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Editor's note: We are thankful to our microtonalist friend Yahya Abdal-Aziz, an expert on Maqam music, for his kind consent for the use of the tables prepared by him. These two tables are a very simple and practical summary of some basic harmonic facts -- a refreshing re-visit to the immensely important topic of the Harmonic Series. The tables have been extracted from one of his messages to the Tuning Group.
Some basic harmonic facts -- a summary by Yahya Abdal-Aziz
.....Overtone......................Cents
Note..Integer....Cents.Semitone...adjust
C.1.........1.....0.00........0........0
C.2.........2..1200.00........0........0
G.2.........3..1901.96........7........2
C.3.........4..2400.00........0........0
E.3.........5..2786.31........4......-14
G.3.........6..3101.96........7........2
Bb.3-.......7..3368.83.......10......-31
C.4.........8..3600.00........0........0
D.4.........9..3803.91........2........4
E.4........10..3986.31........4......-14
F#.4-......11..4151.32........6......-49
G.4........12..4301.96........7........2
Ab.4+......13..4440.53........8.......41
Bb.4-......14..4568.83.......10......-31
B.4........15..4688.27.......11......-12
C.5........16..4800.00........0........0
Db.5.......17..4904.96........1........5
D.5........18..5003.91........2........4
Eb.5.......19..5097.51........3.......-2
E.5........20..5186.31........4......-14
F.5-.......21..5270.78........5......-29
F#.5-......22..5351.32........6......-49
Gb.5+......23..5428.27........6.......28
G.5........24..5501.96........7........2
G#.5-......25..5572.63........8......-27
Ab.5+......26..5640.53........8.......41
A.5........27..5705.87........9........6
Harmonic...Note...Semitone..Count
....1.......C........0........1
....3.......G........7........2
....5.......E........4........3
....7.......Bb-.....10........4
....9.......D........2........5
...11.......F#-......6........6
...13.......Ab+......8........7
...15.......B.......11........8
...17.......Db.......1........9
...19.......Eb.......3.......10
...21.......F........5.......11
...23.......Gb+......6.......12
...25.......G#-......8.......13
...27.......A........9.......14
+ or - indicates a change of between an eighth-tone (25c) and a quarter-tone (50c) sharper or flatter than the nominal.
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