Totally disconnected group

The Greenwood function correlates the position of the hair cells in the inner ear to the frequencies that stimulate their corresponding auditory neurons. Empirically derived in 1961 by Donald D. Greenwood, the relationship has shown to be constant throughout mammalian species when scaled to the appropriate cochlear spiral lengths and audible frequency ranges. Moreover, the Greenwood function provides the mathematical basis for cochlear implant surgical electrode array placement within the cochlea.

Experimental methods and results

In 1961, Professor Donald D. Greenwood utilized experimental methods within the field of psychoacoustics to measure the frequency resolution between critical bands within the human cochlea and develop a function correlating the anatomic location of the inner ear hair cells and the frequencies at which they are stimulated (Greenwood 1961a,b).

Georg von Békésy demonstrated physiologically that different frequencies of sound stimulated different regions of the cochlea (Wilson 2004). Based upon the findings of Békésy, Greenwood placed four students under the age of 29 with presumably healthy cochleas in isolation chambers and introduced pure tones within the range of audible frequencies (20-20,000 Hz). Upon application of each tone, he then introduced a second pure tone of the same frequency and then raised and lowered the frequency until it was sufficiently different from the original frequency to become audible (Greenwood 1961a). Subjects responded with a handheld device allowing Greenwood to record exactly at what frequency interval the two pitches were audible and distinct. Experiments were performed over the entire range of audible frequencies (Greenwood 1961a).

The Greenwood function

By summing the experimentally derived critical bandwidths over the length of the human cochlea, Greenwood developed the following function that describes the relationship between the frequency of a pure tone and the position of the hair cells measured as the fraction of the total length of the cochlear spiral in which it resides:

$f=\underset{0}{\overset{x}{\int }}\mathrm{\Delta }{f}_{cb}=A(10^{ax}-K)$

• f is the characteristic frequency of the sound in hertz
• A is a scaling constant between the characteristic frequency and the upper frequency limit of the species
• a is the slope of the straight-line portion of the frequency-position curve, which has shown to be conserved throughout all investigated species after scaling the length of the cochlea
• x is the fractional length along the cochlear spiral measured from the apical end of the cochlea to the region of interest. 0 < x < 1.
• K is a constant of integration that represents the divergence from the log nature of the curve and is determined by the lower frequency audible limit in the species.

Applications of the Greenwood function

The Greenwood function is species-dependent and has shown to be preserved in mammals when normalized to the species-dependent range of auditory frequencies and cochlear spiral length (Greenwood 1990). For humans, the recommended values for the constants are $f=165.4(10^{2.1x}-1)$ (Greenwood 1990). According to Greenwood's paper, a = 2.1, if x is relative to the cochlea length, and a = 0.06 if x is calculated in mm.

For individuals with sensorineural hearing loss surgical implantation of a cochlear implant is indicated. The success of a cochlear implant relies in part upon electrode array placement within the cochlea in which the positioning is based on the frequency-spatial relationship empirically described by the Greenwood function. By aligning the electrodes with the positions of the auditory ganglia contacting the basilar membrane as described by the Greenwood function, the cochlear implant electrode array stimulates auditory ganglia associated with the reception of frequencies associated with speech recognition. Electrode array insertion depth is guided by the frequency map created by the Greenwood function, and allows electrical stimulation of neurons involved in stimulating the area of the brain responsible for speech recognition while minimizing ganglia stimulation in noise-generating regions. Well-placed electrode arrays in patients receiving cochlear implants can allow otherwise deafened auditory systems to achieve hearing and recognize speech. (Chivukula et al. 2006, Wilson 2004)

Greenwood function applied

A typical cochlear implant electrode array may be inserted at a depth of 22–25 mm into the cochlea [1]. At an insertion depth of 25mm into the base of the cochlear spiral, the distance from the apex of the cochlea to the deepest electrode is 10 mm using the mean value of 35 mm for the length of a standard human cochlea translating to x=10/35 in the Greenwood function (Greenwood 1990). Therefore the lowest frequency heard by someone wearing this cochlear implant is calculated by the Greenwood function to be:

$f=165.4(10^{\frac{2.1*10}{35}}-0.88)=513\mathrm{H}\mathrm{z}.$

513 Hz equates roughly to the frequency of a C5 key of a piano. Lower frequency stimulation has been theorized to lead to a greater degree of background noise that impedes rather than aids speech recognition (Wilson 2004).

See also

• Bark scale
• Critical band
• Equivalent rectangular bandwidth
• Mel scale

References

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  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang