User:Holger Stoltenberg/sandbox

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

Table 1: Number of different intervals as a function of the highest implemented mode

Mode 1 up to Mode 16 Mode	Number of new intervals found at this mode	Aggregated 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

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]