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| '''Navigating tonal space''' | | '''Navigating tonal space''' |
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| == Number of distinct intervals ==
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| 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 know how many ''different'' intervals are present, since some obviously occur more than once. <br>
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| 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 - like any other interval - it is only considered once as we scan.
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| Table 1 summarizes the scanning results from Mode 1 through Mode 16.
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| : <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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| |- style="background-color:#6b82c6; color:#484848;"
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| ! <span style="font-weight:normal"> Mode 1 <br /> up to <br /> Mode 16 </span> <br /> Mode
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| ! <span style="font-weight:normal"> Number of <br />new intervals <br />found at <br />this mode </span>
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| ! Aggregated <br />number <br />of different <br />rational intervals
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| ! <span style="font-weight:normal"> Total number<br />of intervals<br />scanned </span>
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| ! <span style="font-weight:normal"> Mode<br />found in<br />octave<br />number </span>
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| |-
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| | style="background-color:#e2e2e2; color:#484848;" | '''16'''
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| | 8
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| | style="background-color:#e2e2e2;" | 79
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| | 120
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| | 5
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| |-
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| | style="background-color:#e2e2e2;" | '''15'''
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| | 8
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| | style="background-color:#e2e2e2;" | 71
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| | 105
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''14'''
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| | 6
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| | style="background-color:#e2e2e2;" | 63
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| | 91
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''13'''
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| | 12
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| | style="background-color:#e2e2e2;" | 57
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| | 78
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''12'''
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| | 4
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| | style="background-color:#e2e2e2;" | 45
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| | 66
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''11'''
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| | 10
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| | style="background-color:#e2e2e2;" | 41
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| | 55
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''10'''
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| | 4
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| | style="background-color:#e2e2e2;" | 31
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| | 45
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''9'''
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| | 6
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| | style="background-color:#e2e2e2;" | 27
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| | 36
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''8'''
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| | 4
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| | style="background-color:#e2e2e2;" | 21
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| | 28
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| | 4
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| |-
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| | style="background-color:#e2e2e2;" | '''7'''
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| | 6
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| | style="background-color:#e2e2e2;" | 17
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| | 21
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| | 3
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| |-
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| | style="background-color:#e2e2e2;" | '''6'''
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| | 2
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| | style="background-color:#e2e2e2;" | 11
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| | 15
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| | 3
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| |-
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| | style="background-color:#e2e2e2;" | '''5'''
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| | 4 <small>''(...)''</small>
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| | style="background-color:#e2e2e2;" | 9
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| | 10
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| | 3
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| |-
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| | style="background-color:#e2e2e2;" | '''4'''
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| | 2 <small>''(3rd, b7th)''</small>
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| | style="background-color:#e2e2e2;" | 5
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| | 6
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| | 3
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| |-
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| | style="background-color:#e2e2e2;" | '''3'''
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| | 2 <small>''(4th, 6th)''</small>
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| | style="background-color:#e2e2e2;" | 3
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| | 3
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| | 2
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| |-
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| | style="background-color:#e2e2e2;" | '''2'''
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| | 1 <small>''(5th)''</small>
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| | style="background-color:#e2e2e2;" | 1
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| | 1
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| | 2
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| |-
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| | style="background-color:#e2e2e2;" | '''1'''
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| | 0
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| | style="background-color:#e2e2e2;" | 0
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| | 0
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| | 1
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| |}
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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.]] |