|13

|[[52/49]]

|{{monzo| 2 0 0 -2 0 1 }}

|102.87

|thoruru unison

|hammerisma

|13

| [[14641/13312]]

|{{monzo| -10 0 0 0 4 -1 }}

|164.74

|

|

7edo is the first edo in which regular temperament theory starts to make sense as a way of subdividing the steps into [[mos scale]]s, with three different ways of dividing it, although there is still quite a lot of ambiguity as each step can be considered as the sharp extreme of one temperament or the flat end of another. 1/7 can be considered the intersection of sharp [[porcupine]] and flat [[tetracot]] temperaments, as three steps makes a 4th and four a 5th. 2/7 can be interpreted as critically flat [[Mohajira]] or critically sharp [[amity]], and creates mosses of 322 and 2221. 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first edo with a non-equalized, non-1L''n''s pentatonic mos. This is in part because 7edo is a [[The Riemann zeta function and tuning #Zeta edo lists|strict zeta edo]] (close to low-complexity JI for its size), and is the second edo with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the edo's meantone and mavila interpertations.

<references/>