The first five octaves of Tonal Space contain a fairly large number of intervals footed on a common tonic of 0 ¢. The intervals are well structured in rows, with each row corresponding to a mode of the overtone scale. It may be of interest to the reader to learn how many ''different'' intervals are present, since some are obviously doubled. <br>
! Counting from <br />Mode 1 <br /> up to <br /> Mode 16
To find out, we will scan the Horizon Chart line by line (mode by mode), from the bottom up. Mode 1 has no intervals between the fundamental and the next octave. In Mode 2 we find a pure fifth, the third harmonic. This is the first time the pure fifth appears, and it will not be counted again as we scan.
! Number of <br />new intervals <br />found at <br />this mode
Table 1 summarizes the scanning results from Mode 1 through Mode 16.
! Accumulated <br />number <br />of different <br />rational intervals
! Total number<br />of intervals<br />scanned
! Mode<br />found in<br />octave<br />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: Count of different intervals depending on the highest implemented mode
: <u>Table 1</u>: Count of distinct intervals depending on the highest implemented mode
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[[File:Rob Ickes performing with Blue Highway California USA June 2010.jpg|thumb|180px|Rob Ickes performing with his band, Blue Highway, on June 21, 2010.]]
[[File:Rob Ickes performing with Blue Highway California USA June 2010.jpg|thumb|180px|Rob Ickes performing with his band, Blue Highway, on June 21, 2010.]]
The first five octaves of Tonal Space contain a fairly large number of intervals footed on a common tonic of 0 ¢. The intervals are well structured in rows, with each row corresponding to a mode of the overtone scale. It may be of interest to the reader to learn how many different intervals are present, since some are obviously doubled.
To find out, we will scan the Horizon Chart line by line (mode by mode), from the bottom up. Mode 1 has no intervals between the fundamental and the next octave. In Mode 2 we find a pure fifth, the third harmonic. This is the first time the pure fifth appears, and it will not be counted again as we scan.
Table 1 summarizes the scanning results from Mode 1 through Mode 16.
Table 1: Count of distinct intervals depending on 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.Heather Leigh-0981Dobro 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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