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Skip fretting system 58 2 15: Difference between revisions

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Jeff Brown (talk | contribs)
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Replace some text with a picture that makes it clearer, and adjust the remaining text a little.
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== Where the first primes intervals lie ==
== Where the lowest harmonics lie ==
 
=== As a diagram ===


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.
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.
[[File:58-edo 15x2.png|thumb|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]]


                  headstock on this side
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.)
            -  -  -  - 13  -  -  -  -  1  -  -
            13  -  -  -  -  1  -  -  -  -  -  -
            -  1  -  -  -  -  -  -  7  -  5  3
            -  -  -  -  7  -  5  3  -  -  -  -
            7  -  5  3  -  -  -  -  -  -  -  -
            -  -  -  -  -  -  -  -  -  9  -  -
            -  -  -  -  -  9  -  -  -  - 11  -
    bass    -  9  -  -  -  - 11  -  -  -  -  -  treble
    strings  -  - 11  -  -  -  -  -  -  -  -  -  strings
            -  -  -  -  -  -  -  -  -  -  -  -
            -  -  -  -  -  -  -  -  -  -  -  -
            -  -  -  -  -  -  -  -  -  -  -  -
            -  -  -  -  -  -  -  -  -  -  -  -
            -  -  -  -  -  -  -  -  -  - 13  -
            -  -  -  -  -  - 13  -  -  -  -  1
                    bridge on this side
 
=== As a table ===
 
{| class="wikitable"
! note
! fretboard position
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 58 steps = 2 % 1
| string 4 fret - 1
|-
| 34 steps = 3 % 2
| string 2 fret 2
|-
| 19 steps = 5 % 4
| string 1 fret 2
|-
| 47 steps = 7 % 4
| string 3 fret 1
|-
| 27 steps = 11 % 8
| string 1 fret 6
|-
| 41 steps = 13 % 8
| string 3 fret - 2
|-
| 5 steps = 17 % 16
| string - 1 fret 10
|-
| 14 steps = 19 % 16
| string 0 fret 7
|-
| 30 steps = 23 % 16
| string 2 fret 0
|-
| 50 steps = 29 % 16
| string 2 fret 10
|-
| 55 steps = 31 % 16
| string 3 fret 5
|}
 
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.


== Adaptation to Mystery Temperament ==
== Adaptation to Mystery Temperament ==
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