Pythagorean intonation whistle?

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Nopiffle
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Pythagorean intonation whistle?

Post by Nopiffle »

I'm looking for someone who could make me a high quality whistle either of silver or silver-plated, and in Pythagorean tuning. In C or Bb, haven't decided which yet. Ronaldo Rey says he doesn't do silver, but suggests I try Humphrey. I can't find a website for Humphrey, does anyone have contact info for him? It seems also that Lir make silver whistles, but presumably not with Pythagorean intonation? Any other suggestions?
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Re: Pythagorean intonation whistle?

Post by Mr.Gumby »

A recent thread a bit further down the page:

Humphrey website
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Re: Pythagorean intonation whistle?

Post by pancelticpiper »

By Pythagorean I'm assuming you're referring to the tuning system also called "Five-Limit Just Intonation" or JI for short.

Each note the the scale is an exact beatless consonance with the tonic tone.

As you're probably aware it's how pretty much all bagpipes are tuned, due to each note of the scale being heard against the tonic.

In actual practice the difference between Equal Temperament and Just Intonation, on whistles, is small, and really only impacts three notes, the Major 3rd, Major 6th, and sharp 7th.

Here are the notes on a D whistle in JI with the variance from ET noted
D 0
E +4
F# -14
G -2
A +2
B -16
C# -14

C# is a special case because the same hole also has to produce C natural and to do this most whistlemakers make their C# flat as a rule.

Many whistlemakers with use JI as their normal practice, or some form of compromise between JI and ET.

In any case, here are two whistles of mine, each cost around $10 and both play great.

On the right is a whistle tuned to ET, on the left is a whistle tuned to JI.

As can be seen the only difference is a couple pieces of electrical tape :thumbsup:

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Re: Pythagorean intonation whistle?

Post by Mr.Gumby »

By Pythagorean I'm assuming you're referring to the tuning system also called "Five-Limit Just Intonation" or JI for short.

I don't think it is actually quite the same as JI, Richard. See:


pythagorean vs just intonation
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Re: Pythagorean intonation whistle?

Post by Byll »

Hmmm. Mr.Gumby, pancelticpiper, et al.: I have watched this thread, hoping that someone would ask the question. That did not happen. This leads me to the conclusion, that somehow in my education, I truly missed something... I find the whole Pythagorean intonation discussion fascinating, but any knowledge of it is missing in my history.

Ergo, I will ask said question, now: What is it that Pythagorean intonation allows to a performer, that standard tuning of the A440 variety, does not? Where and why is it used, and when? My American university experiences did not discuss, nor suggest any experimentation concerning Pythagorean intonation, on either the under-graduate or post-graduate level. Alas, I am ignorant of the issue. Any help will be appreciated.
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Re: Pythagorean intonation whistle?

Post by Mr.Gumby »

It's not so much about A=440, it's about the intervals, the relations between the notes of the scale.

dolmetsch.com has more, possibly more than you want to know, on the various temperaments, see here
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Re: Pythagorean intonation whistle?

Post by Byll »

I am not able to make that link work, Mr. Gumby. I guess my biggest query concerns any practical/musical reason for using this intonation, instead of the standard garden variety...
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Re: Pythagorean intonation whistle?

Post by Mr.Gumby »

Byll wrote: Wed May 03, 2023 12:18 pm I am not able to make that link work, Mr. Gumby.
It works perfectly fine for me.

The use and benefits depend on which temperament you're looking at. Look at the link a few posts back, that compares pythagorean and just intonation.

Form me the sweetening of the thirds (ET thirds are plain ugly) and pure harmonies in just temperament is important but various tunings and temperaments address slightly different issues.
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Re: Pythagorean intonation whistle?

Post by stringbed »

The Pythagorean and just tuning systems are defined solely in terms of pure intervals and are therefore not temperaments. The former is characterized by pure octaves and fifths, giving major thirds that are markedly wide. There is a corresponding meantone tuning with pure octaves and major thirds but narrow fifths. Just tuning includes all three pure intervals but the price paid for it is a pitch level that will wander during the course of a performance.

It is applicable to the voice and instruments with flexible tuning albeit with greater headache than is generally realized. Temperaments are schemes that sacrifice a bit of the purity of the fifths and/or thirds to provide systems for tuning fixed-pitch instruments that divide the octave 12 semitones. The now ubiquitous equal temperament is characterized by equally sized semitones but there are many alternatives (including the subdivision of the octave into more than 12 microtonal segments). There's a good explanation of the underlying problem with just intonation here.
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Re: Pythagorean intonation whistle?

Post by pancelticpiper »

Mr.Gumby wrote: Tue May 02, 2023 6:12 am
I don't think it is actually quite the same as JI, Richard. See:

pythagorean vs just intonation
Interesting, to wrap my head around it I would have to see a scale in cents.

I have a chart with 9 tunings but Pythagorean isn't included.

Pythagorean intervals show up on this excellent chart, along with the harmonic intervals of JI

https://www.kylegann.com/Octave.html

The oddest thing to me is the old traditional sharp 4th of the Highland pipes. (Nowadays pipers all use the Perfect 4th.)

What were they hearing? It's around the 43rd harmonic, which is very high and faint. Why use that rather than the powerful concordance of the Perfect 4th?
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Re: Pythagorean intonation whistle?

Post by Nanohedron »

pancelticpiper wrote: Fri May 05, 2023 6:10 am The oddest thing to me is the old traditional sharp 4th of the Highland pipes. (Nowadays pipers all use the Perfect 4th.)

What were they hearing? It's around the 43rd harmonic, which is very high and faint. Why use that rather than the powerful concordance of the Perfect 4th?
I'd never heard of this before. Was it kind of like a Lydian mode with a flattened seventh?
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Re: Pythagorean intonation whistle?

Post by Nopiffle »

Thanks to all who've replied so far. Some interesting general technical points on Pythagorean and JI tuning. However, what I'm after is suggestions for anyone who might be able to actually make me a Pythagorean-tuned silver or silver-plated whistle. It's specifically for playing and performing with other instruments/singers in Pythagorean tuning. Does anyone know of a maker who'd potentially be interested?
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Re: Pythagorean intonation whistle?

Post by Sirchronique »

Nopiffle wrote: Sat May 06, 2023 6:37 am Thanks to all who've replied so far. Some interesting general technical points on Pythagorean and JI tuning. However, what I'm after is suggestions for anyone who might be able to actually make me a Pythagorean-tuned silver or silver-plated whistle. It's specifically for playing and performing with other instruments/singers in Pythagorean tuning. Does anyone know of a maker who'd potentially be interested?
I would recommend asking the individual makers that you are interested in. This seems like the type of thing that no one would advertise, but some might be willing to do. Humphrey and Sindt both do silver whistles. You’d be expanding your options by not restricting it solely to silver instruments. Is there a reason you are specifically after this material?
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Re: Pythagorean intonation whistle?

Post by MadmanWithaWhistle »

Nopiffle wrote: Sat May 06, 2023 6:37 am Thanks to all who've replied so far. Some interesting general technical points on Pythagorean and JI tuning. However, what I'm after is suggestions for anyone who might be able to actually make me a Pythagorean-tuned silver or silver-plated whistle. It's specifically for playing and performing with other instruments/singers in Pythagorean tuning. Does anyone know of a maker who'd potentially be interested?
I can't currently cast solid silver tubes, but what about a whistle with a silver headjoint and silver foot ring, on a bronze body tube (which may also be oxidized for a handsome black finish)? If you can specify the offsets from equal temperament, I should be able to create something fitting your needs. Drop me a line via my website - https://www.barterloch.com/pennywhistles-1. I'm in the midst of making some updates to reflect our new headjoint design and solid bronze body tubes, so please forgive some of the formatting oddities. The second image on that page shows our updated bronze tube. I'm recording more sound samples and getting product photos of our revised design next Tuesday.
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