64/61: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 64/61
| Monzo = 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
| Cents = 83.11519
| Name = harry minor semitone
| Name = harry minor semitone
| Color name = 61u2, siwu 2nd
| Color name = 61u2, siwu 2nd
| FJS name = m2<sub>61</sub>
| Sound = jid_64_61_pluck_adu_dr220.mp3
| Sound = jid_64_61_pluck_adu_dr220.mp3
}}
}}


'''64/61''' = 2<sup>6</sup> ⋅ 61<sup>−1</sup>, the harry minor semitone, makes for a good tuning for [[Gravity family#Harry|harry temperament]], and in particular is only 0.001 cents flat of the POTE generator for [[13-limit]] harry. It also makes for an excellent tuning for the generator of [[Kleismic family#Tritikleismic|tritikleismic temperament]]; hence, harry consists of two parallel tracks of 64/61 steps and tritikleismic of three parallel tracks. As a fraction of an octave 64/61 falls between 9\[[130edo|130]] and 7\[[101edo|101]]. It can also be described as the [[Octave reduction|octave-reduced]] 61st [[subharmonic]].
'''64/61''' is the [[Octave reduction|octave-reduced]] 61st [[subharmonic]]. It is flat of the [[256/243|Pythagorean limma (243/128)]] by [[244/243]]. It can also be described as the harry minor semitone, as it makes for a good tuning for [[harry]] temperament, and in particular is only 0.001 cents flat of the [[POTE tuning|POTE generator]] for [[13-limit]] harry. It also makes for an excellent tuning for the generator of [[tritikleismic]] temperament; hence, harry consists of two parallel tracks of 64/61 steps and tritikleismic of three parallel tracks. As a fraction of an octave 64/61 falls between 9\[[130edo|130]] and 7\[[101edo|101]].  
 
== See also ==
* [[61/32]] – its [[octave complement]]


[[Category:61-limit]]
[[Category:Second]]
[[Category:Second]]
[[Category:Semitone]]
[[Category:Semitone]]
[[Category:Octave-reduced subharmonics]]

Latest revision as of 10:05, 7 December 2024

Interval information
Ratio 64/61
Subgroup monzo 2.61 [6 -1⟩
Size in cents 83.11519¢
Name harry minor semitone
Color name 61u2, siwu 2nd
FJS name [math]\displaystyle{ \text{m2}_{61} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 11.9307
Weil height (log2 max(n, d)) 12
Wilson height (sopfr(nd)) 73

[sound info]
Open this interval in xen-calc

64/61 is the octave-reduced 61st subharmonic. It is flat of the Pythagorean limma (243/128) by 244/243. It can also be described as the harry minor semitone, as it makes for a good tuning for harry temperament, and in particular is only 0.001 cents flat of the POTE generator for 13-limit harry. It also makes for an excellent tuning for the generator of tritikleismic temperament; hence, harry consists of two parallel tracks of 64/61 steps and tritikleismic of three parallel tracks. As a fraction of an octave 64/61 falls between 9\130 and 7\101.

See also

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