NPT pure chord demo mp3

I have uploaded an mp3 to the JohnOSullivan folder in the "Files" section. It consists of 13 chords whose notes conform to my NPT just tuning system (see message #88725). The chords are in the keys of E, F, F#, G etc up to the next E. I have chosen only major sounding chords so there's nothing too new or exotic here but it's clearly better than 12TET.

The chords have only four notes. I have found that when one or more notes are squeezed into a chord (all the dyads may be good on their own) then periodicity often suffers and although you won't hear any wolf notes the chord sounds a bit "stressed".

Below are some examples, a list of chords that have as many notes as possible (over a two octave range) and all the individual intervals/dyads are good (according to my calculator).

E, G#, B, E, G#, B, E.

F, G#, B, D#, F, G#, B, D#.

F#, B, D, F#, B, D, F#.

G, A#, C, D, G.

G, B, D, G, B, D, G.

G#, B, D#, F, G#, B, D#.

A, B, E, G, B, E, G.

A#, C, D, G.

A#, C, E, G, A#, C.

B, D, F#, B, D, F#, B.

C, D, G, D, G, B.

C#, D#, F, G#, B, D#, G#, B.

D, F#, B, D, F#, B, D.

D#, F, G#, B, D#, F, G#, B, D#.

E is 1/1, F is 15/14, F# is 9/8 etc (see message #88725).

Has anyone tried my calculator(v7.0)? Can you find a clearly consonant interval that my calculator says is dissonant, or a clearly dissonant interval that my calculator says is consonant? Try the calculator, if it's accurate it should serve as a useful tool when working out scales.

John.

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:

> Has anyone tried my calculator(v7.0)? Can you find a clearly consonant interval that my calculator says is dissonant, or a clearly dissonant interval that my calculator says is consonant?

Easily, as it says 3001/2000, to pick an example at random, is highly dissonant. What's the consonance list for it?

Gene,

thanks for the comment. The calculator states that some intervals that sound good return a negative value and that these intervals are not *pure* but are very close to a *pure* interval. E.g. 3001/2000 is not a *pure* interval but it's very close to 3/2, a true interval.

How strong is 3001/2000? For me the threshold for deviation from a *true* interval is 6.775 cents (256/255). My formula for the consonance value of untrue intervals that are within 6.775 cents of a true interval is...

p*((6.775 - q)/6.775)

where p is the strength value of the *true* interval and q is the deviation in cents of the untrue interval from the true interval.

In this case, 3/2 (the *true* interval) has a value of 28.381 (according to the calculator), so 'p' is 28.381. 3001/2000 differs from 3/2 by 0.577 cents so 'q' is 0.577.

28.381*((6.775 - 0.577)/6.775) = 25.9639

25.9639 is the strength value of the 3001/2000 interval.

The calculator also states that the numbers entered should be less than 144 (I'm going to bump this up to 255 in the next version). I suspect that if the numerator and denominator entered are both less than 144 then the interval is either perfectly good or bad with no grey areas (i.e. if the result for an interval is negative then there are *no* good intervals that are close to it (within 6.775 cents).

I hope to update the calculator which will show the 'grey area' intervals that are not in themselves pure, but are very close to a pure interval.

John.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
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>
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> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
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> > Has anyone tried my calculator(v7.0)? Can you find a clearly consonant interval that my calculator says is dissonant, or a clearly dissonant interval that my calculator says is consonant?
>
> Easily, as it says 3001/2000, to pick an example at random, is highly dissonant. What's the consonance list for it?
>