Diatonic tuning system
This code now allows defining diatonic tuning systems, which once defined, selects the intervals. It is very easy to add a new tuning system: just one line. Plus adding its name were you want to have it on the keyboard. A tuning system is defined by giving intervals, which can be given in different units (ratio, log, cents), and their diatonic coordinates, plus an octave which needs not be the interval ratio 2 or be equal to 2m+5M. Intermediate pitches are supported (but at most one for the moment). Also a function that computes all ETs, plus some other illustrating tuning systems. In order to illustrate that the octave needs not the interval ratio 2, Georgian style tunings have been added, which divides the perfect fifth into four equal steps, so that m = M and the octave is slightly sharp. Plus Bohlen-Pierce scales, dividing the ratio 3 into 13 steps, with the octave 5m+4M. And the intermediate pitches are illustrated by Just intonation relative Pythagorean (might also be used for Turkish music description), Turkish E53, and Persian style tunings. So with just one neutral second added, one can cover a lot. Details: see the file. Stay tuned! Hans
Hans;
In order to illustrate that the octave needs not the interval ratio 2,
This is a very confusing sentence to me, roughly on par with "to demonstrate a Km needs not consist of a hundred meters...". Could you kindly link to a explanation of the why and how of this? I'm quite interested in tunings but I know little about the established theory and I thought the octave as a doubling in frequency was the one thing I *could* depend on. Clearly this was naïve so it would be nice to get a definition of "octave" from the perspective that you're using. Yours, Kas.
On 3 May 2009, at 19:26, Kassen wrote:
In order to illustrate that the octave needs not the interval ratio 2,
This is a very confusing sentence to me, roughly on par with "to demonstrate a Km needs not consist of a hundred meters...". Could you kindly link to a explanation of the why and how of this?
Sure.
I'm quite interested in tunings but I know little about the established theory and I thought the octave as a doubling in frequency was the one thing I *could* depend on. Clearly this was naïve so it would be nice to get a definition of "octave" from the perspective that you're using.
Basically, it is shortage of terminology. The word "octave" means the eighth scale degree, the same as the pure eighth P8, often fixed to the ratio 2. But when generalizing, first the octave needs not be the interval ratio 2. And it seems common to use it to denote the span of a whole scale, even if the number of scale degrees in it is not seven - just my impression. So, when generalizing, I simply decided to use the word "octave" for the whole scale span, and use P8 for the eighth scale degree. Try the Georgian scale Ge and the Bohlen-Pierce scales BP and BPM to see hat happen when you try to play a traditional octave. I just made this up terminology for now. So if there is a better suggestion, just let me know. :-) Hans
On 3 May 2009, at 19:26, Kassen wrote:
In order to illustrate that the octave needs not the interval ratio 2,
This is a very confusing sentence to me, roughly on par with "to demonstrate a Km needs not consist of a hundred meters...". Could you kindly link to a explanation of the why and how of this?
The word "diapason" can mean "all notes in the scale". So I will change that.
I'm quite interested in tunings but I know little about the established theory and I thought the octave as a doubling in frequency was the one thing I *could* depend on. Clearly this was naïve so it would be nice to get a definition of "octave" from the perspective that you're using.
The octave is the eighth scale degree, just the interval numbered eight, which needs not be the interval ratio 2. (In Swedish, one prefers the Latin names, for example, the 7th is called "septima", so a distinction between octave an 8th is not possible.) Also, the interval ratio 2 needs not be a doubling of the frequency, because one may use a tuning that stretches or compresses the scale. So the octave needs not be the interval ratio 2, the diapason needs not be the octave, and the interval ratio 2 needs not be a doubling of the frequency. Hans
2009/5/3 Hans Aberg
This code now allows defining diatonic tuning systems, which once defined, selects the intervals. It is very easy to add a new tuning system: just one line. Plus adding its name were you want to have it on the keyboard.
I've been noodling on this and I like it. Thanks. -- Tom Lieber http://AllTom.com/
On 13 May 2009, at 20:01, Tom Lieber wrote:
This code now allows defining diatonic tuning systems, which once defined, selects the intervals. It is very easy to add a new tuning system: just one line. Plus adding its name were you want to have it on the keyboard.
I've been noodling on this and I like it. Thanks.
Great! I will do more, but I've been noodling too :-). I use two keyboards, for treble and bass, right now by just making a copy of the file and changing the device number. A class TuningSystem object chooses intervals which can be used in other ways than being controlled from the typing keyboard. I have added a class Tuning (admitting a primitive form of stretch tuning) which should simplify such uses. But the core is in what I posted. Hans
participants (3)
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Hans Aberg -
Kassen -
Tom Lieber