Expanding tonal space: Difference between revisions

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==General applicability==

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:

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]]~~

Listen to the following audio examples...

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

[[File:Fig-5 tonal space 753i aug.png|thumb|420px|right|Fig.5: Selection of different augmented chords]]

:{| class="wikitable"

!Chord

!Play

|-

|mode16 aug (16:20:25) 2 stacked pure 3rds||[[File:TS_aug_L16_p25_C_P-I_Fig-5.mp3|80px]]

|-

|mode14 aug (14:18:22) sounds equal to (7:9:11)||[[File:TS_aug_L14_C_P-I_Fig-5.mp3|80px]]

|-

|mode11 aug (11:14:17) no, this is not major...||[[File:TS_aug_L11-14-17_C_P-I_Fig-5.mp3|80px]]

|-

|mode10 aug (10:13:16) extra wide 3rd||[[File:TS_aug_L10_C_P-I_Fig-5.mp3|80px]]

|-

| mode8 maj (8:10:12) '''pure major''' for reference ||[[File:TS_maj_lin_8_C_P-I_Fig-5.mp3|80px]]

|}

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.

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====[[Expanding tonal space/planar extensions|Part II: Planar extensions]]====

====[[Expanding tonal space/projections|Part III: Projections]]====

====[[Expanding tonal space/third dimension|Part IV: Third dimension]]====

==See also…==

@@ Line 225: / Line 225: @@
 ==General applicability==
-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:
+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. <br>
-[[File:Fig-5 tonal space 753i aug.png|480px|center]]
+Listen to the following audio examples...
-<center><small><u>Fig.5</u>: Selection of different augmented chords </small></center>
+[[File:Fig-5 tonal space 753i aug.png|thumb|420px|right|<u>Fig.5</u>: Selection of different augmented chords]]
+:{| class="wikitable"
+!Chord
+!Play
+|-
+|mode16 aug (16:20:25)<br>2 stacked pure 3rds||[[File:TS_aug_L16_p25_C_P-I_Fig-5.mp3|80px]]
+|-
+|mode14 aug (14:18:22)<br>sounds equal to (7:9:11)||[[File:TS_aug_L14_C_P-I_Fig-5.mp3|80px]]
+|-
+|mode11 aug (11:14:17)<br>no, this is not major...||[[File:TS_aug_L11-14-17_C_P-I_Fig-5.mp3|80px]]
+|-
+|mode10 aug (10:13:16)<br>extra wide 3rd||[[File:TS_aug_L10_C_P-I_Fig-5.mp3|80px]]
+|-
+|<br>mode8 maj (8:10:12)<br>'''pure major''' for reference<br><br>||[[File:TS_maj_lin_8_C_P-I_Fig-5.mp3|80px]]
+|}
 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.
@@ Line 237: / Line 250: @@
 ====[[Expanding tonal space/planar extensions|Part II: <span style="font-weight:normal">Planar extensions</span>]]====
 ====[[Expanding tonal space/projections|Part III: <span style="font-weight:normal">Projections</span>]]====
+====[[Expanding tonal space/third dimension|Part IV: <span style="font-weight:normal">Third dimension</span>]]====
 ==See also…==