4edo: Difference between revisions
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Add intervals, notation and solfege |
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=== Harmonics === | === Harmonics === | ||
{{Harmonics in equal|4}} | {{Harmonics in equal|4}} | ||
== Intervals == | |||
{| class="wikitable center-all" | |||
|+ Intervals of 4edo | |||
! rowspan="2" | [[Degree]] | |||
! rowspan="2" | [[Cent]]s | |||
! rowspan="2" | [[Interval region]] | |||
! colspan="4" | Approximated [[JI]] intervals* ([[error]] in [[¢]]) | |||
! rowspan="2" | Audio | |||
|- | |||
! [[3-limit]] | |||
! [[5-limit]] | |||
! [[7-limit]] | |||
! Other | |||
|- | |||
| 0 | |||
| 0 | |||
| Unison (prime) | |||
| 1/1 (just) | |||
| | |||
| | |||
| | |||
| [[File:piano_0_1edo.mp3]] | |||
|- | |||
| 1 | |||
| 300 | |||
| Minor third | |||
| [[32/27]] (+5.865) | |||
| [[6/5]] (-15.641) | |||
| [[7/6]] (+33.129)<br>[[25/21]] (-1.847) | |||
| [[19/16]] (+2.487) | |||
| [[File:piano_1_4edo.mp3]] | |||
|- | |||
| 2 | |||
| 600 | |||
| Tritone | |||
| | |||
| | |||
| [[7/5]] (+17.488)<br>[[10/7]] (-17.488) | |||
| [[24/17]] (+3.000)<br>[[99/70]] (-0.088)<br>[[17/12]] (-3.000) | |||
| [[File:piano_1_2edo.mp3]] | |||
|- | |||
| 3 | |||
| 900 | |||
| Major sixth | |||
| [[27/16]] (-5.865) | |||
| [[5/3]] (+15.641) | |||
| [[42/25]] (+1.847)<br>[[12/7]] (-33.129) | |||
| [[32/19]] (-2.487) | |||
| [[File:piano_3_4edo.mp3]] | |||
|- | |||
| 4 | |||
| 1200 | |||
| Octave | |||
| [[2/1]] (just) | |||
| | |||
| | |||
| | |||
| [[File:piano_1_1edo.mp3]] | |||
|} | |||
<nowiki>*</nowiki> based on treating 4edo as a subset of [[12edo]], itself treated as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible. | |||
== Notation == | |||
{| class="wikitable center-all" | |||
|+ Notation of 4edo | |||
! rowspan="2" | [[Degree]] | |||
! rowspan="2" | [[Cent]]s | |||
! colspan="2" | [[12edo]] [[subset notation]] | |||
|- | |||
! [[5L 2s|Diatonic]] interval names | |||
! Note names (on D) | |||
|- | |||
| 0 | |||
| 0 | |||
| '''Perfect unison (P1)''' | |||
| '''D''' | |||
|- | |||
| 1 | |||
| 300 | |||
| Augmented second (A2)<br>'''Minor third (m3)''' | |||
| E#<br>'''F''' | |||
|- | |||
| 2 | |||
| 600 | |||
| Augmented fourth (A4)<br>Diminished fifth (d5) | |||
| G#<br>Ab | |||
|- | |||
| 3 | |||
| 900 | |||
| '''Major sixth (M6)'''<br>Diminished seventh (d7) | |||
| '''B'''<br>Cb | |||
|- | |||
| 4 | |||
| 1200 | |||
| '''Perfect octave (P8)''' | |||
| '''D''' | |||
|} | |||
In 4edo: | |||
* [[ups and downs notation]] is identical to standard notation; | |||
* mixed [[sagittal notation]] is identical to standard notation, but pure sagittal notation exchanges sharps (#) and flats (b) for sagittal sharp ([[File:Sagittal sharp.png]]) and sagittal flat ([[File:Sagittal flat.png]]) respectively. | |||
== Solfege == | |||
{| class="wikitable center-all" | |||
|+ Solfege of 4edo | |||
! [[Degree]] | |||
! [[Cents]] | |||
! 12edo subset<br>standard [[solfege]]<br>(movable do) | |||
! 12edo subset<br>[[Uniform solfege]]<br>(2-3 vowels) | |||
|- | |||
| 0 | |||
| 0 | |||
| '''Do''' | |||
| '''Da''' | |||
|- | |||
| 1 | |||
| 300 | |||
| Ri (A2)<br>'''Me''' (m3) | |||
| Ru (A2)<br>'''Na''' (m3) | |||
|- | |||
| 2 | |||
| 600 | |||
| Fi (A4)<br>Se (d5) | |||
| Pa (A4)<br>Sha (d5) | |||
|- | |||
| 3 | |||
| 900 | |||
| '''La''' | |||
| La (M6)<br>Tho (d7) | |||
|- | |||
| 4 | |||
| 1200 | |||
| '''Do''' | |||
| '''Da''' | |||
|} | |||
== Music == | == Music == | ||