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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
10edf is related to [[17edo]], but with the [[3/2|perfect fifth]] rather than the [[2/1|octave]] being just. The octave is compressed by about 6.68{{c}}, a small but significant deviation. 10edf is [[consistent]] to the [[integer limit|7-integer-limit]], but not to the 8-integer-limit. In comparison, 17edo is only consistent up to the 4-integer-limit. This makes 10edf a suitable tuning perhaps in the [[5-limit]], but overcompressed in any other limits, as well as the no-5 13-limit, where 17edo is best at. | |||
=== Harmonics === | |||
{{Harmonics in equal|10|3|2|intervals=integer|columns=11}} | |||
{{Harmonics in equal|10|3|2|intervals=integer|columns=12|start=12|collapsed=true|Approximation of harmonics in 10edf (continued)}} | |||
[ | === Subsets and supersets === | ||
Since 10 factors into primes as {{nowrap| 2 × 5 }}, 10edf contains [[2edf]] and [[5edf]] as subset edfs. | |||
== Intervals == | |||
{| class="wikitable center-all right-2" | |||
|- | |||
! # | |||
! Cents | |||
! [[1L 3s (fifth-equivalent)|Neptunian]] notation<br>using 8\10edf | |||
! [[Ed9/4|Neapolitan]] notation<br>using 3/10edf | |||
|- | |||
| 0 | |||
| 0.0 | |||
| C | |||
| F | |||
|- | |||
| 1 | |||
| 70.2 | |||
| ^C, vDb | |||
| F^, Gb | |||
|- | |||
| 2 | |||
| 140.4 | |||
| C#, Db | |||
| F#, Gd | |||
|- | |||
| 3 | |||
| 210.6 | |||
| vD | |||
| G | |||
|- | |||
| 4 | |||
| 280.8 | |||
| D | |||
| G^, Ab | |||
|- | |||
| 5 | |||
| 351.0 | |||
| ^D, vE | |||
| G#, Ad | |||
|- | |||
| 6 | |||
| 421.2 | |||
| E | |||
| A | |||
|- | |||
| 7 | |||
| 491.4 | |||
| ^E, vF | |||
| A^, Hb | |||
|- | |||
| 8 | |||
| 561.6 | |||
| F | |||
| A#, Hd | |||
|- | |||
| 9 | |||
| 631.8 | |||
| ^F, vC | |||
| H | |||
|- | |||
| 10 | |||
| 702.0 | |||
| C | |||
| B | |||
|- | |||
| 11 | |||
| 772.2 | |||
| ^C, vDb | |||
| B^, Cb | |||
|- | |||
| 12 | |||
| 842.3 | |||
| C#, Db | |||
| B#, Cd | |||
|- | |||
| 13 | |||
| 912.5 | |||
| vD | |||
| C | |||
|- | |||
| 14 | |||
| 982.7 | |||
| D | |||
| C^, Db | |||
|- | |||
| 15 | |||
| 1052.9 | |||
| ^D, vE | |||
| C#, Dd | |||
|- | |||
| 16 | |||
| 1123.1 | |||
| E | |||
| D | |||
|- | |||
| 17 | |||
| 1193.3 | |||
| ^E, vF | |||
| D^, Eb | |||
|- | |||
| 18 | |||
| 1263.5 | |||
| F | |||
| D#, Eb | |||
|- | |||
| 19 | |||
| 1333.7 | |||
| ^F, vC | |||
| E | |||
|- | |||
| 20 | |||
| 1403.9 | |||
| C | |||
| F | |||
|} | |||
== Music == | |||
; [[Peter Kosmorsky]] | |||
* [https://www.archive.org/details/10Edf ''10 edf''] (archived 2011) | |||
== See also == | |||
* [[17edo]] – relative edo | |||
* [[27edt]] – relative edt | |||
* [[44ed6]] – relative ed6 | |||
[[Category:Listen]] | |||