User:Holger Stoltenberg/sandbox: Difference between revisions
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The model of tonal space is well suited for comparing chords. No matter what intervals you '''mark on any horizontal line''', the result will always be a chord made up of rational intervals that share a common denominator. Such a chord is therefore a subset of the harmonic series. | The model of tonal space is well suited for comparing chords. No matter what intervals you '''mark on any horizontal line''', the result will always be a chord made up of rational intervals that share a common denominator. Such a chord is therefore a subset of the harmonic series. | ||
A final example: If you want to create a major ''b''7 chord, you will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. If you want to replace the upper 7/4 interval with, say, a 9/5 interval, find the ''Least Common Denominator'' (''LCM'', which is 4*5=20 in this case), and you get a 20:25:30:36 chord, which lives in Mode 20 (not shown) and sounds noticeably more dissonant. | A final example: If you want to create a major ''b''7 chord, you will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. If you want to replace the upper 7/4 interval with, say, a 9/5 interval, find the ''Least Common Denominator'' (''LCM'', which is 4*5=20 in this case), and you get a 20:25:30:36 chord, which lives in Mode 20 (not shown) and sounds noticeably more dissonant. | ||
== See also… == | |||
Sethares, William A. ''Tuning Timbre Spectrum Scale.'' London: Springer Verlag , 1999. | |||
[p65, ''3.7. Overtone Scales''] | |||