36/35: Difference between revisions

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autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
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Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
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switched to infobox interval
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<div style="float:right; margin-top:0em; border: 1px solid black;">  <!-- todo: transform into [[Template:Infobox Interval]] -->
{{Infobox Interval
{| <!-- class="wikitable" -->
| Icon =  
! colspan="3" | Basic Informations
| Ratio = 36/35
|-
| Cents = 48.77038
| Ratio: '''36/35''' || Monzo: '''{{Monzo| 2 2 -1 -1 }}''' || Size: '''48.77038 [[cent|&cent;]]'''
| Monzo = 2 2 -1 -1  
|-
| Name = septimal quarter tone
| colspan="3" | [[File:ji-36-35-csound-foscil-220hz.mp3]] <small>[[:File:ji-36-35-csound-foscil-220hz.mp3|[info]]]</small>
| Sound = ji-36-35-csound-foscil-220hz.mp3
|}</div>
}}


The '''septimal quarter tone''' (ratio: 36/35, size: 48.77038 [[cent|cents]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].
The '''septimal quarter tone''' (ratio: 36/35, size: 48.77038 [[cent|cents]]) is the difference between [[10/9]] and [[8/7]], [[7/6]] and [[6/5]], [[5/4]] and [[9/7]], [[14/9]] and [[8/5]], [[5/3]] and [[12/7]], and [[7/4]] and [[9/5]]. It has a numerator which is both the sixth square number and the eighth [[triangular number]], leading to it being the product of two [[superparticular]] commas both as [[64/63]] × [[81/80]] and as [[66/65]] × [[78/77]]; it is also [[45/44]] × [[176/175]], [[51/50]] × [[120/119]], [[128/125]] × [[225/224]], [[50/49]] × [[126/125]] and [[56/55]] × [[99/98]].

Revision as of 14:04, 11 October 2018

Interval information
Ratio 36/35
Factorization 22 × 32 × 5-1 × 7-1
Monzo [2 2 -1 -1⟩
Size in cents 48.77038¢
Name septimal quarter tone
FJS name [math]\displaystyle{ \text{P1}_{5,7} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 10.2992
Weil height (log2 max(n, d)) 10.3399
Wilson height (sopfr(nd)) 22

[sound info]
Open this interval in xen-calc

The septimal quarter tone (ratio: 36/35, size: 48.77038 cents) is the difference between 10/9 and 8/7, 7/6 and 6/5, 5/4 and 9/7, 14/9 and 8/5, 5/3 and 12/7, and 7/4 and 9/5. It has a numerator which is both the sixth square number and the eighth triangular number, leading to it being the product of two superparticular commas both as 64/63 × 81/80 and as 66/65 × 78/77; it is also 45/44 × 176/175, 51/50 × 120/119, 128/125 × 225/224, 50/49 × 126/125 and 56/55 × 99/98.

Links

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