Ed wrote:
> How far down on the piano can you play various intervals?
>
> I thought there was a lower limit for each interval (e.g., octaves OK
> anywhere on the keyboard, fifths OK in the second octave or above,
> thirds...etc, or something like that), but I can't find it.
>
> To my surprise, I haven't been able to find anything online. Am I
> using the wrong terminology?
>
> Thanks,
>
> Ed
The so-called Low Interval Limits are just guidelines for arrangers and
composers. They assume a low limit for the various interval types,
beyond which the interval loses clarity and becomes "muddy".
There is an acoustical basis for this.
The idea is that any interval whose acoustical root is below the audible
range of human hearing will sound muddy.
The lowest A on a Grand Piano is A27.5hz.
This note is notated 2 octaves below the A on the 1st space of the bass
clef staff.
Human hearing extends a bit below this, but for the purposes of the LIL
We usually use A27.5 as the lowest practical acoustical root for any
interval type.
So, we're really talking about intervals that exist within the harmonic
overtone series of A27.5, which proceeds as follows:
A0 A1 E2 A2 C#3 E3 G3
27.5 55 82.5 110 137.5 165 192.5
A3 B3 C#4 D#4 E4 F#4 G4 G#4
220 247.5 275 302.5 330 357.5 385 412.5
A4 Bb5 B5 C5 etc.
440 467.5 495 522.5 etc.
Note: C4 = middle C.
So, the lowest practical P5th interval is between A1 and E2.
That's the A that is 1 octave below the A on the 1st space of the bass
clef staff, and the E above it. It's also the open A string on a
regularly tuned bass guitar or string bass.
Lowest practical P4th is between E2 and A2.
A2 is the A on the bottom space of the bass clef staff. E2 is a P4th
below that.
Lowest practical maj 3rd is A2-C#3.
That's the bass clef's lowest space and the C3 above it on the 2nd space.
Lowest practical min 3rd is C#3-E3.
Lowest practical maj 6th is E2-C#3.
Lowest practical min 6th is C#3-A3.
A3 is the 4th line of the bass clef staff. C#3 is below that.
Lowest practical min 7th is A2-G3.
Lowest practical maj 7th is E3-D#4.
Lowest practical aug 4th is A3-D#4.
Lowest practical dim 5th is D#4-A4. (But in 12 tone equal temperament,
aug 4ths and dim 5ths are essentially the same sound, so the LIL for aug
4ths usually applies to dim 5ths as well.)
Lowest practical maj 2nd is G3-A3.
Lowest practical maj 9th is G3-A4.
Lowest practical min 2nd is D#4-E4.
Lowest practical min 9th is D#4-E5.
But in practice these limits get exceeded all the time, *well* below the
given practical limits.
Just use your ears. If an interval sounds too muddy, then use another
interval or take it up an octave.
The timbre of the instruments involved will play an im****tant part too.
an instrument with a weak fundamental tone and lots of upper partials
may be able to play lower intervals than an instrument with a pronounced
fundamental and few audible upper partials.
--
Joey Goldstein
<http://www.joeygoldstein.com>
<http://homepage.mac.com/josephgoldstein/AudioClips/audio.htm>
joegold AT sympatico DOT ca
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