User:Holger Stoltenberg/sandbox: Difference between revisions

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For each note rendered, the model should effectively determine the current deviation from 12-tone equal temperament (12edo) in order to control the intonation of a commercial sound module or software plug-in on the fly.

==How to expand tonal space – the interval axis==

Like ''frequency'', ''musical pitch'' is one-dimensional. Fig. 1 illustrates the horizontal axis of tonal space, which we call the ''interval axis''. It points in keyboard direction from low keys to high keys. The first harmonic ''(h1)'' is known as the common ''fundamental'' of all upcoming overtone scales.~~ [Fig. 1]~~

Like ''frequency'', ''musical pitch'' is one-dimensional. Fig. 1 illustrates the horizontal axis of tonal space, which we call the ''interval axis''. It points in keyboard direction from low keys to high keys. The first harmonic ''(h1)'' is known as the common ''fundamental'' of all upcoming overtone scales.

[[:File:Fig-1 tonal space 0845c r-axis.gif|~~Fig-1 tonal space 0845c r-axis.gif~~]]

[[File:Fig-1 tonal space 0845c r-axis.gif|500px|center]]

: Fig. 1: One octave (from first harmonic h1 to second harmonic h2)

Fig. 1: One octave (from first harmonic h1 to second harmonic h2)

==The mode axis==

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[Fig. 2]

: Fig. 2: Overtone scales from Mode 1 (''h1'') to Mode 4 ''(h4)'' on a 2D-plane of tonal space

Fig. 2: Overtone scales from Mode 1 (''h1'') to Mode 4 ''(h4)'' on a 2D-plane of tonal space

The result of visualizing more modes of the overtone scale (up to Mode 16) is shown in Fig. 3:

@@ Line 11: / Line 11: @@
 For each note rendered, the model should effectively determine the current deviation from 12-tone equal temperament (12edo) in order to control the intonation of a commercial sound module or software plug-in on the fly.
 ==How to expand tonal space – the interval axis==
-Like ''frequency'', ''musical pitch'' is one-dimensional. Fig. 1 illustrates the horizontal axis of tonal space, which we call the ''interval axis''. It points in keyboard direction from low keys to high keys. The first harmonic ''(h1)'' is known as the common ''fundamental'' of all upcoming overtone scales.<br>[Fig. 1]
+Like ''frequency'', ''musical pitch'' is one-dimensional. Fig. 1 illustrates the horizontal axis of tonal space, which we call the ''interval axis''. It points in keyboard direction from low keys to high keys. The first harmonic ''(h1)'' is known as the common ''fundamental'' of all upcoming overtone scales.
-[[:File:Fig-1 tonal space 0845c r-axis.gif|Fig-1 tonal space 0845c r-axis.gif]]
+[[File:Fig-1 tonal space 0845c r-axis.gif|500px|center]]
+: <small>Fig. 1: One octave (from first harmonic h1 to second harmonic h2)</small>
-<small>Fig. 1: One octave (from first harmonic h1 to second harmonic h2)</small>
 ==The mode axis==
@@ Line 23: / Line 22: @@
 [Fig. 2]
+: <small>Fig. 2: Overtone scales from Mode 1 (''h1'') to Mode 4 ''(h4)'' on a 2D-plane of tonal space</small>
-<small>Fig. 2: Overtone scales from Mode 1 (''h1'') to Mode 4 ''(h4)'' on a 2D-plane of tonal space</small>
 The result of visualizing more modes of the overtone scale (up to Mode 16) is shown in Fig. 3: