User:Holger Stoltenberg/sandbox: Difference between revisions

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==Polar projection of tonal space ==

In polar projection of the model, the horizontal ''mode'' lines form circles:

[[File:Fig-4 tonal space POLAR 149.png|~~458px~~|center]]

[[File:Fig-4 tonal space POLAR 149.png|496px|center]]

<center>Fig.4: A plane of tonal space in polar projection (up to Mode 16)</center>

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==General Applicability==

In ~~this~~ model a ''chord'' is composed of at least two stacked intervals with frequency ratios taken from the harmonic series in ascending order. The chord should be footed on the tonic of the particular mode. Skipped harmonics within a chord may remain mute. Fig.5 shows a comparison of four augmented chords that sound quite different:

In the model discussed so far a ''chord'' is composed of at least two stacked intervals with frequency ratios taken from the harmonic series in ascending order. The chord should be footed on the tonic of the particular mode. Skipped harmonics within a chord may remain mute. Fig.5 shows a comparison of four augmented chords that sound quite different:

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

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

@@ Line 94: / Line 94: @@
 ==Polar projection of tonal space ==
 In polar projection of the model, the horizontal ''mode'' lines form circles:
-[[File:Fig-4 tonal space POLAR 149.png|458px|center]]
+[[File:Fig-4 tonal space POLAR 149.png|496px|center]]
 <center><small><u>Fig.4</u>: A plane of tonal space in polar projection (up to Mode 16)</small></center>
@@ Line 100: / Line 100: @@
 ==General Applicability==
-In this model a ''chord'' is composed of at least two stacked intervals with frequency ratios taken from the harmonic series in ascending order. The chord should be footed on the tonic of the particular mode. Skipped harmonics within a chord may remain mute. Fig.5 shows a comparison of four augmented chords that sound quite different:
+In the model discussed so far a ''chord'' is composed of at least two stacked intervals with frequency ratios taken from the harmonic series in ascending order. The chord should be footed on the tonic of the particular mode. Skipped harmonics within a chord may remain mute. Fig.5 shows a comparison of four augmented chords that sound quite different:
 [[File:Fig-5 tonal space 753i aug.png|480px|center]]
 <center><small><u>Fig.5</u>: Selection of different augmented chords </small></center>