7edo: Difference between revisions

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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~~. 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.

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

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The usual [[Musical notation|notation system]] for 7edo is the [[chain-of-fifths notation]], which is directly derived from the standard notation used in [[12edo]].

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. There is no distinction between major or minor, so every interval has the [[interval quality]] "perfect" instead.

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.

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@@ Line 18: / Line 18: @@
 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. 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.
 A Ugandan Chopi xylophone measured by Haddon (1952) was also tuned to this system.
@@ Line 128: / Line 128: @@
 The usual [[Musical notation|notation system]] for 7edo is the [[chain-of-fifths notation]], which is directly derived from the standard notation used in [[12edo]].
-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. There is no distinction between major or minor, so every interval has the [[interval quality]] "perfect" instead.
+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.
 {| class="wikitable center-all"