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This page presents a topic of primarily mathematical interest.
While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.
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1 equal division of the 4th harmonic (abbreviated 1ed4) is a nonoctave tuning system that uses equal steps of 4/1, or exactly 2400 ¢.
| Prime factorization
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n/a
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| Step size
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2400 ¢
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| Octave
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1\1ed4 (2400 ¢)
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| Twelfth
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1\1ed4 (2400 ¢)
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| Consistency limit
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1
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| Distinct consistency limit
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1
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Theory
Harmonics
Approximation of harmonics in 1ed4
| Harmonic
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2
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3
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4
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5
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6
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7
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8
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9
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10
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11
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12
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| Error
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Absolute (¢)
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+1200
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+498
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+0
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-386
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-702
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-969
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+1200
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+996
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+814
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+649
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+498
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| Relative (%)
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+50.0
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+20.8
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+0.0
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-16.1
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-29.2
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-40.4
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+50.0
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+41.5
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+33.9
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+27.0
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+20.8
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| Step
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1
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1
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1
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1
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1
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1
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2
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2
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2
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2
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2
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Approximation of harmonics in 1ed4
| Harmonic
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13
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14
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15
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16
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17
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18
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19
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20
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21
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22
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23
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24
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| Error
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Absolute (¢)
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+359
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+231
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+112
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+0
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-105
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-204
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-298
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-386
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-471
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-551
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-628
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-702
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| Relative (%)
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+15.0
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+9.6
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+4.7
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+0.0
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-4.4
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-8.5
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-12.4
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-16.1
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-19.6
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-23.0
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-26.2
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-29.2
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| Step
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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2
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Intervals
- 2400 cents
- 4800 cents
- 7200 cents
- etc…
