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==== [[Expanding tonal space|Part I:]] <span style="font-weight:normal">Expanding tonal space</span> ====
==== [[Expanding tonal space|Part I:]] <span style="font-weight:normal">Expanding tonal space</span> ====


'''Navigating tonal space'''
'''Navigating tonal space'''


This article describes how to ...


{| class="wikitable" style="text-align:center;"
== Number of distinct intervals ==
|- style="background-color:#efefef;"
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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: {| class="wikitable" style="text-align:center;"
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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.]]
''plane of tonal space''.


[[File:Heather Leigh-0981.jpg|thumb|260px|Heather Leigh-0981]]
[[File:Heather Leigh-0981.jpg|thumb|260px|Heather Leigh-0981]]
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