Moon Sidereal Month (Cosmic Octave)
227.43 Hz
Nearest note: A♯3, 42 cents below standard tuning
A tone calculated from a measured cycle, by doubling its frequency 29 times. It is calculated, not recorded.
How well is this supported?
Calculated from a measured value by a stated method. You can check the arithmetic. What the result means is a matter of interpretation.
The cycle is measured. The tone is calculated from it by doubling, so that it can be heard. Nothing in space makes this sound.
The button plays a plain tone. Start with the volume low. Phone and laptop speakers play low notes quietly; headphones or a speaker help.
Where this number comes from
Measured against the stars, the Moon goes around the Earth in 27.321661 days. 1 ÷ 2,360,592 seconds, doubled 29 times, is 227.43 Hz. That is a B♭, about 42 cents below standard tuning.
- Step 1. Start with the length of the cycle
Moon orbit relative to the fixed stars: 27.321661 days.
- Step 2. Turn it into a frequency
One divided by that many seconds is 4.24 × 10⁻⁷ Hz. That is far too slow to hear.
- Step 3. Double it 29 times
Doubling a frequency raises it by one octave: the same note, higher. After 29 doublings it is 227.43 Hz.
- Step 4. Name the note
227.43 Hz is a B♭, 42 cents below standard tuning. A cent is one hundredth of the step between two neighboring piano keys. To play in tune with this tone, an instrument sets its A to 429.33 Hz instead of 440.
- Step 5. Keep doubling and the number lands in the range of light
41 more doublings give the frequency of light with a wavelength of 599 nm, which is yellow. This is arithmetic. It pairs a tone with a color; it does not show that the two are connected.
The method is Hans Cousto’s. Planet gongs explained walks through it and says what it does and does not show.
Facts
- Frequency
- 227.43 Hz
- One cycle takes
- 27.32 days
- Wavelength in air (20 °C)
- 1.51 m
- Nearest note
- A♯3, 42 cents below standard tuning
- Kind of statement
- Octave of an astronomical cycle
- Filed under
- Earth, Moon & Sun
Tuning Data
The row for this tone in Hans Cousto’s tables, with the tempo and pendulum length that follow from it.
- Cycle
- Moon orbit relative to the fixed stars
- Length of the cycle
- 27.321661 days
- Octaves up
- 29
- Concert pitch (A)
- 429.33 Hz
- Difference from A = 440 Hz
- -42.49 cents
- Tempo
- 106.61 beats per minute
- Pendulum length
- 7.9 cm / 3.10 in
- Color by octave
- Yellow (599 nm)
Tempo and pendulum length, octave by octave
| Octave | Frequency | One cycle | Tempo | Pendulum |
|---|---|---|---|---|
| 22tempo | 1.78 Hz | 562.81 ms | 106.61 BPM | 7.9 cm |
| 23 | 3.55 Hz | 281.41 ms | 213.22 BPM | 2.0 cm |
| 24 | 7.11 Hz | 140.70 ms | Too fast to count | Too short to build |
| 25 | 14.21 Hz | 70.35 ms | Too fast to count | Too short to build |
| 26 | 28.43 Hz | 35.18 ms | Too fast to count | Too short to build |
| 27 | 56.86 Hz | 17.59 ms | Too fast to count | Too short to build |
| 28 | 113.72 Hz | 8.79 ms | Too fast to count | Too short to build |
| 29tone | 227.43 Hz | 4.40 ms | Too fast to count | Too short to build |
Intervals built on this tone
| Ratio | Interval | Frequency | Note | Concert A | Cents from 440 |
|---|---|---|---|---|---|
| 1/1 | Perfect unison | 227.43 Hz | A#3 | 429.33 Hz | -42.50 |
| 81/80 | Syntonic comma | 230.27 Hz | A#3 | 434.70 Hz | -20.99 |
| 531441/524288 | Pythagorean comma | 230.53 Hz | A#3 | 435.19 Hz | -19.04 |
| 128/125 | Diesis | 232.89 Hz | A#3 | 439.63 Hz | -1.44 |
| 648/625 | Greater diesis | 235.80 Hz | A#3 | 445.13 Hz | +20.07 |
| 25/24 | Chroma | 236.91 Hz | A#3 | 447.22 Hz | +28.18 |
| 16/15 | Diatonic semitone | 242.59 Hz | B3 | 432.25 Hz | -30.77 |
| 10/9 | Minor whole tone | 252.70 Hz | B3 | 450.26 Hz | +39.91 |
| 9/8 | Major whole tone | 255.86 Hz | C4 | 430.30 Hz | -38.59 |
| 8/7 | Septimal whole tone | 259.92 Hz | C4 | 437.13 Hz | -11.32 |
| 6/5 | Minor third | 272.92 Hz | C#4 | 433.23 Hz | -26.86 |
| 5/4 | Major third | 284.29 Hz | C#4 | 451.28 Hz | +43.82 |
| 4/3 | Perfect fourth | 303.24 Hz | D#4 | 428.85 Hz | -44.45 |
| 3/2 | Perfect fifth | 341.15 Hz | F4 | 429.82 Hz | -40.54 |
| 8/5 | Minor sixth | 363.89 Hz | F#4 | 432.74 Hz | -28.81 |
| 5/3 | Major sixth | 379.05 Hz | F#4 | 450.77 Hz | +41.86 |
| 7/4 | Natural seventh | 398.00 Hz | G4 | 446.74 Hz | +26.33 |
| 16/9 | Pythagorean minor seventh | 404.32 Hz | G#4 | 428.36 Hz | -46.41 |
| 9/5 | Just minor seventh | 409.37 Hz | G#4 | 433.72 Hz | -24.90 |
| 15/8 | Major seventh | 426.43 Hz | G#4 | 451.79 Hz | +45.77 |
| 2/1 | Octave | 454.86 Hz | A#4 | 429.33 Hz | -42.50 |
Source notes
The sidereal month measures the Moon against the fixed stars instead of the Sun.
Source: Hans Cousto — Tuning Data / Sun Earth Moon Planets. View the source PDF.
License: CC BY-NC-ND 4.0, as stated in Stimmdaten.pdf (German edition), page 2.
Values are reproduced from Cousto’s tables. Tempo, pendulum length and interval tables are calculated by this site from those values.
See every tone in the tables: Open the tuning data reference.
Sources
- Hans Cousto — Tuning Data: Earth, Moon, Planets, Sun
The tables that the tuning pages on this site reproduce.
Hans Cousto, Tuning Data — Earth Moon Planets Sun. Planetware.
View source: Hans Cousto — Tuning Data: Earth, Moon, Planets, Sun - Hans Cousto — Tuning Data / Sun Earth Moon Planets — Moon — Sidereal Month
The sidereal month measures the Moon against the fixed stars instead of the Sun.
View source: Hans Cousto — Tuning Data / Sun Earth Moon Planets — Moon — Sidereal Month
More about the pitch
The same note in every octave
Each step doubles or halves the frequency. Tap one to hear it.
Entries close in pitch
Within 35 cents of this tone, in any octave. A cent is one hundredth of the step between two neighboring piano keys. Being close in pitch does not mean two things are connected.