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| == Where the first primes intervals lie == | | == Where the lowest harmonics lie == |
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| === As a diagram ===
| | The diagram below (or at right, or somewhere) is of a hypothetical 12-string guitar in this tuning. It shows where each of the odd harmonics through the 29th lies. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc. |
| | [[File:58-edo 15x2.png|thumb|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]] |
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| In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
| | Since 58-edo is consistent in the 17-limit + 29 group, the location of any interval in that group can be determined from the corresponding harmonics. (For instance, to rise by 7:5, go up two strings and down one fret, because that takes you from harmonic 5 to harmonic 7.) |
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| headstock on this side
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| - - - - 13 - - - - 1 - -
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| 13 - - - - 1 - - - - - -
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| - 1 - - - - - - 7 - 5 3
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| - - - - 7 - 5 3 - - - -
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| 7 - 5 3 - - - - - - - -
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| - - - - - - - - - 9 - -
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| - - - - - 9 - - - - 11 -
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| bass - 9 - - - - 11 - - - - - treble
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| strings - - 11 - - - - - - - - - strings
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| - - - - - - - - - - - -
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| - - - - - - - - - - - -
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| - - - - - - - - - - - -
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| - - - - - - - - - - - -
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| - - - - - - - - - - 13 -
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| - - - - - - 13 - - - - 1
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| bridge on this side
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| === As a table ===
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| {| class="wikitable"
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| ! note
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| ! fretboard position
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| |-
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| | 0 steps = 1 % 1
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| | string 0 fret 0
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| |-
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| | 58 steps = 2 % 1
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| | string 4 fret - 1
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| |-
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| | 34 steps = 3 % 2
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| | string 2 fret 2
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| |-
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| | 19 steps = 5 % 4
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| | string 1 fret 2
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| |-
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| | 47 steps = 7 % 4
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| | string 3 fret 1
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| |-
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| | 27 steps = 11 % 8
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| | string 1 fret 6
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| |-
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| | 41 steps = 13 % 8
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| | string 3 fret - 2
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| |-
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| | 5 steps = 17 % 16
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| | string - 1 fret 10
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| |-
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| | 14 steps = 19 % 16
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| | string 0 fret 7
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| |-
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| | 30 steps = 23 % 16
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| | string 2 fret 0
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| |-
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| | 50 steps = 29 % 16
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| | string 2 fret 10
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| |-
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| | 55 steps = 31 % 16
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| | string 3 fret 5
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| |}
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| From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.
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| == Adaptation to Mystery Temperament == | | == Adaptation to Mystery Temperament == |