648/625: Difference between revisions

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'''648/625'''
{{Infobox Interval
|3 4 -4>
| Name = diminished comma, major diesis
| Color name = g<sup>4</sup>2, quadgu 2nd,<br>Quadgu comma
| Sound = jid_648_625_pluck_adu_dr220.mp3
| Comma = yes
}}


62.5651 cents
The interval '''648/625''' is known as the '''diminished comma''' or '''major diesis'''. It is the amount by which four [[6/5]] minor thirds exceed an [[2/1|octave]], in other words (6/5)<sup>4</sup> / 2.  


[[File:jid_648_625_pluck_adu_dr220.mp3]] [[:File:jid_648_625_pluck_adu_dr220.mp3|sound sample]]
== Approximations ==
This interval is approximately one step of [[19edo]], which is the amount by which four 19edo minor thirds exceed an octave.  


The interval 648/625 (about 62.6 cents) is known as the diminished [[Comma|comma]] or major diesis, and is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)^4 / 2. Tempering it out leads to [[5-limit|5-limit]] [[Diminished|diminished temperament]]. This is approximately one step of [[19edo|19edo]], which is the amount by which four 19edo minor thirds exceed an octave.
== Temperaments ==
[[Category:comma]]
Tempering out this comma leads to the [[5-limit]] [[diminished (temperament)|diminished]] temperament.
 
[[Category:Diminished]]
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 07:52, 3 November 2024

Interval information
Ratio 648/625
Factorization 23 × 34 × 5-4
Monzo [3 4 -4⟩
Size in cents 62.56515¢
Names diminished comma,
major diesis
Color name g42, quadgu 2nd,
Quadgu comma
FJS name [math]\displaystyle{ \text{d2}_{5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 18.6276
Weil norm (log2 max(n, d)) 18.6797
Wilson norm (sopfr(nd)) 38
Comma size medium

[sound info]
Open this interval in xen-calc

The interval 648/625 is known as the diminished comma or major diesis. It is the amount by which four 6/5 minor thirds exceed an octave, in other words (6/5)4 / 2.

Approximations

This interval is approximately one step of 19edo, which is the amount by which four 19edo minor thirds exceed an octave.

Temperaments

Tempering out this comma leads to the 5-limit diminished temperament.

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