7edo: Difference between revisions

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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 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]].
=== Prime harmonics ===
{{Harmonics in equal|7}}
 
=== As an equalized diatonic scale ===
7edo unifies the seven [[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]].


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.
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.


7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].
The step from seventh to octave is too large as a leading tone. Possibly lending itself to a “sevenplus” scale similar to [[elevenplus]].


=== In non-Western traditions ===
=== In non-Western traditions ===
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A [[Ugandan]], [[Chopi]] xylophone measured by Haddon (1952) was also tuned something close to this.
A [[Ugandan]], [[Chopi]] xylophone measured by Haddon (1952) was also tuned something close to this.


=== Prime harmonics ===
It has often been stated that 7edo approximates tunings used in Thai classical music, though 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>
{{Harmonics in equal|7}}


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


Subset of [[14edo]] and [[21edo]].
7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]].
 
There is a [[interval quality|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, though 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 ==
== Intervals ==