User:Holger Stoltenberg/sandbox: Difference between revisions

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! <span style="font-weight:normal"> Mode<br />found in<br />octave<br />number </span>
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Revision as of 11:43, 22 February 2025

Expanding tonal space

Expanding tonal space/planar extensions


< User:Holger Stoltenberg

Expanding tonal space/projections


Part I: Expanding tonal space

Don't forget about the function

Part I: Expanding tonal space

Navigating tonal space

This article describes how to ...

Counting from
Mode 1
up to
Mode 16 		Number of
new intervals
found at
this mode 		Accumulated
number
of different
rational intervals 		Total number
of intervals
scanned 		Mode
found in
octave
number
16 8 79 120 5
15 8 71 105 4
14 6 63 91 4
13 12 57 78 4
12 4 45 66 4
11 10 41 55 4
10 4 31 45 4
9 6 27 36 4
8 4 21 28 4
7 6 17 21 3
6 2 11 15 3
5 4 9 10 3
4 2 (3rd, b7th) 5 6 3
3 2 (4th, 6th) 3 3 2
2 1 (5th) 1 1 2
1 0 0 0 1


Mode 1
up to
Mode 16
Mode 		Number of
new intervals
found at
this mode 		Accumulated
number
of different
rational intervals 		Total number
of intervals
scanned 		Mode
found in
octave
number
16 8 79 120 5
15 8 71 105 4
14 6 63 91 4
13 12 57 78 4
12 4 45 66 4
11 10 41 55 4
10 4 31 45 4
9 6 27 36 4
8 4 21 28 4
7 6 17 21 3
6 2 11 15 3
5 4 9 10 3
4 2 5 6 3
3 2 3 3 2
2 1 1 1 2
1 0 0 0 1
Rob Ickes performing with his band, Blue Highway, on June 21, 2010.

plane of tonal space.

Heather Leigh-0981
Dobro guitar - Bluegrass Band, Kentucky (2011-10-16 by Navin75)

See also…

Sethares, William A. Tuning Timbre Spectrum Scale. London: Springer Verlag , 1999. [p65, 3.7. Overtone Scales]

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