Yahoo Tuning Groups Ultimate Backup tuning Complementary information

Carl,

Since you are not sure what I have plotted, I give here a complementary explanation.

1) I sent you 4 plots related to the ancient seven tone JI scale where Cmaj, Fmaj, Bmaj tone ratios regarding the tonic are 1, 1.25, 1.5:

- Plot A: Cmaj chord wave (Sum of the 3 sinusoidal components of Cmaj). Here, positive and negative peaks are marked with a point along a display period of 0.1 seconds. The peak wave shape and any section of the plot presents a cyclical and aesthetic distribution along the time; these features make possible the recognition of JI -Cmaj as an optimal triad. Please note that for reaching to this conclusion I only needed to work with pure sinusoids, that is, free of overtones and the absence of timbre since a chord still is a chord with or without the timbre.

- Plot B: Cmaj chord wave peaks. Each point mark of plot A is transferred to plot B and the display period is increased to 2 seconds to enable the visualization of the triad sound. In the plot we only see the point marks of plot A shown in twelve rows. The plot appearance is extremely simple and the symmetry of rows is evident. This was all I needed to conclude that JI - Cmaj triad is an optimal chord; the same for JI - Fmaj and JI - Bmaj.

About JI - Dmaj, the plot method of evaluation will detect that it is an out of tune triad since (1.66666./1.125) = 1.48148148. instead of 1.5.

I know that you are acquainted with all these details, I would like to plot this out of tune triad to see how it looks and send it to you.

3) Despite the timbre gives color to the chord, in my opinion we should separate its applications: music and chord measurements.

You wrote "To establish validity, one would have to plot a variety of chords, each in a variety of timbres."

4) Since the evaluation rely on the combined wave shape to be examined along seconds, pure sine waves had to be used.

Should you want to evaluate a triad by this method, just send it to me to process it and see how it looks as well as to get your final opinion on this matter which will be respected.

Thanks

Mario

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🔗Carl Lumma <carl@...>

Hi Mario,

> Please note that for reaching to this conclusion I only needed
> to work with pure sinusoids, that is, free of overtones and the
> absence of timbre since a chord still is a chord with or without
> the timbre.

If the things you observe on the plots go away or change when
a different timbre is used, I would say that invalidates the
analysis.

> This was all I needed to conclude that JI - Cmaj triad is
> an optimal chord; the same for JI - Fmaj and JI - Bmaj.

If you used the usual JI diatonic scale,

1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

with 1/1 = C, then Cmaj and Fmaj are the same chord. Bmaj
depends on what values are given for D# and F#. As explained
in my offlist e-mail, it is best simply to say directly which
chords you are analyzing, holding their root frequency
constant, rather than pulling them from a scale.

> I know that you are acquainted with all these details, I would
> like to plot this out of tune triad to see how it looks and send
> it to you.

Also important is the plotting method used -- for instance,
the sample rate. It's a lot of work to show something about
chord quality visually and in fact of the many attempts I've
seen over the years, none were successful. I don't want to
discourage you from undertaking it, but if you give up I won't
accuse you of being lazy. :)

> 4) Since the evaluation rely on the combined wave shape to
> be examined along seconds, pure sine waves had to be used.

I don't understand this, but at any rate, it is essential
to show your method is relevant to timbres typically used
in music-making (sine tones are not!). Like I said, a lot
of work.

-Carl

🔗Mario Pizarro <piagui@...>

Hi Carl,

Thanks for answering my message. Our viewpoints entered to the area of pure reasoning I think.
>
> If the things you observe on the plots go away or change when
> a different timbre is used, I would say that invalidates the
> analysis.
>

>> If it is introduced any intensity of "oversounds"on a sinusoidal sound >> wave we get >> a slightly irregular mixed tone wave (not necessarily a >> musical tone or a chord) >> A tone with timbre would have been made and a >> distorted sound wave too. The >> soundwave analyzer duty is to plot the >> sound wave current to evaluate how pure >> is the sound. The oversounds >> used to get the timbre caused abnormal plots. >>Since the purpose is the >> production of normal combined sound waves, >>oversounds shouldnï¿½t be >> used. (Sorry for the imagination)

>>When a student is using the Fourier analysis, the job is going well >>provided the >>input function is not a very complex expression like the >>branches of a tree. >>Similarly, if a triad is going to be analyzed, the >>analyzer input must only contain >>figures that represent the pure tone >>frequencies without the timbre.

Carl,
Tomorrow I will continue with your last three paragraphs

Regards

Mario
October 17

----- Original Message ----- From: "Carl Lumma" <carl@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, October 17, 2010 3:39 PM
Subject: [tuning] Re: Complementary information

> Hi Mario,
>
>> Please note that for reaching to this conclusion I only needed
>> to work with pure sinusoids, that is, free of overtones and the
>> absence of timbre since a chord still is a chord with or without
>> the timbre.
>
> If the things you observe on the plots go away or change when
> a different timbre is used, I would say that invalidates the
> analysis.
>
>> This was all I needed to conclude that JI - Cmaj triad is
>> an optimal chord; the same for JI - Fmaj and JI - Bmaj.
>
> If you used the usual JI diatonic scale,
>
> 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
>
> with 1/1 = C, then Cmaj and Fmaj are the same chord. Bmaj
> depends on what values are given for D# and F#. As explained
> in my offlist e-mail, it is best simply to say directly which
> chords you are analyzing, holding their root frequency
> constant, rather than pulling them from a scale.
>
>> I know that you are acquainted with all these details, I would
>> like to plot this out of tune triad to see how it looks and send
>> it to you.
>
> Also important is the plotting method used -- for instance,
> the sample rate. It's a lot of work to show something about
> chord quality visually and in fact of the many attempts I've
> seen over the years, none were successful. I don't want to
> discourage you from undertaking it, but if you give up I won't
> accuse you of being lazy. :)
>
>> 4) Since the evaluation rely on the combined wave shape to
>> be examined along seconds, pure sine waves had to be used.
>
> I don't understand this, but at any rate, it is essential
> to show your method is relevant to timbres typically used
> in music-making (sine tones are not!). Like I said, a lot
> of work.
>
> -Carl
>
>
>
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> ESET NOD32 Antivirus ha comprobado este mensaje.
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🔗Mario Pizarro <piagui@...>

Carl,

>
> If the things you observe on the plots go away or change when
> a different timbre is used, I would say that invalidates the
> analysis.
>
>> On the contrary, if they change (or go away), it means that the original >> and changed >> plots are being (had being) charged by timbre waves >> which do not pertain to the triad >> itself.

>> If it is introduced some "oversounds" or sound harmonics on a sinusoidal >> sound
>> wave we get a slightly irregular mixed tone wave (not necessarily a
>> musical tone) A tone with timbre would have been made and a
>> distorted sound wave too.
>
> If the things you observe on the plots go away or change when
> a different timbre is used, I would say that invalidates the
> analysis.
>
>>The sound of a triad with timbre is formed by three sinusoids representing >>the triad >> tones plus their harmonics. The triad tones and the >>timbre print on the chord wave plot >> their combined sinusoidal waves. >>The plot shows the result of the combined sinusoidal >> triad tones mixed >>with variables that nothing have to do with music; however they >> >>improve the musical expression.

>> You have the plot Cmaj - JI - 0.1 sec of display that I sent you >> yesterday; this >> response does not include timbre, >> nevertheless the plot appearance asserts that the >> triad is a tuned >> one. If the timbre would have been included , some degree of >> >> distortion would have appeared. If you agree, I can make a plot with >> the same triad plus >> the timbre represented by 3% amplitude, 2nd and 3d >> harmonics to reach a conclusion.

>> Since Cmaj - JI - 0.1 sec plot shows a periodic [(0.045 - 0.03) = 0.015 >> sec] and >> aesthetic display, so the triad is a tuned triad; in >> this case it is not necessary to transfer >> the peak marks to a second >> plot called "chord wave peaks". However I made this plot >> and sent it >> to you, its display period is 2 seconds, and contains 12 rows of peak >> marks.

>> When the triad comes from a 12 tone scale the number of peak marks >> increases >> considerably and the plotted wave shape may be >> periodic and aesthetic, somewhat >> aesthetic, or chaotic.

>> Should the triad tones carry overtones the timbre is part of the process, >> each overtone >> origins its peak marks, introducing some amount of >> distortion on the plot.

> Also important is the plotting method used -- for instance,
> the sample rate. It's a lot of work to show something about
> chord quality visually and in fact of the many attempts I've
> seen over the years, none were successful. I don't want to
> discourage you from undertaking it, but if you give up I won't
> accuse you of being lazy. :)

>> A popular phrase in my country says: "May be you are right but let me >> kill my worm"

>> If I give up, I would abandon at least one of my basic concepts.

>> Once I sent you one of the Piagui scales in cents, I had asked your >> opinion about it. >> Some days later you responded saying that D major >> doesnï¿½t look similar to the rest of >> triads or something like that. >> Your opinion was important so I reexamined all the chord >> wave peaks of >> that scale paying attention on Dmaj. The result coincided with your >> >> opinion: A group of small and thin peaks appeared in the plot. The >> remaining plots >> looked free of peaks. The D triad sound when put >> on the oscilloscope looked normal.

> 4) Since the evaluation rely on the combined wave shape to
> be examined along seconds, pure sine waves had to be used.
>> Sorry, I forgot to complete the idea.
> I don't understand this, but at any rate, it is essential
> to show your method is relevant to timbres typically used
> in music-making (sine tones are not!). Like I said, a lot
> of work.

Thanks

Mario
----- Original Message ----- From: "Carl Lumma" <carl@...>
To: <tuning@yahoogroups.com>
Sent: Sunday, October 17, 2010 3:39 PM
Subject: [tuning] Re: Complementary information

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