Tuning

[7/4]

BTW, that Helmholtz book is a monster - another must own. Had it for a while but have not studied it to the extent of some other books I have. This makes me want to read it cover to cover.

I never did, I think I tried. I use it more as a reference book. A long time ago I did read Genesis cover to cover, but now just for reference. Like I said before, the JI Primer is worth studying in detail.

Maybe I should take a spin through all three soon again...wouldn't hurt.

[snailed]

Is the JI Primer available as a .pdf anywhere?

Just found an interesting quote from Johnston that sums up how I feel about the use of these techniques in the big picture:

Only very gradually did I begin to realize the extent of the inharmonicity of the piano's wrapped metallic strings in its lower register, with the basic compromise that necessitated no matter how one might tune the strings. Another problem was the use of three strings tuned in unison for the high registers. More and more this situation seemed symbolic to me of the human condition. One may aim at perfection, but to get even a bit closer to it involves being ruthlessly aware of the resistance and the imperfection of our raw materials, body, mind, and habitual behavior. This painful process struck me as significant material for art.

(available as a video lecture from radiom.org, not sure if it's been printed elsewhere)

[Stephen]

OK, I've got to grips with all of snailed's first post and it looks like I've got a good grounding as I am familiar with all the standard intervals and aware which are most consonant and most dissonant, though probably couldn't identify them all by ear. A few questions:

if you excite a string tuned to 600hz, or vibrating at 600 cycles per second, there is an octave at 1200hz, a fifth at 1800hz

Surely there is also a fifth beneath 1200hz? say 900hz, or is that a third?

If every semitone step is identical then I was hoping that would mean say 25hz between each, but that can't work as there must be a wider gap in frequency between two high Cs than two high Cs (say bottom C is 20hz then the c2 must be 40hz, and if c7 is 2000 hz then c8 is 4000hz) now my head hurts. because how can one octave only have 20hz interval which another has 2000!?

I have just checked this against my bible and I seem to be right, so I will just have to live with the fact that some octaves are numerically bigger than others.

Sadly as I am mostly applying this stuff to grand pianos that are not mine I can't get into retuning the buggers to JI. I will check the library for the recommendations above. So what about keys, if I actually wanted to play in say D minor, how on earth do I know what other notes are 'allowed'?

[snailed]

OK, as far as the first question (will get to figuring out what notes are in what keys a bit later) it is, I believe to the best of my understanding, because frequency in relation to pitch is logarithmic. This confused the hell out of me at the time when I first learned it, and I then turned my brain off and watched TV for about 3 days. Meaning here, as you increase, there are bigger and bigger gaps. To measure an interval is best to do in the terms of cents - which will always be consistent. There are always 1200 cents in an octave, so it is best suited for expressing musical intervals. I should have given cent equivalences as well!

This site has a good converter.

Here is something I found on a site on perfect pitch that explains it a bit:

The only physical relationship between the chromatic scale and the ear is that both operate on a logarithmic scale in order to accommodate a large frequency range. We know that the ear operates on a logarithmic scale because harmonies have a special meaning and harmonies are ratios and ratios are easiest to manipulate on a logarithmic scale. Thus, although we are not born with PP (perfect pitch, -snailed), we are born to recognize harmonies. The effect of the logarithmic human hearing is that the ear hears a large difference in pitch between 40 and 42.4 Hz (a semitone or 100 cents), but hears almost no difference between 2000Hz and 2002.4 Hz (about 2 cents), for the same difference of 2.4 Hz. The human ear responds to all frequencies within its range and is not calibrated on an absolute scale at birth. This is in contrast to the eye, which responds to color on an absolute scale (everyone sees red as red from birth without any training, and this perception never changes with age) because color detection is achieved using chemical reactions that respond to specific quanta (wavelengths) of light. Some people who can identify certain pitches with specific colors can acquire perfect pitch by the color that the sound evokes. They are effectively calibrating the ear to an absolute reference. Most students learn PP by associative memory.

edit: Also, thanks for bringing this up, it is an excellent question. I don't think I've ever understood it as concretely as now, having had to look and check into it more.

[bryan]

plain English definition of standing waves

Waves that give up their bus seats.
HEY! I'll be here all evening, but seriously folks...

Wave phenomena typically travel outward from their origin, but a standing wave continually regenerates in place. An example: Finding a low frequency resonance of a room by slowly changing the frequency until at one point the sound got particularly loud. At that particular frequency you could walk across the room, experiencing regular repeating zones of loud in phase sound and much quieter out of phase nodal spots. In this case the room's resonant frequency was reinforcing the oscillator's sound, positive feedback.

Hmm.. or maybe better, a fixed string on a piano or guitar or whatever exhibits a standing wave: the wave traveling along the length of the string is a standing wave because once the wave reaches the end of the string it travels back into itself vs. the wave we know as sound traveling away from the string in the air, which does not travel back into itself.

What we know as matter is comprised of standing waves upon standing waves... but as far as we're concerned the physical universe seems largely static and solid. Heh heh, getting a bit carried away. It's a lot to wrap one's head around!

[snailed]

Thanks for that, bryan!

I figured this might be of some use to some of you. I'd been looking for this for a long while, and I guess it was only printed in an academic edition which is very expensive (even though there is a copy on bookfinder, it's not available, I checked).

It's James Tenney's A History of 'Consonance' and 'Dissonance'. Some kind soul was nice enough to scan this in and then message me about it on soulseek, so much thanks goes to the original scanner. Don't know if he posts here, but sent a message asking. Anyway, to those interested, enjoy.

Download here

[Dohol]

Thanks for that, bryan!

I figured this might be of some use to some of you. I'd been looking for this for a long while, and I guess it was only printed in an academic edition which is very expensive (even though there is a copy on bookfinder, it's not available, I checked).

It's James Tenney's A History of 'Consonance' and 'Dissonance'. Some kind soul was nice enough to scan this in and then message me about it on soulseek, so much thanks goes to the original scanner. Don't know if he posts here, but sent a message asking. Anyway, to those interested, enjoy.

Download here

Wow! Thanks so much for that,

[bryan]

Anyway, to those interested, enjoy.

Download here

Definitely interested. Thanks a lot for upping that, snailed.

[ryan]

thanks for bringing this up. i've been tuning my roommates (p_ano) piano lately. i'm trying to get it done by ear. its a cable upright that doesn't hold tuning for long so its good practice. the first time we tuned we tried to tune by perfect fifths and ended up with major dissonance in F and G major, which might have been due to the fact that it was a collaborative effort and it took a long time and we just sort of gave up towards the end and went with some preparations. I tried again a few weeks ago and got it pretty close to equal tempered in a about 3 hours with a lot of cross checking, and the bottom and high ends not perfect because of the piano's slightly muddy tone, which sweetened up nicely with the tuning.

its due for another pass, so I think my question is: is a JI perfect fifth equivalent to an equal tempered fifth? because I tend to tune by perfect fifths often, being a violinist. in the past i've had intonation problems with piano accompaniment. is this due to tuning my strings to perfect fifths?

[snailed]

its due for another pass, so I think my question is: is a JI perfect fifth equivalent to an equal tempered fifth? because I tend to tune by perfect fifths often, being a violinist. in the past i've had intonation problems with piano accompaniment. is this due to tuning my strings to perfect fifths?

Yeah, playing with piano accompaniment in ET, you will always have to do some adjusting. The fifth is actually one of the closest to a just interval, at least compared to some of the other, more tempered intervals. The ET perfect fifth is about 2 cents flat of the JI fifth, enough to compound and cause problems if you are tuning in chains of fifths, and enough to cause a sensitive ear playing in pure fifths to make slight adjustments to conform to an ET instrument. Here's a good wiki article with a chart that shows you cent differences between the ET intervals and some common just intervals: Wiki article

Good luck with the piano tuning project - if you're tuning in stacks of fifths, you are going to get some dissonances as far as wolf intervals go. Read the entry on Pythagorean Tuning (here) to get some insight into that, it can be pretty helpful to know that you can expect some pretty major dissonances playing in more remote keys, even if you tune very accurately in pure fifths.

[7/4]

You've discovered the difference between 12 tone equal temperament and Pythagorean tuning.







.

[ryan]

so i've got to learn to hear those two cents worth, eh? or learn to hear ET seconds? if anybody here ever tuned a piano to ET by ear, got any tips?

[ryan]

You've discovered the difference between 12 tone equal temperament and Pythagorean tuning.







.

its not that i've never noticed the difference while i'm playing, i'm just trying to learn to recognize which is which. any one know how the 22 shrutis fit into this?

[7/4]

You've discovered the difference between 12 tone equal temperament and Pythagorean tuning.

its not that i've never noticed the difference while i'm playing, i'm just trying to learn to recognize which is which.

In Pythagorean, the 5ths are in tune while the thirds are "different". Try playing a major triad in each key while cycling around the cycle of 5ths.

any one know how the 22 shrutis fit into this?

Not much of a comparison. Two different tunings for different applications.



edit for grammar.

[ryan]

You've discovered the difference between 12 tone equal temperament and Pythagorean tuning.

its not that i've never noticed the difference while i'm playing, i'm just trying to learn to recognize which is which.

In Pythagorean, the 5ths are in tune while the thirds are "different". Try playing a major triad in each key while cycling around the cycle of 5ths.

any one know how the 22 shrutis fit into this?

Not much of a comparison. Two different tunings for different applications.



edit for grammar.

cross checking with thirds is how a squeezed it down to (almost) ET this past round, though I'm not exactly clear on what exactly I was listening for. I'll let you know if I need an editor. Anyone else feel free to chime in...

[snailed]

Something which might help is to have a digital oscillator capable of playing very precise tones - do whatever math is needed, or use the wiki chart for reference, and use it as some sort of way to "check" your work. I've used this, and while a sine tone doesn't have the harmonic richness to properly compare the two, you can use it to get a rough idea. If you can't find anything I might be able to whip up a quick MSP patch for you, but I'm pretty sure there are some freeware sine wave generators out there. When you do get that, it might be handy to make examples of scales for reference and ear training, then you can just open them up any time you want to compare the two. Can't really comment on anything regarding comparisons to Indian music, not my area, but I do know they tune their drones to a pure fifth and octave.

[7/4]

cross checking with thirds is how a squeezed it down to (almost) ET this past round, though I'm not exactly clear on what exactly I was listening for. I'll let you know if I need an editor. Anyone else feel free to chime in...

I think piano tuners squeeze 5ths and count beats. That's a temperament, an adjustment to a just tuning so you can play in tune in most keys and then the ultimate solution - 12 tone equal temperament - in all 12 keys.

[7/4]

Something which might help is to have a digital oscillator capable of playing very precise tones - do whatever math is needed, or use the wiki chart for reference, and use it as some sort of way to "check" your work. I've used this, and while a sine tone doesn't have the harmonic richness to properly compare the two, you can use it to get a rough idea. If you can't find anything I might be able to whip up a quick MSP patch for you, but I'm pretty sure there are some freeware sine wave generators out there. When you do get that, it might be handy to make examples of scales for reference and ear training, then you can just open them up any time you want to compare the two.

A digital tuner is the best way to go if you can afford it.

Keep in mind that whole inharmonicity of a piano bit, I have no idea how to tune a stretch tuning.

Can't really comment on anything regarding comparisons to Indian music, not my area, but I do know they tune their drones to a pure fifth and octave.

There's that 22-tone sruiti scale/tuning and then you have to consider that it varies in practice. The sruiti scale I've seen is a 5 limit scale, the folks I studied with taught seven limit, string players tune their open strings in 5ths as do Santur/Santoor players.

[bryan]

I think piano tuners squeeze 5ths and count beats.

What do you mean by "squeeze"? Is it that they get the 5th exactly, then... umm.. OK, I just found a page that answered my question..

The interval from the C to G in the lower octave is tuned to a beatless natural fifth, then flattened slightly to a beat rate of .7 beats per second forming an equal tempered fifth.

Hey Ryan, check it out. This'll probably help you. Scroll down to the Piano Tuning section:

http://www.precisionstrobe.com/apps/pia ... emper.html

[7/4]

I think piano tuners squeeze 5ths and count beats.

What do you mean by "squeeze"? Is it that they get the 5th exactly, then... umm.. OK, I just found a page that answered my question..

The interval from the C to G in the lower octave is tuned to a beatless natural fifth, then flattened slightly to a beat rate of .7 beats per second forming an equal tempered fifth.

Hey Ryan, check it out. This'll probably help you. Scroll down to the Piano Tuning section:

http://www.precisionstrobe.com/apps/pia ... emper.html

Squeeze = make the 5th interval smaller. It's a technical term I made up last night.