Expanding tonal space: Difference between revisions

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The model of tonal space is well suited for the design and comparison of chords. No matter what intervals we '''mark on any horizontal line''', the result will always be a chord made up of just intervals that share a common denominator. Therefore, any such chord is a local subset of the harmonic series at its proper position.

A final example: If we want to create a major ''b''7 chord, we will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. ~~If we 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 we~~ get a 20:25:30:36 chord, which lives in Mode 20 (not shown) ~~and~~ sounds noticeably more dissonant.

A final example: If we want to create a major ''b''7 chord, we will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. To replace the upper 7/4 interval with, say, a 9/5 interval, we determine the ''Least Common Denominator'' (''LCM'', which is 4*5=20 in this case) to get a 20:25:30:36 chord, which lives in Mode 20 (not shown) and sounds noticeably more dissonant.

== Find out more about tonal space… ==

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 The model of tonal space is well suited for the design and comparison of chords. No matter what intervals we '''mark on any horizontal line''', the result will always be a chord made up of just intervals that share a common denominator. Therefore, any such chord is a local subset of the harmonic series at its proper position.
-A final example: If we want to create a major ''b''7 chord, we will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. If we 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 we get a 20:25:30:36 chord, which lives in Mode 20 (not shown)  and sounds noticeably more dissonant.
+A final example: If we want to create a major ''b''7 chord, we will find four suitable pitches in the horizontal Mode 4-line (Fig.3) from m=0 to m=3. To replace the upper 7/4 interval with, say, a 9/5 interval, we determine the ''Least Common Denominator'' (''LCM'', which is 4*5=20 in this case) to get a 20:25:30:36 chord, which lives in Mode 20 (not shown) and sounds noticeably more dissonant.
 == Find out more about tonal space… ==