1/4-comma meantone calculation for Anglos

[Luke Hillman]

I just ran into some fascinating questions on another forum as I was trying to get my head around how to calculate frequencies for a 1/4-comma meantone scale given a reference note.

 

Since Anglos have two "home" keys...

• Which reference note would I use?
  • on a C/G Anglo, would I use C as the reference for the whole thing? OR,
  • would I use C for the C row, and G for the G row? OR
  • would I use C for the C row and THEN use the C row's G as the reference note for the G row?
  • Or something else?
• and what about the accidental row?

 

Is there some standard way of tuning an Anglo to 1/4-comma? Or does everyone have their own preferred way?

 

 

Edited February 28, 2023 by Luke Hillman

[seanc]

I don’t know much about this specifically.  But, if you are doing predominantly Irish. Would it make more sense to use D as the tone center?

 

Or at least base your reference tone on the key you use most? 

[Luke Hillman]

1 minute ago, seanc said:

I don’t know much about this specifically.  But, if you are doing predominantly Irish. Would it make more sense to use D as the tone center?

 

Or at least base your reference tone on the key you use most? 

 

Good question -- I don't know! I suppose, if so, that you'd want the whole keyboard tuned that way, instead of using different reference tones for each row...?

 

I had assumed that the playing styles most likely to benefit from meantone temperament are ones that make heavy use of harmonies and chords, which is not something I think of when I think of Irish music, though I've heard—can't remember where—that quarter-comma is popular among Irish concertinists. Irish isn't my scene, though, so I'll wait for someone more knowledgeable to explain.

[David Barnert]

Just be glad you’re not playing a B/C melodeon! 

[seanc]

2 hours ago, Luke Hillman said:

 

Good question -- I don't know! I suppose, if so, that you'd want the whole keyboard tuned that way, instead of using different reference tones for each row...?

 

I had assumed that the playing styles most likely to benefit from meantone temperament are ones that make heavy use of harmonies and chords, which is not something I think of when I think of Irish music, though I've heard—can't remember where—that quarter-comma is popular among Irish concertinists. Irish isn't my scene, though, so I'll wait for someone more knowledgeable to explain.

Again not an expert. But my understanding is that the further you go from your center the less good it will sound. So it it is set up for c… once you get past (making this up here) E or Eb it is very out.

The the above.. as c is your center, and you have adjusted your 3ds to be more pure (relative to the C) when you now make that your root note, it is significantly out of tune from a standard tuned instrument.

 

or at least that is my understanding. And how you strive to get more “pure” intervals.

 

[Steve Schulteis]

I'm also not an expert, but I've been looking into different temperaments recently myself. My understanding is that multiple keys can sound just fine in quarter comma (and the number of keys that sound decent can be increased by adding distinct sharps and flats). An Anglo, which I'm sure many people play in just three or four keys most of the time anyway, seems like a reasonable candidate for quarter comma. I don't see any reason to tune the rows differently. I'd much rather keep the whole instrument consistent with itself.

There's an old thread or two on this forum that addresses the question of where to center the tuning and a lot of confusion about what exactly people mean by "center":

 

 

 

This is the best explanation I found for determining the actual mathematical relationships:

 

 

I also got a lot out of this series:

 

[Little John]

13 hours ago, Luke Hillman said:

Since Anglos have two "home" keys...

• Which reference note would I use?
  • on a C/G Anglo, would I use C as the reference for the whole thing? OR,
  • would I use C for the C row, and G for the G row? OR
  • would I use C for the C row and THEN use the C row's G as the reference note for the G row?
  • Or something else?

 

The answer is "something else". Reference everything to A=440Hz, whatever instrument you're playing (even B/C melodeon David!) or whatever keys your anglo has. Why? Firstly because in the keys most commonly used for folk music, this will minimise the difference between 1/4 comma (or 1/5 comma) tuning and Equal Temperament. Secondly because when you're giving an A for other instruments to tune to it will be exactly the pitch they are expecting. (If your reference is any other note, A will not be at 440Hz.)

[SIMON GABRIELOW]

Very interesting debate here.. I is always interesting how some tunes sound with ease on a particular instrument, say in one key, and yet if you try same tune transposed to another key altogether; then it can be less easy on the ears, and very awkward to play. There seems to be that happy medium where the thing sounds just right in feel; then best to stick with it at that point.

Example here, I am learning to play ( very early stages) a Chalumeau ( a sort of early version and wooden clarinet).  I try tune transposed to different keys for practice.. the same tune sounds awkward in C major, and yet played in A minor seems nicer to play!😊

Its all very mysterious.

[alex_holden]

3 hours ago, Little John said:

 

The answer is "something else". Reference everything to A=440Hz, whatever instrument you're playing (even B/C melodeon David!) or whatever keys your anglo has. Why? Firstly because in the keys most commonly used for folk music, this will minimise the difference between 1/4 comma (or 1/5 comma) tuning and Equal Temperament. Secondly because when you're giving an A for other instruments to tune to it will be exactly the pitch they are expecting. (If your reference is any other note, A will not be at 440Hz.)

 

The tuning app I use (Tonal Energy) has a setting to automatically adjust the pitch so that A4 still ends up at 440Hz (or whatever frequency you give it) even if the root note of the scale isn't A.

[Little John]

To illustrate my earlier comments, here is a table I constructed when I was considering fifth comma meantone tuning for my Crane duet. It compares aligning G with ET with aligning A with ET. It shows how if G is aligned, the commonly used C# and G# are starting to differ from ET by amounts that could be audible in some circumstances; and D# is even worse. [Less than 10 cents difference is generally considered not noticeable whilst 20 cents is considered noticeable. Opinions differ as to where in between it starts to become noticeable. No one has ever commented on the tuning my fifth comma tuned concertinas aligned ("centred") on A.]

 

The wolf fifth is assumed in this table to be at Eb - G# (so you wouldn't have the D# except on an English concertina). Shifting the wolf fifth to Bb - D# would give a D# at the expense of an Eb.

 

[David Barnert]

4 hours ago, Little John said:

Reference everything to A=440Hz, whatever instrument you're playing (even B/C melodeon David!) or whatever keys your anglo has.

 

The question was not what frequency should A4 be tuned to, but what key should be favored in the 1/4-comma meantone temperament (and should the two rows of an anglo use different 1/4-comma meantone temperaments). The two can be answered independently of each other. No matter how you structure the 1/4-comma meantone temperament (ie., where you place the wolf tone) in a given key, you can still tune the whole scale up or down an arbitrary constant amount so that A4 lands on 440 (or wherever you want it, as @alex_holden points out).

[Little John]

1 hour ago, David Barnert said:

The two can be answered independently of each other.

 

It's true that the two questions are separate but both need to be addressed.

 

1 hour ago, David Barnert said:

... what key should be favored in the 1/4-comma meantone temperament ...

 

This is slightly misleading. With 1/4-comma, 1/5-comma or any other -comma there are six keys that are equally favoured and six that are not. See the bottom two rows of my table above. Shifting the wolf fifth changes the favoured keys. So, for example, shifting the wolf to D# - Bb you would lose Bb major and gain E major.

[seanc]

2 hours ago, David Barnert said:

 

The question was not what frequency should A4 be tuned to, but what key should be favored in the 1/4-comma meantone temperament (and should the two rows of an anglo use different 1/4-comma meantone temperaments). The two can be answered independently of each other. No matter how you structure the 1/4-comma meantone temperament (ie., where you place the wolf tone) in a given key, you can still tune the whole scale up or down an arbitrary constant amount so that A4 lands on 440 (or wherever you want it, as @alex_holden points out).

 

To me.. Assuming that the player is playing accross the rows and using the third row. Tuning the C and G to different standards seems like a really bad idea. 

 

Hypothetically, You could cet into a situation where you are doing a scale/ run up on the push, then that same scale down on the pull. Where one is in tune and the other is not. To me that would be maddening. Some keys that would be more noticable than others. 

 

At least if both rows are tuned to the same standard, the box will at least be uniformly in tune with itself.

 

 

But it seems that tuning the A to 440 regardles to the tone center, seems to not be the way to go. in the above chart, If tuned to G the A should be 440 -5.6 or 434.4 to be in tune with itself.  Or C should be 440- 8.4 or 431.6.  I assume you'd need to shift ALL the notes around to make that A hit a 440?

 

 

 

[alex_holden]

14 minutes ago, seanc said:

 

But it seems that tuning the A to 440 regardles to the tone center, seems to not be the way to go. in the above chart, If tuned to G the A should be 440 -5.6 or 434.4 to be in tune with itself.  Or C should be 440- 8.4 or 431.6.  I assume you'd need to shift ALL the notes around to make that A hit a 440?

 

Exactly, you shift everything to make A4 work out to 440.

[Little John]

30 minutes ago, seanc said:

But it seems that tuning the A to 440 regardles to the tone center, seems to not be the way to go. in the above chart, If tuned to G the A should be 440 -5.6 or 434.4 to be in tune with itself.  Or C should be 440- 8.4 or 431.6.  I assume you'd need to shift ALL the notes around to make that A hit a 440?

 

I agree with everything in this post except for that last paragraph, quoted above. 440 refers to the frequency in Hz (or cycles/second). 5.6, 8.4 etc. in the table refers to cents, i.e. hundredths of a semitone. They don't mix.

 

The first row shows that if G (in meantone tuning) is tuned to be exactly the same frequency as G in Equal Temperament tuning, then A will be 5.6 cents flatter than the A in ET. If you tune all the notes up 5.6 cents to make the A in meantone match the A in ET you simply end up with the second block in the table.

 

The purpose of the table is to illustrate that matching A to the A in ET minimises the discrepancy between mean-tone tuning and equal temperament in the keys from two flats to four sharps.

[seanc]

20 minutes ago, Little John said:

 

I agree with everything in this post except for that last paragraph, quoted above. 440 refers to the frequency in Hz (or cycles/second). 5.6, 8.4 etc. in the table refers to cents, i.e. hundredths of a semitone. They don't mix.

 

The first row shows that if G (in meantone tuning) is tuned to be exactly the same frequency as G in Equal Temperament tuning, then A will be 5.6 cents flatter than the A in ET. If you tune all the notes up 5.6 cents to make the A in meantone match the A in ET you simply end up with the second block in the table.

 

The purpose of the table is to illustrate that matching A to the A in ET minimises the discrepancy between mean-tone tuning and equal temperament in the keys from two flats to four sharps.

I am really not familiar with dealing in cents.  But... Not really grasping the math here.. If you are 5.6 or 8.4 cents.. Does that translate into Your X note is 5.6% or 8.4% off? 

 

how this equates to what you hear..  Making that 8.4 your tone center and trying to play with others. Does that make it more noticable/ more out of tune? 

 

Also, is that a constant? would your G note always be 8.4 off? or does it become 4.2 down an octave and 16.8 up an octave?

 

 

[Clive Thorne]

Genuine question: Is there a problem playing non equal temperament instruments alongside equal temperament instruments, or indeed with instruments of a different non-equal temperament?

 

If not then great. If so, then unless you're a purist or a strictly solo player then I'd suggest sticking with equal temperament as I suspect that the vast majority of instruments are (please correct me if I am wrong).

 

[Łukasz Martynowicz]

Just now, Clive Thorne said:

Genuine question: Is there a problem playing non equal temperament instruments alongside equal temperament instruments, or indeed with instruments of a different non-equal temperament?

 

If not then great. If so, then unless you're a purist or a strictly solo player then I'd suggest sticking with equal temperament as I suspect that the vast majority of instruments are (please correct me if I am wrong).

 

 

Instruments in different temperaments were played together since the very invention of temperaments in Renaissance, as lutes were usually tuned in equal temperament and keyboard instruments were not. However, how badly out of tune with each other instruments in such ensembles sound depends very much on the tune itself - how melody and harmony interact, which intervals are used, which key the tune is in, how modern the tune is etc. It also depends very much on which temperaments are clashed together. Go on YT and search for videos illustrating different temperaments and listen to differences, "side by side" comparisons etc. And if you're interested in some most extreme musical experience, search for microtonal music in -TETs larger than 12-TET (the common equal temperament). Personally, I can't stand microtonal music other than traditional music from India, as everything sounds false all the time to me. When clashing two different temperaments together, you can get the same "microtonal" quality to resulting music.