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ratios of intervals in different tunings

🔗kopiez@xxxxxxxxxxxx.xx

9/3/1999 1:59:56 PM

Can anybody check the ratios of my interval table? I'm a bit confused,
because JI Calc. and RealTimeTuner show different values at some places or
no ratios at all?
This information is important for an investigation using an experimental
composition for an intonation experiment

Interval JI5 pyth JI7
--------------------------------------------------------------
maj3 5/4 81/64 5/4
-13.7c 8c -13.7c

min3 6/5 ?/?* 6/5
15.6c 18c

min7 9/5 (?)** ?/?*** 7/4
-3.9c 20c -31.2

*augmented second
**JI Calc shows 16/9
***augmented sixth

Thank you for your support,

Reinhard Kopiez
kopiez@hmt-hannover.de

🔗Paul H. Erlich <PErlich@xxxxxxxxxxxxx.xxxx>

9/5/1999 8:09:31 PM

Reinhard Kopiez wrote,

>Can anybody check the ratios of my interval table? I'm a bit confused,
>because JI Calc. and RealTimeTuner show different values at some places or
>no ratios at all?
>
>Interval JI5 pyth JI7
>--------------------------------------------------------------
>maj3 5/4 81/64 5/4
> -13.7c 8c -13.7c
>
>min3 6/5 ?/?* 6/5
> 15.6c 18c
>
>min7 9/5 (?)** ?/?*** 7/4
> -3.9c 20c -31.2
>
>*augmented second
>**JI Calc shows 16/9
>***augmented sixth

*) the augmented second in Pythagorean tuning is 19683/16384

**) Only regular tuning systems (e.g. meantones, Pythagorean) have definite
values for conventionally named intervals. Just intonation will have several
values for intervals with any conventional name. 9/5 and 16/9 are both minor
sevenths that occur in 5-limit just intonation, and context will usually
help to determine which should be used. 9/5 is the usual seventh of the
"just minor scale". As a dyad, 9:5 is more consonant, but 16:9 occurs in a
pretty consonant triad, 16:12:9.

***) The augmented sixth in Pythagorean tuning is 59049/32768.

>This information is important for an investigation using an experimental
>composition for an intonation experiment

Can you tell us more? As I'm sure you know, there is more to using tuning
systems than constructing an interval table as above.