This is a free analysis generated by recording submitted to me by one of my subscribers.
Contact Me Now if you would like a free analysis of one of your temperaments.
Piano: Unknown Console
Submitted by: 004
A440
We use F2 to create beats with A4 and A440.
We try to tune A4 so that the beats created by F2A4 are the same speed as those created by F2A440.
F2 creates beats because it is flat from pure with A4 and A440.
If the beats are the same speed, then A4 and A440 are the same amount sharp of the fifth partial of F2.
Click the filtered buttons to hear the beating A4 easier.
The faster beating pair indicates the sharper A4 or A440.
4.6 bps
5.4 bps
Frequency of A4: 440.55 (F2A4 beats faster than F2A440)
Cents off: 2.2 (Must be within 1.4 cents)
Mark: 48% (Minimum pass is 80%)
Criteria: No marks lost if 0.9 cents off, or less. Lose 4 marks for every 0.1 cent off after that.
F3F4 and A3A4 Octaves
Criteria: Must be tuned to one of the following sizes.(Note: Only one size is possible because of inharmonicity.)
Small Scale Octave: Pure 4:2 and Pure 6:3 (Within 3%) Common
Medium Scale Octave: Wide 4:2 and Narrow 6:3 (3% - 5%) Less Common
Large Scale Octave: Pure 4:2 and Very Narrow 6:3 (>5%) Rare
Reversed Octave: Narrow 4:2 and Wide 6:3. Very Rare.
(Click Here for the lesson on Octave Sizes.)
A3A4:
= 7.3bps
= 6.8bps
Size of 4:2 A3A4: Narrow (6%)
= 9.0bps= 7.6bps
Size of 6:3 A3A4: Narrow (16%)
F3F4:
= 4.6bps
= 4.4bps
Size of 4:2 F3F4: Narrow (5%)
= 8.7bps= 7.8bps
Size of 6:3 F3F4: Narrow (11%)
Comments on the Octaves F3F4 and A3A4
Both octaves are narrow. The 4:2 and 6:3 are both narrow for each octave.
When you click the F3F4 and A3A4 buttons, you can hear a slight roll in the upper partials.
Notice that the 4:2's are less narrow than the 6:3's. This implies that the piano may have Medium Scaled Octaves, that could be tuned as wide 4:2/narrow 6:3.
It is also possible that they are close enough in size (the 4:2's and the 6:3's) that the octaves may be tuned as pure 4:2/pure 6:3, each within 3%, and then we would identify this piano as having Small Scale Octaves.
CHROMATIC LADDERS
GRADING OF THE TEMPERAMENT
I have designed two different grading schemes for measuring temperaments.
One is based on the error of the frequencies relative to a master tuning. This method is similar to the Registered Piano Technicians exam administered by the Piano Technicians Guild. The "master tuning" is determined by those frequencies that would produce beat speeds that increase by the same ratio as the average ratio of the actual beat speeds.
The second method assigns a penalty for each beat speed that does not fall within a certain limit. M3's must increase by 0 to 10%. P4's must beat between 0.5 and 1.5 beats per second.
Below are the marks calculated by each method. The PTG requires a minimum mark of 80% in many of its exams.
Temperament Mark
Average Ratio Method: 84%
(Similar to RPT method)
Beat Speed Limit Method: 79%
(Represents more directly what the tuner can hear. Preferred method.)
M3 BEAT SPEED PROGRESSIONS
HOW TO USE THE M3 GRAPHS
M3 intervals should increase speed chromatically as smoothly as possible.
1.Listen to the recordings below and look at the graph.
2.Listen to the filtered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Ratio Sensitivity.
3.Listen to the unfiltered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Clarity - the ability to hear beat speeds clearly.

M3, filtered:
M3, unfiltered:
P4 BEAT SPEED PROGRESSIONS
HOW TO USE THE P4 GRAPH
P4 intervals should beat close to 1 bps.
1.Listen to the recordings below while looking at the graph.
2.Listen to the filtered recording and try to confirm aurally that speeds are following what the graph says. This improves your Beat Speed Ratio Sensitivity.
3.Listen to the unfiltered recording and try to hear the quality of a tuned P4 (1 bps), a pure P4 (0 bps), and an out of tune P4 (>1.5 bps). Identifying correct and incorrect P4's are a very powerful refinement tool.
P4, filtered