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]]. | |||
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. | |||
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. | ||
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> | |||
=== Observations === | === Observations === | ||
7edo | 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. | ||
7edo is the unique intersection of the temperaments of [[meantone]] (specifically [[3/4-comma meantone]]) and [[porcupine]]. | |||
== Intervals == | == Intervals == | ||