Interval size measure: Difference between revisions
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=== Gross === | === Gross === | ||
The [[octave]] and the [[decade]] are common coarse units for interval sizes. The [[Wikipedia: Decibel|decibel]], being a relative logarithmic-scale unit for power or root-power quantities, is inappropriate for measuring intervals; the decade is used instead. Similarly, the [[Wikipedia:Neper|neper]] (Np) and the dineper (dNp), like the decibel, are rarely used. However, dinepers have an application in [[logarithmic approximants]]. | |||
Intervals are sometimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music. An early unit for measuring intervals is the "[[tone]]" which dates back to classic Greece. | Intervals are sometimes expressed in the number of scale steps between them. These steps can be of different size, compare for example the names of the major scale in the classic music. An early unit for measuring intervals is the "[[tone]]" which dates back to classic Greece. | ||
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==== Non-octave fine measures ==== | ==== Non-octave fine measures ==== | ||
There are other fine measurements based upon the logarithmic division of other intervals (e.g. 3/1 (twelfth)), a few of which are listed below: | There are other fine measurements based upon the logarithmic division of other intervals (e.g. 3/1 (twelfth)), a few of which are listed below: | ||
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| 1/100 of 13edt (Bohlen-Pierce) scale step | | 1/100 of 13edt (Bohlen-Pierce) scale step | ||
|- | |- | ||
|Euhekt | | Euhekt | ||
|3/1 (twelfth) | | 3/1 (twelfth) | ||
|1900 | | 1900 | ||
|1/100 of 19edt (OnlyPure) scale step | | 1/100 of 19edt (OnlyPure) scale step | ||
|- | |- | ||
| Grad | | Grad | ||
|[[Pythagorean comma|531441/524288]] (Pythagorean comma) | | [[Pythagorean comma|531441/524288]] (Pythagorean comma) | ||
| 12 | | 12 | ||
|[[12edo]] flattens [[3/2]] by this amount | | [[12edo]] flattens [[3/2]] by this amount | ||
|- | |- | ||
| Tuning unit | | Tuning unit | ||
|[[531441/524288]] (Pythagorean comma) | | [[531441/524288]] (Pythagorean comma) | ||
| 720 | | 720 | ||
| | | | ||
|} | |} | ||