41edo: Difference between revisions

{| class="wikitable center-1 right-2 center-5 center-6 center-8 center-9"

! #

! Cents

| Do

|}

=== Interval quality and chord names in color notation ===

Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:

! Quality

! [[Color notation|Color]]

All 41edo chords can be named using ups and downs. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are. Here are the zo, gu, ilo, yo and ru triads:

! [[Color notation|Color of the 3rd]]

! JI Chord

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

{| class="commatable wikitable center-1 center-2 right-3 center-6"

! [[Harmonic limit|Prime<br>limit]]

! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>

== Scales and modes ==

=== Lists of 41edo scales ===

* [[41edo modes]]

=== Harmonic scale ===

41edo is the first edo to do some justice to Mode 8 of the [[harmonic series]], which Dante Rosati calls the "[[overtone scale|Diatonic Harmonic Series Scale]]," consisting of overtones 8 through 16 (sometimes made to repeat at the octave).

| Overtones in "Mode 8":

| 8

=== Nonoctave temperaments ===

Taking every third degree of 41edo produces a scale extremely close to [[88cET]] or 88-cent equal temperament (or the 8th root of 3:2). Likewise, taking every fifth degree produces a scale very close to the equal-tempered <span style="">[[BP|Bohlen-Pierce]]</span>[[BP| Scale]] (or the 13th root of 3). See [[Relationship between Bohlen-Pierce and octave-ful temperaments]], and see this chart:

{| class="wikitable center-all right-3 right-4 right-5 mw-collapsible mw-collapsed"

! colspan="3" | 3 degrees of 41edo near 88cET

! overlap