7edo: Difference between revisions
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'''7 equal divisions of the octave''' ('''7edo''') is the [[tuning system]] derived by dividing the [[octave]] into 7 equal steps of 171.4 [[cent]]s each, or the seventh root of 2. It is the fourth [[prime edo]], after [[2edo|2edo]], [[3edo|3edo]] and [[5edo|5edo]]. It is the third [[The Riemann Zeta Function and Tuning #Zeta edo lists|zeta integral edo]]. | |||
'''7 equal divisions of the octave''' (''' | |||
== Theory == | == Theory == | ||
{| | {{primes in equal|7}} | ||
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. Also Georgian music seems to be based on near-equal 7-step scales. 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). | 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. Also Georgian music seems to be based on near-equal 7-step scales. 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). | ||
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|12edo]] is known as "Hexe[6]". | |||
Typically, | Typically, 7edo 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 [[14edo|14edo]] or [[21edo|21edo]]. | ||
The seventh of | 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|harmonic entropy]] than [[Harmonic seventh|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. | 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. | ||
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([http://www.britannica.com/EBchecked/topic/719112/African-music "African music." Encyclopædia Britannica. 2009. Encyclopædia Britannica Online. 05 Jul. 2009.]) | ([http://www.britannica.com/EBchecked/topic/719112/African-music "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 | A Thai xylophone measured by Morton (1974) "varied only plus or minus 5 cents," from 7edo. A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system. | ||
== Intervals == | == Intervals == | ||
7edo can be notated on a five-line staff without accidentals. There is no distinction between major or minor; each pitch class is unique. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
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== Observations == | == Observations == | ||
Related in a lateral way to traditional Thai music. Subset of [[14edo| | Related in a lateral way to traditional Thai music. Subset of [[14edo|14edo]] and [[21edo|21edo]]. | ||
There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression. | There is a neutral feel between whole tone scale and major/minor diatonic scale. The second (171.429¢) works well as a basic step for melodic progression. | ||
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== Notation== | == Notation== | ||
[[William Lynch]] proposes using numbers 1 through 7 as the nominals of | [[William Lynch]] proposes using numbers 1 through 7 as the nominals of 7edo with sharp signs being possible to expand to 14edo or even 21edo. | ||
== Commas == | == Commas == | ||
7edo [[tempers out]] the following [[comma]]s. This assumes [[val]] {{val| 7 11 16 20 24 26 }}. | |||
{| class="commatable wikitable center-1 center-2 right-4 center-5" | {| class="commatable wikitable center-1 center-2 right-4 center-5" | ||
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== Temperaments == | == Temperaments == | ||
7edo is the first edo in which regular temperament theory starts to make sense as a way of subdividing the steps into [[mos]] scales, 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 MOS's 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-1Lns pentatonic mos. This is in part because 7edo is a [[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. | |||
== Music == | == Music == | ||
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== Ear Training == | == Ear Training == | ||
7edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here]. | |||
[[Category:7edo| ]] <!-- main article --> | [[Category:7edo| ]] <!-- main article --> | ||
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[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Macrotonal]] | [[Category:Macrotonal]] | ||
[[Category:Prime | [[Category:Prime edo]] | ||
[[Category:Zeta]] | [[Category:Zeta]] | ||