33ed4: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''33ed4''' is the [[ed4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080">Equivocal Tuning</span>'''. | '''33ed4''' is the [[ed4|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080;">Equivocal Tuning</span>'''. | ||
It has a [[9/5]] which is 0.6 | It has a [[9/5]] which is 0.6{{c}} sharp, a [[7/5]] which is 0.7{{c}} flat, and a [[9/7]] which is 1.3{{c}} sharp. Therefore it is closely related to [[13edt]], the [[Bohlen–Pierce scale]], although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2|pure fifth]] makes it also interesting. | ||
Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1 | Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1{{c}}). | ||
== Intervals == | == Intervals == | ||
{| class="wikitable right-all mw-collapsible" | |||
{| class="wikitable right-all" | |+ style="font-size: 105%;" | Intervals of 33ed4 | ||
|- | |- | ||
! | ! Degree | ||
! | ! Cents | ||
! | ! Nearest JI<br />interval | ||
! | ! Cents | ||
! | ! Difference<br />in cents | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 20: | Line 20: | ||
| 24/23 | | 24/23 | ||
| 73.7 | | 73.7 | ||
| | | −1.0 | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 56: | Line 56: | ||
| 51/38 | | 51/38 | ||
| 509.4 | | 509.4 | ||
| | | −0.3 | ||
|- style="font-weight: bold" | |- style="font-weight: bold" | ||
| 8 | | 8 | ||
| Line 62: | Line 62: | ||
| 7/5 | | 7/5 | ||
| 582.5 | | 582.5 | ||
| | | −0.7 | ||
|- | |- | ||
| 9 | | 9 | ||
| Line 68: | Line 68: | ||
| 19/13 | | 19/13 | ||
| 657.0 | | 657.0 | ||
| | | −2.5 | ||
|- | |- | ||
| 10 | | 10 | ||
| Line 80: | Line 80: | ||
| 27/17 | | 27/17 | ||
| 800.9 | | 800.9 | ||
| | | −0.9 | ||
|- | |- | ||
| 12 | | 12 | ||
| Line 86: | Line 86: | ||
| 53/32 | | 53/32 | ||
| 873.5 | | 873.5 | ||
| | | −0.8 | ||
|- | |- | ||
| 13 | | 13 | ||
| Line 92: | Line 92: | ||
| 19/11 | | 19/11 | ||
| 946.2 | | 946.2 | ||
| | | −0.7 | ||
|- style="font-weight: bold" | |- style="font-weight: bold" | ||
| 14 | | 14 | ||
| Line 122: | Line 122: | ||
| 32/15 | | 32/15 | ||
| 1311.7 | | 1311.7 | ||
| | | −2.6 | ||
|- style="font-weight: bold" | |- style="font-weight: bold" | ||
| 19 | | 19 | ||
| Line 128: | Line 128: | ||
| 20/9 | | 20/9 | ||
| 1382.4 | | 1382.4 | ||
| | | −0.6 | ||
|- | |- | ||
| 20 | | 20 | ||
| Line 140: | Line 140: | ||
| 29/12 | | 29/12 | ||
| 1527.6 | | 1527.6 | ||
| | | −0.3 | ||
|- | |- | ||
| 22 | | 22 | ||
| Line 176: | Line 176: | ||
| 28/9 | | 28/9 | ||
| 1964.9 | | 1964.9 | ||
| | | −1.3 | ||
|- | |- | ||
| 28 | | 28 | ||
| Line 182: | Line 182: | ||
| 13/4 | | 13/4 | ||
| 2040.5 | | 2040.5 | ||
| | | −4.1 | ||
|- | |- | ||
| 29 | | 29 | ||
| Line 188: | Line 188: | ||
| 44/13 | | 44/13 | ||
| 2110.8 | | 2110.8 | ||
| | | −1.7 | ||
|- | |- | ||
| 30 | | 30 | ||
| Line 194: | Line 194: | ||
| 60/17 | | 60/17 | ||
| 2183.3 | | 2183.3 | ||
| | | −1.5 | ||
|- | |- | ||
| 31 | | 31 | ||
| Line 214: | Line 214: | ||
| 0.0 | | 0.0 | ||
|} | |} | ||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 33 | |||
| num = 4 | |||
| denom = 1 | |||
}} | |||
{{Harmonics in equal | |||
| steps = 33 | |||
| num = 4 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
}} | |||
== Music == | == Music == | ||
* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg | * [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
{{todo|expand}} | |||