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=[[Expanding tonal space]]=
'''** THIS IS A WORK IN PROGRESS **'''<br>
<b>Exploring tonal space</b>
 
This article focuses on the steps required to apply the ''"Tonal Space"'' interval system to a novel musical keyboard instrument.
 
''Tonal Space'' is a concept of musical intonation control that incorporates all modes of the overtone scale while allowing free modulation through twelve chromatic keys. The four-part ''"[[Expanding tonal space|Expanding Tonal Space]]"'' series (Parts I through IV) explains the development of Tonal Space in detail.




'''** This page is being used for testing purposes only. **'''
=[[Expanding tonal space]]=
=[[Expanding tonal space/planar extensions]]=
=[[Expanding tonal space/planar extensions]]=
=[[Expanding tonal space/projections]]=
=[[Expanding tonal space/third dimension]]=
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{{breadcrumb}}
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=[[Expanding tonal space/projections]]=
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==== [[Expanding tonal space|Part I:]] <span style="font-size: 120%;">Expanding tonal space</span> ====
==== [[Expanding tonal space|Part I:]] <span style="font-size: 120%;">Expanding tonal space</span> ====
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'''Navigating tonal space'''
'''Navigating tonal space'''


[[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.]]


== Number of distinct intervals ==
[[File:Heather Leigh-0981.jpg|thumb|260px|Heather Leigh-0981]]
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>
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.


: <u>Table 1</u>: Count of distinct intervals depending on the highest implemented mode
[[File:Dobro guitar - Bluegrass Band, Kentucky (2011-10-16 by Navin75).jpg|thumb|260px|Dobro guitar - Bluegrass Band, Kentucky (2011-10-16 by Navin75)]]


: {| class="wikitable" style="text-align:center;"
== Modern pedal steel (Header before audio controls, audio only) ==
|- style="background-color:#6b82c6; color:#484848;"
[[File:Pedal steel played with reverb.ogg||270px]] A song played on an E9 pedal steel guitar.
! <span style="font-weight:normal"> Mode 1 <br /> up to <br /> Mode 16 </span> <br /> Mode
! <span style="font-weight:normal"> Number of <br />new intervals <br />found at <br />this mode </span>
! Aggregated <br />number <br />of different  <br />rational intervals
! <span style="font-weight:normal"> Total number<br />of intervals<br />scanned </span>
! <span style="font-weight:normal"> Mode<br />found in<br />octave<br />number </span>
|-
| style="background-color:#e2e2e2; color:#484848;" | '''16'''
| 8
| style="background-color:#e2e2e2;" | 79
| 120
| 5
|-
| style="background-color:#e2e2e2;" | '''15'''
| 8
| style="background-color:#e2e2e2;" | 71
| 105
| 4
|-
| style="background-color:#e2e2e2;" | '''14'''
| 6
| style="background-color:#e2e2e2;" | 63
| 91
| 4
|-
| style="background-color:#e2e2e2;" | '''13'''
| 12
| style="background-color:#e2e2e2;" | 57
| 78
| 4
|-
| style="background-color:#e2e2e2;" | '''12'''
| 4
| style="background-color:#e2e2e2;" | 45
| 66
| 4
|-
| style="background-color:#e2e2e2;" | '''11'''
| 10
| style="background-color:#e2e2e2;" | 41
| 55
| 4
|-
| style="background-color:#e2e2e2;" | '''10'''
| 4
| style="background-color:#e2e2e2;" | 31
| 45
| 4
|-
| style="background-color:#e2e2e2;" | '''9'''
| 6
| style="background-color:#e2e2e2;" | 27
| 36
| 4
|-
| style="background-color:#e2e2e2;" | '''8'''
| 4
| style="background-color:#e2e2e2;" | 21
| 28
| 4
|-
| style="background-color:#e2e2e2;" | '''7'''
| 6
| style="background-color:#e2e2e2;" | 17
| 21
| 3
|-
| style="background-color:#e2e2e2;" | '''6'''
| 2
| style="background-color:#e2e2e2;" | 11
| 15
| 3
|-
| style="background-color:#e2e2e2;" | '''5'''
| 4 <small>''(...)''</small>
| style="background-color:#e2e2e2;" | 9
| 10
| 3
|-
| style="background-color:#e2e2e2;" | '''4'''
| 2  <small>''(3rd, b7th)''</small>
| style="background-color:#e2e2e2;" | 5
| 6
| 3
|-
| style="background-color:#e2e2e2;" | '''3'''
| 2  <small>''(4th, 6th)''</small>
| style="background-color:#e2e2e2;" | 3
| 3
| 2
|-
| style="background-color:#e2e2e2;" | '''2'''
| 1 <small>''(5th)''</small>
| style="background-color:#e2e2e2;" | 1
| 1
| 2
|-
| style="background-color:#e2e2e2;" | '''1'''
| 0
| style="background-color:#e2e2e2;" | 0
| 0
| 1
|}


[[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.]]
== Steel bar (Header before image of steel bar) ==
[[File:Steel bar (tonebar) used in playing steel guitar.jpg|thumb|180px|<u>Fig.2</u>: <ref>Eagledj, [https://creativecommons.org/licenses/by-sa/4.0 CC BY-SA 4.0 ], via [https://commons.wikimedia.org/wiki/File:Steel_bar_(tonebar)_used_in_playing_steel_guitar.jpg Wikimedia Commons]</ref> Steel bar (tonebar) used to play certain types of steel guitars.]]<br>


[[File:Heather Leigh-0981.jpg|thumb|260px|Heather Leigh-0981]]
== Text reference (attribution) ==
Eagledj, [https://creativecommons.org/licenses/by-sa/4.0 CC BY-SA 4.0], via [https://commons.wikimedia.org/wiki/File:Steel_bar_(tonebar)_used_in_playing_steel_guitar.jpg Wikimedia Commons]


[[File:Dobro guitar - Bluegrass Band, Kentucky (2011-10-16 by Navin75).jpg|thumb|260px|Dobro guitar - Bluegrass Band, Kentucky (2011-10-16 by Navin75)]]
== Infotext ==
'''** THIS IS A WORK IN PROGRESS **'''<br>
<b>Expanding tonal space/third dimension</b>


==See also…==
== See also… ==
Sethares, William A. ''Tuning Timbre Spectrum Scale.'' London: Springer Verlag , 1999.  
Sethares, William A. ''Tuning Timbre Spectrum Scale.'' London: Springer Verlag , 1999.  
[p65, ''3.7. Overtone Scales'']
[p65, ''3.7. Overtone Scales'']<br><br>
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