User:Holger Stoltenberg/sandbox: Difference between revisions

Line 7:

With a prototypical instrument in place, the search for ''intermediary chords'' in tonal music begins. We can try to identify (and play) supplementary consonant chords that fit seamlessly into the gaps of familiar chord progressions.

The proposed model of tonal space utilizes the uniform structure and simple mathematical description of ''overtone scales'' as well as the closely related ''arithmetic frequency division of the octave'' (AFDO).

The proposed model of tonal space utilizes the uniform structure and simple mathematical description of ''overtone scales'' as well as the closely related ''arithmetic frequency division of the octave'' ([[AFDO]]).

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.

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|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==

@@ Line 7: / Line 7: @@
 With a prototypical instrument in place, the search for ''intermediary chords'' in tonal music begins. We can try to identify (and play) supplementary consonant chords that fit seamlessly into the gaps of familiar chord progressions.
-The proposed model of tonal space utilizes the uniform structure and simple mathematical description of ''overtone scales'' as well as the closely related ''arithmetic frequency division of the octave'' (AFDO).
+The proposed model of tonal space utilizes the uniform structure and simple mathematical description of ''overtone scales'' as well as the closely related ''arithmetic frequency division of the octave'' ([[AFDO]]).
 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.
+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|500px|center]]
-: <small>Fig. 1: One octave (from first harmonic h1 to second harmonic h2)</small>
+: <small><u>Fig.1</u>: One octave (from first harmonic h1 to second harmonic h2)</small>
 ==The mode axis==