User:Holger Stoltenberg/sandbox: Difference between revisions

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[[File:Fig-5 tonal space 753i aug.png|480px|center]]

<center><small><u>Fig.5</u>: Selection of different augmented chords </small></center>

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 the design and comparison of 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.

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 [[File:Fig-5 tonal space 753i aug.png|480px|center]]
 <center><small><u>Fig.5</u>: Selection of different augmented chords </small></center>
-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 the design and comparison of 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.