60afdo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
BudjarnLambeth (talk | contribs)
In afdos, whether or not an interval occurs directly above the root (not in a mode) is very important. One common use of afdos is for primodality , and a primodalist would find it very important that 35afdo contains /5 intervals and /7 intervals above the root. 60afdo is very much not primodal of course, but this still matters. One reason why people might use 60afdo is that they want a subset JI scale that contains lots of simple intervals above the root.
BudjarnLambeth (talk | contribs)
Reworded it to separate the scale from the afdo
Line 3: Line 3:
'''60afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''60odo''' ([[otonal division]] of the octave), divides the octave into sixty parts of 1/60 each. It is a superset of 59afdo and a subset of 61afdo. Added to 59afdo are many 119/ ratios. As a scale it may be known as [[Harmonic mode|mode 60 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-60]] scale.  
'''60afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''60odo''' ([[otonal division]] of the octave), divides the octave into sixty parts of 1/60 each. It is a superset of 59afdo and a subset of 61afdo. Added to 59afdo are many 119/ ratios. As a scale it may be known as [[Harmonic mode|mode 60 of the harmonic series]] or the [[Overtone scale #Over-n scales|Over-60]] scale.  


60afdo is a highly composite afdo, with many ways to form frequency-domain equal subset scales. Due to 60 being 2 x 2 × 3 × 5, this afdo contains many low complexity [[5-limit]] intervals directly above the root, without having to rotate it. 60 is a highly composite afdo, containing within it (directly above the root, without having to rotate) [[1edo|1]], [[2afdo|2]], [[3afdo|3]], [[4afdo|4]], [[5afdo|5]], [[6afdo|6]], [[10afdo|10]], [[12afdo|12]], [[15afdo|15]], [[20afdo|20]] and [[30afdo|30]] afdo.
60afdo is a highly composite afdo, with many ways to form frequency-domain equal subset scales. Due to 60 being 2 x 2 × 3 × 5, this afdo’s associated overtone scale contains many low complexity [[5-limit]] intervals directly above the root, without having to rotate it. Due to 60 being 2 x 2 × 3 × 5, this afdo contains many low complexity [[5-limit]] intervals, including those with 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 or 30 in the denominator.


== Scales ==
== Scales ==

Revision as of 13:03, 15 October 2024

← 59afdo 60afdo 61afdo →
Prime factorization 22 × 3 × 5
Fifth 90/60 (701.955c)

60afdo (arithmetic frequency division of the octave), or 60odo (otonal division of the octave), divides the octave into sixty parts of 1/60 each. It is a superset of 59afdo and a subset of 61afdo. Added to 59afdo are many 119/ ratios. As a scale it may be known as mode 60 of the harmonic series or the Over-60 scale.

60afdo is a highly composite afdo, with many ways to form frequency-domain equal subset scales. Due to 60 being 2 x 2 × 3 × 5, this afdo’s associated overtone scale contains many low complexity 5-limit intervals directly above the root, without having to rotate it. Due to 60 being 2 x 2 × 3 × 5, this afdo contains many low complexity 5-limit intervals, including those with 1, 2, 3, 4, 5, 6, 10, 12, 15, 20 or 30 in the denominator.

Scales

  • Palace: 66/60-72/60-80/60-90/60-99/60-108/60-120/60 (approximated from Porky in 29edo)