7edo: Difference between revisions

{{EDO intro}}

{{Harmonics in equal|7}}

7edo unifies the seven [[5L 2s|diatonic]] scales - Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian - into a single one: 7edo can be used as an interesting diatonic scale choice as well in tunings such as [[14edo]] or [[21edo]].

There is a [[interval quality|neutral]] feel somewhere between a [[6edo|whole tone scale]] and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression.

It has been speculated in ''Indian music: history and structure''<ref>Nambiyathiri, Tarjani. ''[https://archive.org/details/indianmusichistoryandstructureemmietenijenhuisbrill Indian Music History And Structure Emmie Te Nijenhuis Brill]''</ref> that the [[Indian]] three-sruti interval of 165 cents is close enough to be mistaken for 171 cents. (or 1.71 semitones), one step of 7edo.

In [[equiheptatonic]] systems the desire for harmonic sound may dictate constant adjustments of intonation away from the theoretical interval of 171 cents. (Similar to [[adaptive just intonation]] but with equal tuning instead).  

One region of 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]] 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 ([[5/4]], 386 cents), especially at points of rest. In this manner, the principles of equidistance and harmonic euphony are accommodated within one tonal-harmonic system.

=== Observations ===

The seventh of 7edo is almost exactly the 29th harmonic ([[29/16]]), which can have a very agreeable sound with harmonic [[timbre]]s. 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.

 

 

The [[Octave stretch|stretched-octaves]] tuning [[Ed257/128#7ed257/128|7ed257/128]] greatly improves 7edo’s approximation of 3/1, 5/1 and 11/1, at the cost of slightly worsening 2/1 and 7/1, and greatly worsening 13/1. If one is hoping to use 7edo for [[11-limit]] harmonies, then 7ed257/128 is a good choice to make that easier.

The stretched 7edo tuning [[zpi|15zpi]] can also be used to improve 7edo’s approximation of JI in a similar way.

7edo is the 4th [[prime edo]], after [[5edo]] and before [[11edo]]. Multiples such as [[14edo]], [[21edo]], … up to [[35edo]], share the same tuning of the perfect fifth as 7edo, while improving on other intervals.

|  

|  

| [[11/10]] (+6.424)<br />[[32/29]] (-1.006)

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

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

| [[29/16]] (-1.006)<br />[[20/11]] (-6.424)

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

|+ <span style="font-size: 105%">Notation of 7edo</span>

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

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.