36:45:54:64: Difference between revisions

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{{Infobox Chord|36:45:54:64|Name=Ptolemaic dominant seventh}}
{{Infobox Chord|36:45:54:64|ColorName=yo add-7 or y,7}}


'''36:45:54:64''' (or 1⁄1–5⁄4–3⁄2–16⁄9), the ''Ptolemaic dominant seventh chord'', is a [[dominant seventh chord]] found on the dominant scale degree ([[3/2|3⁄2]] or V) of [[Zarlino|Ptolemy's intense diatonic scale (Zarlino)]], perhaps the most common 5-limit diatonic. It combines a [[5/4]] major third with a [[16/9]] Pythagorean minor seventh, creating a [[64/45]] tritone between the two.
{{Nowrap|'''36:45:54:64'''}} is a [[dominant seventh chord]] found on the {{w|dominant (music)|dominant}} scale degree (V or {{Frac|3|2}}) of Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common 5-limit diatonic. It combines a [[5/4]] major third with a [[16/9]] ([[3-limit]]) minor seventh, creating a [[64/45]] tritone between the two.


[[Category:Dominant seventh chords]]
In the [[meantone]] tuning of this chord, the ~16/9 minor seventh is equated with ~[[9/5]], making it equivalent to the meantone tuning of [[20:25:30:36]].
 
[[Category:Dominant seventh chords|##]] <!-- 2-digit first number -->

Latest revision as of 02:27, 24 September 2024

Chord information
Harmonics 36:45:54:64
Subharmonics 1/(240:192:160:135)
Intervals from root 1/15/43/216/9
Cents from root 386¢702¢996¢
Step intervals 5/4, 6/5, 32/27
Step cents 386¢, 316¢, 294¢
Color name yo add-7 or y,7
Prime limit 5
Genus 335 (135)
Intervallic odd limit 45
Otonal odd limit 45
Utonal odd limit 135
Consistent edos (d ≥ 2) 12edo*, 41edo*, 53edo**, 65edo**

36:45:54:64 is a dominant seventh chord found on the dominant scale degree (V or 32) of Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic. It combines a 5/4 major third with a 16/9 (3-limit) minor seventh, creating a 64/45 tritone between the two.

In the meantone tuning of this chord, the ~16/9 minor seventh is equated with ~9/5, making it equivalent to the meantone tuning of 20:25:30:36.