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{{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. | |||
==Intervals== | === Harmonics === | ||
{| class="wikitable" | {{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)}} | ||
! | |||
![[1L 3s (fifth-equivalent)|Neptunian]] notation using 8\10edf | === Subsets and supersets === | ||
![[Ed9/4|Neapolitan]] notation using 3/10edf | 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 | |||
|C | | 0.0 | ||
|F | | C | ||
| F | |||
|- | |- | ||
| 1 | | 1 | ||
|70. | | 70.2 | ||
|^C, vDb | | ^C, vDb | ||
|F^, Gb | | F^, Gb | ||
|- | |- | ||
|2 | | 2 | ||
|140. | | 140.4 | ||
|C#, Db | | C#, Db | ||
|F#, Gd | | F#, Gd | ||
|- | |- | ||
|3 | | 3 | ||
|210. | | 210.6 | ||
|vD | | vD | ||
|G | | G | ||
|- | |- | ||
|4 | | 4 | ||
|280. | | 280.8 | ||
|D | | D | ||
|G^, Ab | | G^, Ab | ||
|- | |- | ||
|5 | | 5 | ||
| | | 351.0 | ||
|^D, vE | | ^D, vE | ||
|G#, Ad | | G#, Ad | ||
|- | |- | ||
|6 | | 6 | ||
|421. | | 421.2 | ||
|E | | E | ||
|A | | A | ||
|- | |- | ||
|7 | | 7 | ||
|491. | | 491.4 | ||
|^E, vF | | ^E, vF | ||
|A^, Hb | | A^, Hb | ||
|- | |- | ||
| 8 | | 8 | ||
|561. | | 561.6 | ||
|F | | F | ||
|A#, Hd | | A#, Hd | ||
|- | |- | ||
|9 | | 9 | ||
|631. | | 631.8 | ||
|^F, vC | | ^F, vC | ||
|H | | H | ||
|- | |- | ||
|10 | | 10 | ||
| | | 702.0 | ||
|C | | C | ||
|B | | B | ||
|- | |- | ||
|11 | | 11 | ||
|772. | | 772.2 | ||
|^C, vDb | | ^C, vDb | ||
|B^, Cb | | B^, Cb | ||
|- | |- | ||
|12 | | 12 | ||
|842. | | 842.3 | ||
|C#, Db | | C#, Db | ||
|B#, Cd | | B#, Cd | ||
|- | |- | ||
|13 | | 13 | ||
|912. | | 912.5 | ||
|vD | | vD | ||
|C | | C | ||
|- | |- | ||
|14 | | 14 | ||
|982. | | 982.7 | ||
|D | | D | ||
|C^, Db | | C^, Db | ||
|- | |- | ||
|15 | | 15 | ||
|1052. | | 1052.9 | ||
|^D, vE | | ^D, vE | ||
|C#, Dd | | C#, Dd | ||
|- | |- | ||
|16 | | 16 | ||
|1123. | | 1123.1 | ||
|E | | E | ||
|D | | D | ||
|- | |- | ||
|17 | | 17 | ||
|1193. | | 1193.3 | ||
|^E, vF | | ^E, vF | ||
|D^, Eb | | D^, Eb | ||
|- | |- | ||
|18 | | 18 | ||
|1263. | | 1263.5 | ||
|F | | F | ||
|D#, Eb | | D#, Eb | ||
|- | |- | ||
|19 | | 19 | ||
|1333. | | 1333.7 | ||
|^F, vC | | ^F, vC | ||
|E | | E | ||
|- | |- | ||
|20 | | 20 | ||
|1403. | | 1403.9 | ||
|C | | C | ||
|F | | 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]] | [[Category:Listen]] | ||